A N AP P ENDIX, O R SECOND PA RT, T O T n E • . COMPLEAT TREATISE O N PERSPECTIVE. CONTAINING A BRIEF HISTORY OF PERSPECTIVE. FROM THE EARLIEST AND MOST AUTHENTIC ACCOUNTS OF IT DOWN TOTHEEIGHTEENTH CENTURY", WHEN IT FIRS.T BEGAN TO FLOURISH IN ENGLAND. J N WHICH, THE METHODS OF PRACTICE, USED BY THE ANCIENTS ARE AND COMPARED WITH THOSE NOW IN USE. ‘ military perspective, BIRD’!--EYE views, &c. THE APPEARANCES OF ASCENDING AND DESCENDING, ON AN UPRIGHT PICTURE- SUCH DECEPTIONS IN VISION ACCOUNTED FOR, AND ILLUSTRATED BY STRIKING REPRESENTATIONS- ■WITH USEFUL AND CRITICAL REMARKS ON ROUND OBJECTS, INGENERAL. the APPLICATION OF PERSPECTIVE TO SCENERY, ALSO TO A SHIP, AND IN LANDSCAPE. PROJECTION ON CURVED SURFACES, WITH OTHER DISTORTIONS, OR ANAMORPHOSES. INVERSE PERS.PECTIVE- ALSO, THE DOCTRINE OF REFLECTION, ON PLANE MIRROURS. .IT CONTAINS A PARALLEL AND CRITICISM ON ALL THE ENGLISH AUTHOR S WHO HAVE W-ROTE TREATISES ON PERSPECTIVE, AND-THE PRINCIP-LES OF DR. BROOK TAYLOR’. PERSPECTIVE COMPARED WITH GUIDUS UBALDUS, and, ‘sgravesande. THE WHOLE DELIVERED IN NINE SECTIONS and ILLUSTRATED BY TEN, LARGE, NEAT. AND CURIOUS, FOLIO PLATES. By THOMAS M A L T O N. MDCCI.XXXIII. INDEX, and TABLE of CONTENTS. Brief Hiftcry of Perspective, from the earlhjl AccvuuU of it \ fromV'Mxw jf\ Thrprincipal PerfpeclivCj'^/^ij/w the i$th Century - A Dfcriplion of Vignola’j and Sirigatti’j Method^ and Procefs A Parallel o/Sirigatri, with the Method on the new Principles An Example, itluf rating the utility and'excellence of the Method by Vignola and Sirigatti, in many Cafes The Principles 0/Vignola’s fccond Rule difplayed ■ — _ _ Iri which may be difeo'Oered great advances towards rendering the Theory and ufe of Vanifliing Points general : The Methods of PraSIice by J. Vredeman Frieze, and A. Eofle A Parallel of their PAethody with that on the ueiv Principles An account of the IPork ufually called the Jefuic’r Perfpeftive An account of Pi.ndrc?.Pozio's Method \ exemplified and compared _ _ 2i An Example of the Method ufed by the old IVriters on PerfipeUive, in projeiiing irregular Solids', or Bodies obliquely fituaied • - _ .. ' The iitilily, deferiptian, anl application of an Apparatus for taking general Views, or complicated Objeas ; without underftanding Perfpeliive - ■ - Other Apparatus deferibed, for taking Views, or~Sketches -- — Military Perspective -- Bird's Eye Virws ',~tke Rationale, and Examples of Cy* Horizontal Piftaresj with an Example Remarks on Deceptions in Vision, and Imagination we are moving on a level with the Horizon - The liJeeeprioh illujlraied, and clearly accounted for refpePling the appearance ^Defcending, whilft Of the Effeils which Right Lines, in any pofition to the Horizon, have on other Lines contiguous to them ibrd. Th' lame ■ ine, on the Picture, may be made to appear either as afeending or defending ; and the fame Space on the Pillurc (having the Jume Vaniffttg Line) may appear either to afeend or defend j exemplified 03 Rimurk's on the Appearances of round ObjeHs - - - - 2^ . Tb' rationale of the apparent curviture of Lines on their Surfaces explained-, and the abfurdity of drawing fuch OifSh without corfidering it, properly, and with due attention — - ^6 .Exaiuples illujiraiing thofe Ohfrvations . - . -■ ^8 The application of Perspective to Scenery ; with Remarks on the Authors who hove treated thereon 40 How to reprefent a given Subject, on various detached Pieces ^ the true places of the Wings, or fide Scenes, being detirmined, abfolulely, by it ; according to the length and declivity of the Stage - 41 The above Procefs exemplified, by a complete Set of Scenes, for an internal View of a Banqueting Houfe, or other place of Entertainment - - - - “ a. Remarks on the ufual Method, by Reticulation - - - - 47 The application ^Perspective to a Ship, in which is laid down, the geometrical ConfiruJlion, and from that, the whole Procefs, how to give its true Figure, in perfpt^ive, from any determined Station, or Point of View 48 SECTION VI. 0 ///;^ utility application ^/Perspective ;V; Landscape — _ ^4 Jhewing^ by a few elementary Problems or Rules, how one ObjeSi in the Pi£lure may be proportioned by another; at any difiance from each other, the parts being di/tinb?. T/v Absurdities pointed out and exemplified, which a great A rtift may be liable to, without underP.anding fomewhat of Perfpedive; or conftdtring, properly, the invariable Laws of Nature -- ” ^9 AND TABLE 0 F S E C T I 0 N CONTENTS, VII. The Method of delineating on curved Surfaces; explained and exempUJiedt hy a given SubjeSI 65 ji Vj,\z\\c\ of other Autho'-s, on the ondTJwhy - - 67 Ordiltorted Reprefentations, in perfpeSiive, onii Anamorphofes; in vjhich^ one U Jhewny and clearly evinced to be a Jpecies of the other ~ —— . ■ 68 VIII. To deferibe the prrfpeBive Contour^ or Outline of a Globe, from any Radius given, in perfpeilive 70 The application of It, from a geometrical Data - ' "Ji Inverfe PerCpedlive, or the reduSiion.of QbfeSls, perfpeSlively drawn, to their geometrical form and proportion 72 TheDo£lrinecfKzkzd.\on,onplaneMirrours - - - 75 SECTION IX, A Parallel and Criticism of the EngUJh Authors, on Perspective ; and the new Principles compared with GuiD'Js Ub.\ldUS, a IVork pvblifoed in 1600 80 o/r’Befnard Lamy ; who publifljcd tn 1701 - - — 84. Rcmaiks on ’sGravefande’s P'erfpe^iveJhewing what advances were made by him, towards rendering the " 8S — ~ —m -, — io5 - 131 - *35 - 138 - 145 - 150 - *55 — 159 knowledge'of Vanijhing Lines and Points univerfal Remarks on H. Dittonh Perfpediive -- - on Dr. Brook Taylor’s Perfpenive on Hamilton’s PerfpeSlive — on Kirby’s Brook Taylor made eafy - • on Ware's Tranfation ^Sirigatti . on Kirby’s Parallel oy'Sirigatti • - on Kirby’s PerfpeSlive of ArchiteSiure ■ on Highmore’s PerfpeSihe —— ■ cn Daniel Fournier’s — — . on Profejfor Cowley’s - • on Dr. Prieftley’s PerfpeSlive —- on Noble’s PerfpeSlive - • on Fergufon’s PerfpeSlive - - ■ " on Clarke’s PerfpeSlive - Remarks on the Reviewers of the Author’s Treatife on various mathematical Authors, and Painters E R R A In order to fad the Error more readily, the fecond Column particularises which Paragraph it is in, in each Page* Note. When two or three fliort Paragraphs come together (between Spaces) they are accounted as one. Page. Par. Line., laft./crOP, readEV. 3. {Qcbefe, reacli^/f. 1. for Q_R, read PCh Bottom, for O M, read oM. for Fa, read Ya. for Ef, read Ee. laft b^ut one, for D Q^, read N Q. two lali, for D's, read N’s. 3. for Rule, read Ruler. 9. for muft, reua may. 4. and 5. Bott, after S, read, or R. 6 . and lafl.'for Af, read cc. 2. for more, read lei's, 6. for C, read O. 4. Ditto. Note*; forQ'I, reaiOY. 3. for E, read F.' laft. yorBDE, readBTDY. Page. Par, Line. 58. 61. 66 . for b, read d. for as, read or. for 7 i\, b2, read at, i2.Tig. 3. 3. ^.jr N C, readyiQ, 67. 4. 2. for B I, read B 2. 71. 2. 2. yirCM, read 72. 16. for read Ao. Prob. I. 2. for AB, read Afl. *72. 2. 2 . /or AC, readme. 5. for flS, r=ad BS. 3. yirabdf, read^hhi. I. for GD, read Gl. 7. reals', D will appear at d. 3. Bott. yor tholV, read thcfc. laft. for a c, read ab. laft. for Page 65, read 67, 5. for right, read left. 79- B 3 - 85. 87. 102. 124. ■ In Page 747Par. 2. L. 6.'the Letter p having drop’d out, the word paffes is tendered affes; and in the 04th Page, Lines-8. and 9. from the bottom; alfo, in P.^ge 108. I’ar. 4.- L. 2, an r is wanting in the word Tetrahedron ( lelraedrn); in P. 1O4. Par. 3. L. 3. it is Tetraliedrion; and in Page 93, Par. 4. L. 5. • is an, inftead 'of on; which, being entirely literary, arc not fo liable to millcad, 6 APPENDIX. PREFACE TO THE READER. I T muft appear fomewhat fingular and uncommon, to offer to the World an Appendix, to a Work which has never been publilhed, otherwife than by delivering it to the Sublcribers ; to feveral of whom, the firft Impreffion has been delivered four or five Years. The fecond Impreffion being, alfo, wholly difpofed of, by the fame means, and upwards of a hundred Hill are wanting, to fupply the Subfcribers *, a third becomes immediately necelTary, before it can be pub¬ lilhed to the World. As an Appendix was originally intended, being mentioned in the firft Propofais, and particularly in the Work, in feveral places, an Apology, for the dekay, may reafonably be expefled-j-; as feveral have kept the Work unbound, on that account. Being mentioned in the Work, it has been noticed by the Critical Reviewers, and treated rather ludicroufly (after fome trifling Criti- clfms on the Work) conluding in thefe Words; “ To this Compleat Preatife on “ Perfpedive, w'e are informed, an Appendix is to be added.” Something of the fame ludicrous kind is alio difplayed, in refpeft of the Title; intimating the Vanity of giving that Appellation to Treatifes, on various Subjedts. I mull own, that it does rather favour of Vanity; and is juttly deemed fo, when bellowed on puerile and ill-digelled Performances, as is fometlmes the Cafe. How far this Treatife merits the Title I have prefumed to give it, mull now be left to the judicious and candid Reader; but, this I will venture to affirm, that, fo far as is ufeful, or really necelTary to the Artift, in delineating, the Subjeft is complete, both in Theory and Pradlice. Much more may and has been laid, in Theory, and that, with great judgment and knowledge, particularly by Mr. Hamilton; and yet, I have thrown fome new Light on the Subjeft, which will make it clearer and better underllood, in general, and chiefly, where it is necefl'ary ; info- much that, I will further fay, if a thorough knowledge of ufeful Perfpedlive cannot be acquired from that Work, it never will. Now, allowing this Treatife to be as perfefl, or complete, as the Vanity of the Author can fuppofe it, there may not be fo much impropriety in adding an Appendix to it, as the critical Gentlemen may im.agine. For, I fhall not fuppofe, but affirm, th.at every Rule, necelTary for the delineation of regular Objedls, that * The fecond Imprefiion confifted of a tlioufand Copies. f This Appendix was in hand when part of the firft fmprcflion was dcftroycd, by the Fire in the Savoy (w'hich impeded its Publication) and two of the Plates have been engraved three or four Years; but being obliged to fet about reprinting the Work (as foon as I could) that, together with my Domeftic Affairs (having loft a moft valuable Companion and Confort) difpofing of my Family, and leaving off Houfe-keeping, and, being much from Home, prevented iny going about to finifti the Appendix fooner. A is P R E F A C E. is, all fuch as are bounded by Planes, or regular curved Surfaces (no other are fit Subjefls for Perlpeclive)are there not only given but applied; ajid that, in the brieleft manner, confiftent wltli pef, icuity, poffible, with all the variety that can occur, in praftice; and alfo, that every Rule is evidently and clearly deduced from an In¬ fallible Theory, previoufly demonftrated ; or, in the moft eoncife manner, demon- flrated there. The Theory and Pradlice of Shadows, in general, of Light and Shade, with other matters necell'ary for perfedling a Piflure, are allb, lully and clearly, inveftigated, in fuch wife as to render the ftudy thereof both interefting and entertaining; calculated not merely for the Artift, but alfo, as a genteel and polite Accomplifnment to the Gentleman. What more can be neceffary, to make the Work a Complete Trcatile? Yet, although the Subjeft of Perfpeftive is, there, fully handled, there are many iitterefting Subjedls, to which Perfpeclive is particularly applicable, not touched -on; and, iiotwithftanding the application of the Rules, given, are uni- verfal, yet there are SubjeiSs, or Cafes, wherein Perfpedlive is moft eflential, that require a further elucidation, to dilplay it to advantage, particularly in the Theatre, wliich is much wanted. To reprefent a given Subjedl on various de¬ tached Pieces, fo, as to appear, from a determined Station, as one Pifture, requires more knowledge than, fimply, the Rules of Perlpeftive to effedl; to determine the true place of each Wing, what Objefi, or part of the Objeft, fhould be repre- fented thereon, and to proportion each to its Place, fo, as to fall in and unite with the reft, is what very few are converfant in, what none have treated on, with any degree of propriety ; yea, I will be free to fay, that it was not at all underftood by fome who have attempted it, and but very little by many who pradlife it, in Scene Painting. There are many other Cafes, in which Perfpedtive may be advantageoufty dif- played, which I have rnade the Subjedl of this Appendix; for, I did not conceive it neceflary, or proper to be done in the Treatife, wdilch abounds with Examples fufficient to render the Rules of Perlpedive familiar; to have multiplied them, there, had been fuperfluous. There are alfo other Methods of Operation which were formerly in ufe, and are ftill uled, and which are worthy of notice, though not founded on geometrical Principles; thofe I did not choofe to mix with the other, as fome have done, and made their Work merely a Parallel inftead of a regular fcientific Treatife; from the main Plan of which, Digrefllons are unjufti- fiable. The whole of the Matter, here given, is divided into nine Seftions, the Heads of which are as follow; The firft Sedtion of the Appendix ftiews how fome of the old Authors, particu¬ larly Vignola, and Sirigatti, delineated Objedls perfpedlively; the great utility of theirs, and, in fome Cales, the preference of it to the new Methods; at leaft, I have fliewn how one may aftlft and facilitate the other. I have, alfo, in this Sedtion, (hewn and difplay’d the ufe, and application, of an Apparatus for draw- ing, perfpedlively, the moft irregular and complicated Objedls, of any kind (and that, without underftanding Perfpedlive) by the affiftance of which, the Landlcape Painter may take the moft juft Portrait of Nature; which, without Apparatus, or fome mechanical Rule, he cannot, though bleft with the moft judicious Eye, and able Hand. In the fecond Sedlion I have made fome (1 prefume ufeful) Remarks, on what, fome term Military Perfpedlive (an unmeaning Term) which, in reality, is ortho- grapihcal, the Eye being confidered at an infinite diftance. Secondly, on Birds Eye Views, of which, the former is a Species; as it fuppofes the Eye confiderab'ly elevated. And, thirdly, fome further Remarks on horizontal Pidlures. In the third, I have advanced fome further Obfervations on the Afcent and Defcent; fhewing, clearly, the great Deception of Vifion, in thofe Cafes, from Obfervations in Nature; illuftrated with ftriking Reprefentations of both, which {though not real Portraits) may frequently be obferved. The remainder of this 3 In PREFACE. 3 Seftion is applied to round Objefts, in general; pointing out the obvious and moft glaring improprieties daily pradtifed, by many, who do not confider, with the dealt degree of attention, their real and true Appearances. The fourth Seftion is wholly applied to the Theatre; in which (I do not flatter •myfelf, for) I am confident, will be found fuch ufeful and neceflary Inftrudtioiis, for Scenery, and Scene Painting, as have never yet been given; being, at the fame time, eafily reducible to Praftice, in every well conftrudled Theatre. The fifth Ihews how the Rules of Perfpeftive may be fuccefsfuily applied to that moft beautiful and elegant Objeft, a Ship, by thofe who are well acquainted with its geometrical Conftruftion; a thing much wanted by Artifts and others, in tthat line of Painting; but more particularly defired by the ingenious Draftfmen, in all the Royal Dock Yards. In the fixth Sedion, I have (hewn how far Perfpeftive is neceflary to the Landfcape Painter; in which is particularly difplay’d the excellence of the Principles of Brook Taylor’s Perfpedtive; llrewing the great utility of the ele¬ mentary Rules, he has given, thereto; with fome critical Remarks on Landfcape- Painting, in general. In the feventh, I have given and explained a Method of delineating on curved Surfaces, any Subjefl: given, with great exadlnefs; a thing never, that I have feen, done before, to any purpofe; with other Diftortions, and Anamorphofes, on plane Surfaces. In the eighth, Thave iliuftrated, and reduced to Praftice, one of the moft elegant Problems in Brook Taylor’s firft Eflay, which I had either overlooked, or not confidered with that attention neceflary for the inveftigation of fo valuable a Problem, before; it is, to determine the Contour, or PerfpecSive Reprefentation of a Globe, from any Radius, perfpeftively given. Secondly, I have ihewn how to reduce the perfpeflive Reprefentations of certain Objefts, to their original geometrical Figure, or Species; properly, inverfe Perfpeflive. And laftly, I have iliuftrated, more amply than I h.id done before, the Do<3:rine of Refledtions, on polifhed plane, and other Surfaces. The ninth, and laft Seftion (by far the moft copious) contains Criticifms on all the Englifti Writers on Perfpeftive; the Errors, which fome of them (in repute) have run into, are pointed out, and their Excellencies candidly difplay’d. 1 his Seftion may be confidered as a Parallel of the modern Authors; as the firft is, in fome degree, between the Antients and Moderns. This is a Plan of the Appendix; which, probably, may be thought, by the critical Gentlemen, Matter lufficient for an entire Work; but, if they will con- defcend to eonfider the Subjefls here treated on, with candour, I am of opinion, they w'ill not fee much impropriety in propofing an Appendix; not as neceflary to a further elucidation of the Principles given before, or to render the application of the Rules, deduced, more facile; or (as is ufually the Cafe) to fupply fome Omif- fion; but, in order to difplay fuch p.irticular Subjedls as could not, with propriety, be given in the Work ; being confidered, in itfelf, complete, as a regular Syftem of Perlpedive, neceflary to the Art of Delineating; thefe being particular Sub- jefls, to which Perlpedlive is applicable, and neceflary to be well underftood. S E C T I O N 4 SECTION I. Containing a brief HISTORY of PERSPECTIVE; with the Methods of Praftice, ufed by the A N T I E N T S, W HEN I firft fet about this Appendix, it was my intention to write a more copious Hiftory of the rife and progrefs of Peripeclive; but, in reality, my time, ever fince, has been fo taken up otherwife, that, finding great difficulty in obtaining the neceffary information for fuch an undertaking, and, confidering that the advantage refulting from it, to the generality of Readers, would in no wife compenfate for the lofs of Time that might be fpent in the enquiry, I ffiall content myfelf with, and doubt not my Readers will be firtisfied, in giving the beft account of its Origin, which I am, at prefent, in poffeflion of; and employ ray Pen in what, I am confident, will be found more interefting to all who are plcafed with, or real admirers of the Subjedt. When or where Perlpeflive was firft praflifed, or by whom, or, who was the firft that wrote on the Subjedt, I fhall not take upon me to afcertain. He who firft drew from, or copied Nature, was the firft who drew perfpedlively, though probably not the firft who pradfifed drawing by rule; nor perhaps were thole, who drew the beft, capable of writing on the Subjedf. The low ebb in which we find Perfpedtive, a Century ago, evinces the flow progrefs of that Art (for it was not, at that time, brought to a Science) although Geometry was as perfedl, and as well known to many, then as now; yet had they little or no Idea of applying it to Perfpedlive. Notwithftanding feveral Books, in Italian, in French, and other Languages are extant, few, that 1 have met with, are worthy of notice; that by Jacomo Barozzi da Vignolo, in Italian, printed at Rome, in 164.4, feeras to be the moft valuable and ufeful Work, on Perfpedlive, that has fallen in my way, of fo early Date, from whom, it is faid, Sirigatti borrowed his Method. Indeed there is fuch uniformity among the reft, that we may conclude they borrowed from one another; but all of them, in general, are without any leading Principles, by which, the Rules made ufe of may be inveftigated ; indeed they can icarce be called Rules, but Method, being, merely, a mechanical Procefs, dependant on no Principle. Vitruvius informs us, that Agatharcus, cotemporary w'ith fEfchylus who ex¬ hibited a Play at Athens, was the firft who drew a tragic Scene, and that he left fome Notes concerning it; which, fome time after his Death, induced Demo¬ critus and Anaxagoras to write on the Subjedl:; as it is rather conjedtu red than alferted by Diogenes Laertius; becaufe, being able Geometricians, he concludes them equal to the Subjefl:; but that does by no means follow’, feeing that, Geo¬ metry has long been known, and well underftood by many, who, though they applied it, learnedly, to various other Subjedls, yet made no application of it to Perfpeftive. If that Conclufion can with certainty be drawn, we may conclude alfo that Euclid and others were verfed in Perfpeftive; efpecially, as they left fome Elements of Optics to the World, which have a tendency tliereto, and from which, Perfpeftive might, in fome degree be deducible. There is no doubt but it might, as being an optical Science; yet is by far more dependant on Geometry than Optics; which is fupported more by Experiment than by Geometry. Geminus, the Rhodian, an eminent Mathematician, who lived in the time of Cicero, wrote on Perfpeftive; which, if we may credit Lomazzo, he divided into three Parts; viz. Vifion, or Perfpeftive; Sciography, or the doftrine of Shadow’s; 4 and Sea. I. HISTORY OF PERSPECTIVE. 5 and Specularia, or Refledioiis; and wl’.lch feems, as he informs us, defigiied for the pratfice of Painters; the firft part being divided into phifiological and linear. Unfortunately, the Writings of Democritus and his Cotemporary, .-inaxag-oras, arc no longer extant; nor am I clear, if the Works of Geminus are in being, at this time. Among the Romans, Pliny relates that, in the Plays given by Claudius Pulclier, the Reprefentations of Houfes, on the Scenes, were fo very accurate, that the Crows, a Bird of great fagacity, were fo deceived in the Appearance, as to endeavour to alight on the Roofs. But furely, we cannot infer, from thence, that they were Mafters of Perfpedive, who drew the Scenes (for he does not inform us who) the truth of the Lines was not at all necefl'ary for deceiving the Crows; the colouring and imitation of the Slates or Tyles is all that was neceflary thereto. The Roman Crows were perhaps lefs fagacious than that Ipecies of Birds, in England; which leldom, I believe, attempt to come lb near Houfes, but chiefly alight on Trees, or on the Ground. It is allb related, that a Dog, being deceived by the Appearance of Steps, in a piece of Perfpedtive of Dento’s, and imagining that he fnould find a pafliige up them (probably being purfued) he made up to them in full fpeed, and dalhed hu Brains out, againft the Wall ; and thus, by his Death, immortalized the Ai tift. Now I cannot fuppofe, that the Deception arofe merely from the Steps, but from the Appearance of a continuation of the Building; or, of Ibme avenue toother Apartments, up Steps; befides, a very fmall knowledge in Pei-fpedtive is fufficient for delineating a flight of Steps, nor was great accuracy at all neceflary to the Deception; but, more, the efted of Light on them, and the force of Shade. Whether thofe Steps were at the outfide of a Building, or internal, is immaterial; for in refpcd of Steps, Amply, a ftrong Deception may be feen, in the Garden belonging to White-Conduit-Houfe, at the far end. Being in the Garden with two of my Boys, who, from their acquaintance with Perfpedive, were not fo liable to be deceived as a Dog; yet both ran up to them, in expedation that they were real, and I own that I was allb deceived; yet I do not imagine that the Painter of thofe Steps is in any danger of being immortalized, or his Name lb much as fpoken of by Pofterity, unlefs he has performed things more extraor¬ dinary. That Perfpedive was taught in the famous Scliool, which Pamphilius eftablilhed in Sieion, to Apelles and other Difciples of that great Matter, in the time of Alexander; and pradifed, nearly in the fame manner, by thofe great Luminaries, Titian, Raphael, and others of thofe times, I have not the leafl: doubt; but muft own, that I cannot fuppofe it was fo well known to the Greek and Roman Painters, in thofe early times, as fume imagine; fo as, in the age of Pericles, to be reduced to a complete Science, laid down in Theorems, from certain Data, or Poftulate. If it h.ad, I cannot conceive that it Ihould be fo entirely loft, in the Deluge of Gothic Barbarifm which overflowed the World of Science and the fine Arts, in the Weftern Empire, that no traces of it were to be found. Although fuch an Inundation of Ignorance might greatly debilitate and damp the ardour of its Votaries, I cannot luppofe that it would wholly extiuguifli every Ipark of Science, and genius for the imitative Arts; it does not feem probable; for, furelv, no benefit could accrue to the ravagers of thofe times, in deftroying all the Works of Art, Books of Science, and Men of Genius, that came in their way. It will fcarce admit of a doubt, that the antient Greek and Roman Artifts had fome knowledge in, or rather, fome Method of delineating Objeas perfpeaively ; yet, it was long a Myftery to the Moderns, after Painting began to revive among ^hein; nor is it eafy to fix the precile time, when they firft: fet about applying themfelves to the ftudy of it; but It is well known, that it had made but very little progrefs before the begining of the prefent Century. Though we cannot afcertain tlie ^Era when Perfpefllve ceafed to exifl:, or, .more properly fpeaking, to be cultivated in the Weftern Empire, it is imagined that it was pmaifed much later in the Eaftern; for in the 12th Century, John R.zetzes fpeaks concerning it, as it he was well acquainted with its importance to . Painting Sea. I. HISTORY OF PERSPECTIVE, Painting and Ststnary. Alfo, the Greek Painter.":, who, in the 13th Centurj', were employed by the Venetians and Florentines, are luppofed to liave brought iome optierd knowledge with them, into Italy; for, the Difciples of Giotto are praifed for their adherence to Perfpeaive, early in the 14th Century, in which they far furpaffed their Predeceflbrs; infomuch that, it foon made a confiJerable progrefs in Italy, the Lombards and Florentines applying themfelves to the improvement of an Art fo necellary to Painting; and this was, at leall, a Century before the Eaftern Empire was totally overthrown. Amongft the Authors who have treated on Perfpedllve, none is of more antient date than Bartolomeo Bramantino, of Milan, who publifhed his Regole di Perfpeltivn, &c. in 1440 ; he is mentioned by Lomazzo, in the fifth Book, with fome account of his Method; viz. by the Lir.e of Interfeclion, as in Vignola’s fir ft Rule. Leon Battifta Alberti, Painter and Architeft, was one of the greateft Artifts that Age produced. In the account of his Life, which is anne.Ked to his Works, we learn, that he wrote his Treatife De Pidtura, in three Books, in which he treats chiefly of Perfpeftive, in 1450. Baldazzare Peruzzi, of Siena, Geometrician, Painter, and ArchitecI, was born in the year 1481, and applied himfelf to the ftudy of Perlpeftive; from whom, Sebaftian Serlio learned his Method, which he publifhed in Italian, in 1540. This Work was tranflated into Dutch, and from that into Englilh; in which Language, it was printed in t6ii ; and again, with Copper-Plates, in 1657. Commandine, in his Comment on the Pianifphere of Ptolomy, publilhed by him, in Latin, in 1558, difeufles the dobtrine of Perfpedlive. Pietro Cataneo, of Siena, in his Book of Architefture, printed in 1567, fre¬ quently reprehends Serlio ; whole Method for determining the Reprefeutation of a Square, on the Pidlure, was by drawing Lines from the extremes of the given Side on the Pi£lure, to the Center, and intcrfedling one of them, by another, drawn to tlie Point of Diftance ; titan which, if the diftaiice of the oppofite Side, from its Seat, be properly applied, no better Method has, ever fiiice, been found, nor ever can. But, in that, he is not confiftent; for, his firft Diagram is erroneous; yet, he fays it is the perfedleft Rule, and may be proved by a Line in it which is falfe; this Line he omits, in the next, as fuperfluous, and is therefore true. The Method he gives, in preference to Serlio, is that ufeJ by Bramantino, and Battifta Alberti, by the Line of Interfedlion (which I lhall explain hereafter) .and this feems to be done in oppofition to Serlio; as heretofore, Mr. Ware oppofed Kirby, and with the fame Method. Daniel Barbaro, publifhed a Work, on Perfpeiftive, in 1569. Some few more are mentioned in a Catalogue of Authors, who have treated on Architeclure and Perfpedfive, tou'ards the end of a laborious Work, entitled the Abecedario Pittorieo ; whom I lhall pals over, and fpeak of the celebrated Architeft, M. Jacomo Barozzi, of Vignola*; by whom, a Treatife was written, in the year 1583, entitled, Phe Two Rules of PerJpeSlive printed in Italian, at Rome, and pub¬ lilhed by Filippo de Rolfi, with Annotations by Egnatio Danti, Math. Prof, in the Academy of Bologna, in 1644, which Work is now before me, and is worthy of Fiotice. Salomon de Cans, Ingenieur to his ferene highnefs Henry Prince of Wales, and Duke of Cornwall, publiflied a Work in French, printed in London, in 1612; entitled. La Perjpeclive, avec la Raijon des Ombres et Mtroirs, which is not witltouc Merit. His Method is almoft wholly confined to the Line of liiteriedlion, as bv the Authors mentioned above, in which he has laboured more than any of them, having dared to attempt a Corinthian Entablature and Capital, which is tolerable; he has alib a piece of Fortification, a pentagonal Baftion, an intricate and puzling Objedl, and laborious to the laft degree. Here are flights of Steps, a Garden, a Fountain, a Draw-bridge, and the Infide of a Room, in the llile of that Age, with its Furniture, belaboured after the fame Method; alfo a Guittar; but the Annulus and Sphere are beyond human patience, to go tlrrough the Procefs. The Shadow * This Author is tjencrally callctl anti known by the ii»mc Vignola, the place where he was born. of Sea. I. HISTORY OF PERSPECTIVE. of the Neck of the Guittar, on a Table (to the Plane of which it is parallel) is not triilj reprefented ; for, in the pofition it is given, the Shadow would be parallel to the Objea, with which it makes a coiifiderable Angle. In the Sth and ipth Plates, he feems to have fome notion of a Point of Sight and Diftance, but without a Line for the Horizon. His projedlion of Shadows and Refleftions have fomething worthy of notice in them, though performed by the former mechanical Procefs. He criticifes on Sirigatti, for not reprefenting a Globe properly; who publilhed a folio Work, in Italian, in the Year 1596; which Work he calls the Child of his own Brain; but, in reality, is no other than the firft laborious Method, by Vignola; defcribed alio by Cataneo, and Bramantino, in which he has not made the leaft Improvement. Indeed it is not improbable, that, notwithftanding others had publifhed the fame Method, many Years before him, it might be of his own Invention. I judge from Experience, having, myfclf, formerly, fallen into that Method, before I was ac¬ quainted with any but the Jefuit; merely from the fmall knowledge I then had of Lines, geometrically; which I applied to Mouldings parallel to the Picture (as in Ex. 15. B. 3.) fuccefsfully; for, at that time, I was not verled in oblique Pofitions of the Object, which cannot be attained from the Jefuit, or any of the old Authors. And I am of opinion, that the fame Method was firft praftifed by all the old Au¬ thors, both antient and modern; every old Work, of the later Ages, indicates and fupports my opinion- The Procefs is, by having the geomctrlc.il Plan and Eleva¬ tion, or Orthography of the Object, corrcftly drawn; then, the Station being de¬ termined, that is, a Point being aft'umed, at a proper diftance, in nroportion to the Scale of the Drawing, or Plan, in the pofition it is intended to be feen ; and, the place and pofition of the Piflure being deteimined on, which is generally parallel to fome Face of the Objeft, a Line is drawn, reprefenting its Interfeflion whh the Ground, or other Plane, on which the Objed is feated; all which, will be better underftood by an Example. Let Fig. I. No. i. Plate I. be the Plan of a tight angled Parallelopiped, on Plate T the Ground, or other Plane; let F be the Station, from which the Objed is in- p-,,. ' tended to be viewed; and let the Pidure be fuppofed to Hand cred, on the Line LM, its Interfedion with the Ground; ufually called the B.afe, or Ground Line. Then, Right Lines being drawn from every Angle, A, B, C, and D, of the Plan, to the Station Point, F, it is obvious they will cut the Line LM, at a, b, c, and d; and, confequently. Lines, perpendicular to the Interfedion, being drawn on the Pidure, from the Points a, b, and c, will iieceflarily coincide with the perpendicular Lines of the Objed, on the correfponding Points A, B, and C, of the Plan. Let the Station Line, FM, be drawn perpendicular to LM, and let LM be produced; let GHIK be confidered as the upright Face of the Objed, ftanding on FK, a Sedion of the Ground Plane; and, MN being coniidcred as a vertical Sec¬ tion of the Pidure, let EF be drawn parallel to it, i. e. perpendicular to FM, and equal to the height of the Eye. Then, the Lines EG, EH, &c. indicate Vifual Rays, which cut the Pidure in the Points g, h, &c. and determine how high each Angle rifes on the Pidure. Being thus prepared, transfer the Points a, b, c, and d, to the Line FM, at a, b, c, and d, making ab equal to aby be equal to be, &c. trom all which draw Lines perpendicular to FM, as ah, ck, &c. and from the Points g, h, /, and k, draw Lines parallel to FM, cutting the former at g, h, i, k, 1 , m, and n, and join- ing hi, nk, and ml, the Figure is completed. The Lines hi, nk, and ml, being produced, will meet in tlieir vauifliing Point, E, whicli is the Point of View for that Objed, aF being taken equal to aM ; the Diftance is EN. Now, I cannot conceive any thing limpler, or ealier to be conceived than this Operation, every Point being obtained by a mechanical Procels, and every Line geometrically drawn. To render it ftill better underftood, let the Plane EFMN, with the Objed OI, be turned up, on FK, perpendicular; then, fuppofe the Pidure {No. 2-) placed on the Interfedion LM, lo, that the Points a, d, b, and c coincide with a, d, by andc, and OP will coincide with NM, and the parallel Lines ^'g, bh, &:c. s- I. HISTORY OF PERSPECTIVE. Platp T &t:. will then be drawn on the Pldliire the contrary way, from NM parallel to ML, ^ interfeaini- Perpendiculars from a, />, c, ?mdd, as before from a, b, c, and d, which muft be obvious ; the Eye being at E will lee the Piaure (No. 4 ) in the true Point of View, which will coincide with the Objc-a at No. i ; and O will coincide with N. I will now (hew, by way of Parallel, how much more facile the fame Figure i» produced by the Rules of Perfpeaive; for this cannot be called a Rule, but a Method, by which the lame thing is elfcaed. i.-v . In Fig. 2- AD be the Ground Line; at pleafure, take C, diftant from AO, ^ equal to the heioht of the Eve from the Ground (equal to EF, Fig. 1.) and draw EC parallel to AD. Make EC equal to the Diftance of the Piaure (equal EN, Fig I ) CD being drawn perpendicular, make BD equal to the Diftance of the Obi'ea from the Station Line (equal BG, Fig. i.) and make AB equal to AB, Fig. i. that is to tlie width of the Object, and draw AC and BC; then, Ba being made equal to Bif, No. i. and ab to BC, draw aE and bE, curing BC, at h and c; draw parallel to AB, and deferibe a Square, adeb; or, make the Reaangle adeb fimilar to the original Figure, and draw dC and eC; e/being drawn parallel to be, and Jg to de conqileats the Figure, age, fimilar to No. 3, Fig. i. Or, if AFGB be made eiiial, and fimilar, to the original ot that Face; then At_ is the Interleiftion of a Plaiie-arf^, which is not feen, FG of the top, and BG ot the Face ie/e; the reft; is obvious, on infpeaion. On comparing thefe two Figures, the number of Lines neceflary to the Procels of one in refpeft of the other, I am perfuaded that no Perfon would hefitate which to give the preference to; to fay nothing of the inaccuracy the former is liable to ; lo that, when there are a great many Lines in the Objedt, which Ihould tend to the lame Point, it w'ould fcarce be poffible to make them do fo, without fixing the Point firft, which is not necefl'ary in that Operation; nor had they any conception ot it, elpecially when the Objea is oblique, as in the next Figure; and, indeed, as it ought to have been in this, being properly reprefented. Let No. I. Fig. 3. (which ferves alfo to Fig. 4) be the Plan of a Parallelopipcd, as above, the Diftance, or Point of Station, is E, and IL is the Interibaion of the Pidure, or Ground Line, to which the Objed is oblique; AE, BE, &c. being drawn,’cut it at a, b. c, and d, which transfer to No. 3. to the Line FS. Then, the Elevation, at No. 2. muft be drawn, according to the pofition it has to the 'Pidure, thus; having drawn DFS, then transfer all the meafures from EPd thereto, E being confi’dered as the Eye, or Point of Station, in one, may be fuppofed to coincide with S in the other, over which E is perpendicular, and equal to the height of the Eve. SF being made equal to EF, Fig. 4. (the Diftance of the •Pidure) draw FC perpendicular, reprefenting a vertical Sedion, and make FB equal to Fb in the other, BK to ba, and c, and BD to bd-, from which, draw Perpen¬ diculars equal to the height of the Objed, and draw IG. Then, to the Eye, at ■E, draw the Vlfiial Rays BE, GE, &c. iuterfeding CF, at b, g, &c. from all which draw parallel Lines, curing perpendicular Lines from a, b, c, and d, atR, G, k, h,&cc, and, joining kB, Bi, Gh, &c. the Figure is completed. Next, I will'fhew that thelame thing is much ea(ier elFeded by Rule, on the true Principles. Fig. 4. No. i. is the Plan, in its true pofition, in refpedof the Eye, at E and the Pidure at IL, on which it is fuppofed to ftand; the Diftance being EF. ’ Let the Lines, i. e. the Sides of the Figure, DA, AB, &c. be produced, till they cut the Pidure, at I, G, K, and L; and, from E, draw El and EH refpec- tively parallel to them, producing their Vaniftiing Points, I and H, IL being now confidered as the horizontal, Vatii(him> Line. For, if the Pidure be fuppofed to ftand upright on IL, the Eye, at E, being railed out of the Plane, equal to ES. Fig. 3. and a Plane be fuppofed to pafs through the Eye, parallel to the ■Ground, c’uting the Pidure, thofe two Planes will, in this cale, coincide; and confequentlv, the Horizontal Line is the fame with the Ground Line; and EA, EC, &c. may be confidered as Vifual Rays, appearing through the Horizontal Plane. . Thele Fig. 4. Tig. 4. Sea. I. H IS TORY OF PERSPECTIVE. 9 Tliefe tilings being premifed, take Gg eqnrd to tlie height of the Eye, perpen¬ dicular to C L, and, at that diltance, draw il parallel to it, on which, take gi, gk, and 1 , equai to G I, GK, and L; then, drawing gH, iH, kl, and 11 , which, by their Interlcctio.IS, give the perfpeflive Plan ot A BCD, No. i. Draw Perpendi¬ culars fiom a, by and f, and on Gg, fet up the height of the Objedt, at J, and draw ) H, curing the Perpendiculars, trom b and r, at g and by from both which, draw Lines to I; and, where gl cuts the Perpendicular on it, f, draw J H, interledling h\ at /, which completes the p'igure ; as at No. 3. hig. 3. above. In thi.- Procels it ni.ay be obfei ved, that the Lines EA, EB, &c. are of no ufe ; but, by them, the correfpondence between the two Methods is obvious; the Per¬ pendiculars from a, b, c, and d, exadlly coinciding with a, b, c, and d; ab and be determining the widths of the Faces AB, BC, on the Piflure. The Reprefentations, on each PIflure being compared, will be found fimilar, in every refpeiS; but it muft be evident, that the Method, in Fig. 3. is not only more operofe, but much more liable to Error, in the Procels. N. B. The Line QR, in Fig. t. is the true pofitlon of the Pidlure, in refpecl of the Plan at No. i. perpendicuiar to the Station Line, FD, which blfeiSs the Optic Angle AFC, under which It is feen. This Figure may, to fome, appear different from Prob. 21. Seft. 5. Book 3. and the Examples in the lixth Seflion, on account of the Plan being inverted, above the Vanllhing Line, being ufually below the Ground Line il; and, the place of tile Eye (which is, heie, at E) above the Vaiiilhiiig Line. But, it fliould be remembered, that, in lliewiiig how to prepare the Picture, in the third Seflioii, this is llicwii to be the true pofition, and the other is inverted, for realbiis there given; for, it muft be obvious, that if the Pifture flood ereft on IL, then, the Obje£l ftanding on its Seat (the Plan, No. i.) tlie Eye being elevated, at E, equal to Gg the given height; the Picture, then, being truly placed, between the Eye and the Objedt, would exadlly coincide with it, the Vifual Rays cuting the Piifture in the feveial Points corrclponding with their Originals. And it muft alfo be obvious, that if the Plan was inverted, that is, turned over, on IL, and, in that ftate, brought down below il, the leveral Points, I, G, K, and Lw'ould be tranfpofed to i, g, k, and 1 ; and, if the Triangle lEH be alfo turned over on IH, above the Vaiiiftiing Line, then would El and EH be ftill refpeftively parallel to the Sides of the Figure, and the Vaiiifliiiig Points would be the fame. It is aho (hewn, in the 21ft Problem, that there is no necefiity for the original Figure being drawn; the Seat of the hither Angle being given, on the Pifture, with its diftaiice from its Seat, together with the Inclination of the Sides of the Figure to the Pidlure, their Mealures being known, is all that is wanted. But, if a geome¬ trical Plan of the Objedl be already drawn, on any other Paper, the pofition of the Pidlure, and the Station may be determined; or rather, the Station being determined, the Pofition is a necellary Coniequence; as it is fhevvn, in the Preliminary Obferva- tions. Art. 4. Sedt. III. the Diftaiice of the Pidlure being at diferetion, the Scale of Proportion, for the Drawing, will be according to it, and the Interfedling Points will be found nearer together, or farther afunder, .is the Pidlure is nearer to or far¬ ther from the Obj.dt. Fig. 5. No. I. is a regular Pentagon, S the Station from which it is viewed, gH is the Interfedlion, or Ground Line, and SHd, perpendicular to it, the Station Line; the Right Lines SA, SB, &c. determine the apparent place of each Angle, in re- fpedt ot the Station Line, and the width of each Face, on the Pidlure, if the Objedt be a perpendicular Prilm; as ab of AB, be of BC, and ag of AG. Then, to de¬ termine how high each Angle rifes on the Pidlure, make SE (perpendicular to SH) equal to the height of the Eye, and produce gH; draw Aa, Bb, &c. perpendicular to Hd, and, from E, draw Lines to a, b, g, &c. cuting HE', at a, b, g, &c. which give the height of each Angle, refpedtively; then, having transferred the Meafures from gH to SH, at c, b, d, &c. from all which, draw Lines perpendicular to SH, and from a. b, g, &c. on FH, draw Lines parallel to SH cuting them, and join AB, BC, &c. which complete the Figure ; as at No. 2 ; for which, E is the Point of View, Sc being made equal to He. C If F‘g- 5 - ll ( 1 , i ■\ JO Sea. I. HISTORY OF PERSPECTIVE. Plate I. If Reader be defirous of feeing a Parallel to this Figure according to the new Principles, I refer him to Prob. 23. Seft. V. of my Treatlfe; in which, he ■will readily perceive the Excellence of the Rules there given, and effedted by means of Vanifhing and Interfedling Points. That this Method is fimple, and adapted to the moft ordinary Capacity, is certain; fuch as, one might reafonably conclude, would firft be fuggefted, by allw'ho fet about to think of a Method of projedling Objedls perfpedfively, by Rule, before he was acquainted with any, for that purpofe; hut how far it is excelled, by the Rules now in ule, muft be obvious to ail who have pradlifed both. Although this Method of Vignola’s, or Sirigatti, is, of itfelf, extremely laborious and tedious, yet, with its Affiftance, the Procefs may be confiderably abridged and expedited. If a perfpedtive Drawing of a Building, externally, be wanted, it is necellary, firfl, to determine a Station, from which, the Objedf makes the moft pleafing Pidture; which being determined, a rude Sketch ol it, with the Meafures annexed to it, is all that is necellary, in order to projedt it, truly, by the Rules of Perfpedllve ; the Diftance, and Pofition of the Pldlure being afcertained, and the Inclination of fome Face of the Objedt thereto; and which, 1 muft own, is not eafily done, without a corredt Plan of the Building. Now', a corredl: Plan is effen- tlallv necellary to he drawn, before we can proceed by Sirigatti’s Method; and, confidering it is but the bare Outline that is necellary, there is no great labour in drawing one ; which being done, all the other Preliminaries are eafily fettled. But it is not necellary to be on the lame Paper with the intended Pidiure, as it has been done here ; it is better on a feparate Sheet, and, provided it be not too Imall, may be by any Scale; for, if it be lefs than the Scale intended for the Drawing, the Lines, being produced beyond the Plan, may be extended to any Dimenfions; as in Ex. 15. Sedf. 7- Book 3. Fig. 85. of an Entablature. The Station being firft determined, if the Building has any deep Recedes, the bearing of the hither part on the other is eafily marked, from which, the Station Line is determinable in the Plan; on which the Diftance muft be let off, and the Pofition of the Pidlure is allb determined. I lhall illullrate it by an Example. p- g Fig. 6. No. .1. is the Front of the Plan of a Building, and S is the Station from ' which it is intended to be drawn ; the Bearing of the hither external Angle F on the Window at M, iufficiently indicates the Station to be lomewhere in the Line FS; the diftance from A or F, determines w-here. This being premifed, from the real Building, we now refer to a Plan, on Paper, for which the outline, only, is needfu], in order to deteimiiie the pofition of the Pidture. From M, or as near to the Corner as the Angle F" appeared to cut it, draw MF, and produce it, at diferetiou; and, by a Scale of the proportion the Plan is drawn to, fet off ASi, or FS, equal to the meafure of the Diftance intended, or meafured, and draw BS; and RS, from the extreme of the End AR, which runs out of the Plate; bifedtthe Angle BSR, by the Right Line SC, which is the Station Line, to which, the Pidlure (PQ) muft be perpendicular; C is its Center, and 3 C its Diftance; and FAC is the Inclinatioa of the Front, to the Pidlure. PQ, it is maiiifeft, is the true Pofition of the Pidlure, from the Station S, for the I Objedl at No. t ; the Center, or Point of View, being in the middle, and confe- quently, each Extreme is feen under equal Angles; in which pofition, it deviates the leaft rcffible trora a portion of the Circumference of a Circle, deferibed on S with the Radius SC ; whereas, a Pidlure parallel to the Front of the Building vvill fubtend an Angie more than double BSR, which is the leaft poflible, from the Station S, about 35 Degrees; in which cale, the Diftance is confiderably more than the width or the pidlure, as it is advifed in the Preliminary Oblervations never to be lefs, feeing it is produdlive of Diftortion. F'or a parallel p dlure, as DB, SD is the Station Line, which always hifedls the Optic Aii'^lc ; conlequeiitly, D b.ing its Center, the Optic Angle is double BSD. The Procels for deliueatiiig a perlpedlive Plan, according to this Pofition, is the lame as the feregoing Figure; the Iiiterlcdlions of the Lines AS, FS, &c. being ' mai'ketl Sea. I. HISTORY OF PERSPECTIVE. marked with correfpondlng Letters, on 25 D, may be transferred to DS, as at No. 2. Then, drawing SE perpendicular, and equal £0 the height of the Eye (which is, here, for want of room, inverted, in relpefl of the preceding Figures) and, pro¬ ducing FA, KL, and HN to the Station Line, curing it at a, b, and c, draw Ea, Eb, and Ec, curing DB at i, &cc. from which, draw parallel Lines, curing Perpendiculars, at A, R, &c. No. 2. which, being properly joined, by Right Lines, complete the Plan, in that polition of the Piflure, for which, E is the Point of View; as all the Lines which reprelent AR, FN, &c. (being perpendicular to DB) neceflarily vanilh there (Cor. Theo. 4.*) which, being known, facilitates the Ope¬ ration, greatly, and is more correfl:. For the inclined Pidlure, PQ, the fame Lines, FS, BS, &c. cut it alfo, in the correlponding Points, W'hich may be transferred to AB, No. 3. Then, SC being the Station Line, draw SO perpendicular to it, equal to the height of the Eye; and, from every Angle of the Plan draw Lines perpendicular to SC, cuting it, as in the Figure, from all which draw Lines to O, cuting CQ, which is now conlidered as a vertical Seflion, being parallel to SO ; as may ealily be conceived, by fuppofing both to ftand upright on the Paper, at the Points S and C. As A B (No. 3.) is not in the Line CS (but, for conveniency, may be placed any where) parallel Lines cannot be drawn from the Divifions on CQ; but, as is more ufual, the meafures Cr, Ch, and all the intermediate ones, mull be transferred, with Compafles, to the Perpendiculars on AB, refpeftively, particular care being taken to apply thofe which correfpoiid. By joining thole Points, properly, by Right Lines, as in the Figure (No. 3 ) the Plan is,completed. This Operation may, and 1 know it will, at firft, appear intricate; and perhaps more fo, on account of the meafures, both for the Ground Line, and vertical Jnterfeflion being on the fame Line; which, it may be obferved, is the fame in Fig. I. and 5. but inverted, and therefore do not interfere with each other; and alfo, on account ot the two Piflures, or Pofitions being together, yet are very dif- tingullhable, and eafy to be feparated, fo as not to miftake one for the other ; for, it is not to be fuppeled that, in pradlice, there would be occafion for both, at the fame time. Although in all the Books which treat on this Method, in a compli¬ cated Plan, there appears thegreatefl confufion of Lines imaginable, yet the difficulty is by no means fo great as it appears; for, by'taking all the principal Parts firfl, and the intermediate Divifions after, the Procefs is not fo perplexed ; for otherwife, if all the Lines are.drawn, and remain altogether, it would he almoft irapoffible to diftinguiffi one from the other. At any rate, to delineate a complicated Objefl:, entirely by this method, without making ufe of Vaniffiing Points, is too much for hum.in patience; but, with the mutual affiftance of each other, the JPtocEls is abridged, confiderably. As it.is abfolutely nece/Tary to have a geometrical Plan of the Outline of a Building, which has various Breaks and Recedings, and Inclinations of the Faces, in order to determine the true Pofition of the Picture, and afcertaln the Vaniffiing Points, &c. which being obtained, the places of every Angle of the Building, the Windows, Doors, Steps, dec. are all transferred to the Plfture, by fixing a Pin in the Station Point, and applying a Ruler to the feveral Angles and Apertures in the Plan; and drawing a few of the principal Lines, the intermediate parts may be marked \yith a Pencil only, which diftinguilhes them better, than by drawing Lines from every one; and, when iorae parts are obtained, the Marks, or Lines may he rubbed out, if they interfere with others, that are wanted. The true Places and Diame¬ ters of Columns, with their exaft Diminutions, and Intervals between them, toge¬ ther with the Angles of the Plinths of their Bafes, let the pofition of the Picture be what it may, are accurately obtained, beyond any other means whatever; in Ihort, the true place of every Part, on the Ground Plan, are the beft and readieft acquired by this Method; but, the parts which are elevated would, on a Pifture, to which the Ohjed is obliquely fituated, be an endlefs trouble to determine, folely h_y the fiune means. ' In the lirft Imprefuon, it is the jifth Theorem. Sefl;. I. l 2 HISTORY OF PERSPECTIVE. Plate T Fiff. 7. is a Perfpeftive of the Building, on the parallel Pidlure; in which, every i ■ Angle is of equal height, in front, and the Windows arc between paralLl Lutes t 7 ' the Fronts are geornetrical, and limilar to the Originals, as well as to each other. ’ In order to obtain the height of the receding Parts, an Elevation muft be drawn, as in Fig. i. or it may be done without, thus; to determine the heiglit of the Aiiole at H,"('Fig. 6. No. t.) A Perpendicular, from H, cuts the Ground Line at c; luppofe the height of the Building equal to cN; apply a Ruler to E and N, and mark the place where it cuts the Piaure DB, as at/, make H/ (Fig. 7.) equal to cf, and join IK, as in the Figure; bv the fame means the height ot any other Line’ may be obtained. Bur, having determined the Point of View, or, more pro¬ perly, the Center of the Piaure, as here, at D, and lince all the receding Lines tend there, the other Procefs, by a geometrical Elevation is unneceflary; feeing that, a Line’from A'to D cuts a Perpendicular from H, at I, the true height of that Angle. It is not neceffary to fay more, in refpea of the parallel Piaure, which, indeed, was the only mode of drawing, perfpeaively, in thole Times. Pig. 8. is the fame Object, oil a Picture properly fituated; as on PQ, tig. 6. in which, the Ground Plan is the fame as No. below; the Ground Line is A B, anfvvering to KB, below; from which, all the Angles of the Building are drawn, perpendicular. Q In this Figure, becaufe the Angle A touches the Piaure PQ (Fig. 6.) A a, which I'S- reprefents that Angle on the Piaure, has its full geometrical height, in proportion to the Plan. To determine the heights of the parts whicli recede, according to this Method, a geometrical Elevation muft be drawn, according to its lituation with the Pidure; or thus, for the Angle B; Bb being drawn perpendicular to SC, let off, from b, the height of the Building bB, and draw BO, curing the Piaure at Q; make Bb, Fig. 8. equal to CQ; and if on bB the heights of the Windows, &c. are let off, and Lines drawn to O, CQ will be divided in the fame proportion, which muft be traiisferied to Bb, Fig. 8. The Dlvlfions on the two extreme Corners of the Building, for the Windows, &c. being thus obtained, and being all of the Lme height, on each Story, joining thofe Divifions by Right Lines, and Perpendiculars being drawn, give the places ot the Windows in each Piei; and it is maiufeft, that if the two Extremes be divided proportionally, the Lines which join them will tend to the fame Point with A A, on the Ground, and ab, at the top of the Building. All the other Angles muft: be determined after the fame manner; as Hh, by a Perpendicular, at li. Fig. b. but, bow much the Procels is facilitated, by means ot Vaiulhing Points, will foon be perceived. Having drawn the horizontal Vaoifh- iiig Line, and determined the Vaiiilhing Points, as at Fig. 6. SP being parallel to the End of the Building determines one, at P, the other is where SE, being pro¬ duced, would meet PQ produced; or it will he diftant from C, a third Proporti¬ onal to PC and SC. The centre of the Piaure being fixed at C, Fig. 8., diftant Irom the corner A a equal to AC (Fig. 6.) on the Horizontal Line; make CP equal to CP, P is the vanilhing point of all the lines parallel to AR, the other is out of the bounds of the Piaure, determinable as above. Now, let the places of all the Angles of the Building, which are in fight, be determined as at Fig. 6, on PQ and triuisferr’d to AB. Fig. 8. at A, F, &c. from all which draw perpen¬ dicular lines indefinite ; and Aa being made equal to the knovvn or determined height of the Building, draw Lines to the Vanilhing Point of the Front frorn^ e.ich extreme, cuting the Perpendiculars, at f, g, and b, the refpeaive height of eacli; the Windows, in thofe Piers, are obtained by the fame means. The Di¬ vifions, for tlie blank Windows, in the returning Face, being alfo determined on GH, and perpendicular Lines drawn from each, GP, gP, &c. being drawn, cut them in their refpeaive heights, and determine the Angle Hh ; through each ex¬ treme of which, and the Divifions thereon. Lines being drawn to the Vanilhing Point of the Front determine the height of the Windows in the Recefs. To per¬ form all this by Sirigatti’s Method is not only tedious but liable to error; by Vaiiilliing Points there can be none, being truly determined. To Sea. i. HISTORY OF PERSPECTIVE. '3 To obtain the Divifions of the two Piers, perfpeflively, the diftance of the Vanifhing Point of the Front muft be laid down on the Horizontal Line, as at D. and the true geometrical meafures fet off, from A, on the Ground Line, at G, &c. from which, Lines drawn to D give the Points F, G, and B, but not always fo accurately determined as the other, on account of their interfering AB obliquel vj for, when the Horizon is very low, or the Diftance of the Building from the Pi’c- ture confKlerable, the obliquity is Inch, that the Points of Interlbaion cannot be afcertained; in which calc, recourfe muft be had to an extra Plan, at a greater diftance from the Horizon ; fo that, in many refpefts, the method of determining them, as above, is by far the moft accMrate and eligible; and, particularly, in refpccl: of Columns and other detached parts of the Building, with manv Minutias, which to obtain with exaancfs, recourle muft be had to a gcomctricarPlan. Thus, I prefume that 1 have fufficlently evinced, not merely by Words, but by Example slip, that the Method of projefting Objefls perfperivelv, as by Sirigatii or Vignola, is not to be defpifed, and rejefled ; but, in many cafes to be preferred, when it tends to facilitate and expedite the Procefs; and when, by means thereof, the Parts are more accurately determined. I muft not omit takin? notice of a Circumftance in the 28th Plate (the Queen’s Palace) which is, I find,^a Paradox to fome Perfons, viz. that the Center of the Piaure (improperly called the Point of Sight) Ihould be in the Front of the Building, the End being feen. If proper attention be given to Fig. 6. I am perfuaded that the Myftery will fooii vanifli. At the Station S, it is evident that the End, AR, of a Building, on the Plan, No. r. would be feen; and confequently, the Center cannot fall on the Front, the Pifture being parallel to it, as DB; for it is at D, the diftance of from the Corner, for that Pifttire. But, on the Piflure PQ, the Center is at C, for SC is perpen¬ dicular to It; which, being produced, falls on the Building at L, and yet the End remains vifible, as it neceffarily muft, to a Perfon ftanding at S. D is the Center of the Pifture Fig. 7. but C is the Center or Point of View for the other Piaure, Fig. 8. yet the End of the Building is equally feen, in both. Thus much for the firft of the two Rules, by Vignola; for the fecond, fuffice it to fay, that it is the fame, in every refpea, as the Jefuit’s. It conveys a very juft Idea of the Horizontal Line and Point of Sight, alfo of the Diftance taken therein ; by means of which two Points every thing is effeaed, in the fame manner as on the true Principles, at this time, rcfpeaing right angled Objeas, having one Face, or Side, parallel to the Piaure ; for which, the firft Propofition, in his Theory, feems well calculated, which, is the leading Principle: It is as follows. In every Triangle, fituatcd between two parallel Lines; (more properly thus) a Right Line being drawn through any Angle of a Triangle, parallel to the oppofite Side ; if two Points be taken in the upper Parallel (that is, which pafl’es through the Angle) equally diftant from the Angle of the Triangle ; and, if there be drawn two Lines from the oppofite Angles, at the Bafe, curing the Sides of the Triangle, a Line being drawn through the Interfeaions fhall be parallel to the Bafe. ConftruHion. In the Triangle ABC, * let DE be drawn through the Angle A, Fig. X. parallel to the Bafe, or Side fubtending the Angle A, i.e. to BC, and let two Lines (BE and CD) be drawn, to the Points D and E, equidiftant from A, curing AB and AC at F and G; a right Line, EG, being drawn, will be parallel to BC. Demonftratlon. Becaufe DE is parallel to BC, the Triangles ADF, FCB are umilar; confequently, AF : FB ; : AD : BC (Eu.4. 6.) and, for the fame reafon, AG.GC. .AEiBC, the Triangles AEG, CBC being fimilar. But, AD is equal to ye AE; wherefore, A D : BC AE ; BC ; and confequently, AF : FB ;; AG : GC; therefore, EG is parallel to BC. (Eu. 2. 6.) ' ' ' Although this Theorem is neither more nor lefs than the 2d of the 6th Book of Euclid, yet the manner of inveftigation, here ufed, is very ingenious, and extremely— well calculated to ferve the purpofe intended, in Perfpeflive. For, confidering BG 6 <. * This Figure, for want of room, in the Plate, is inverted. D as u Sea. I. HISTORY OF PERSPECTIVE. Plate I. the Side of a Square parallel to the Piaure, and DE the Horizontal Line ; the Vertex A, of the Triangle, may be confidered as the Point of Sight (properly, the Center of the Piaure) and the Points D and E its Diftance, laid down on the Ho¬ rizontal Line; coufequently, BFGC reprefents a Square, having one Side parallel to the Piaure, feen at the Diftance AE; E being the true place of the Eye, tran- fpofed to the Vanilhing Line of the Horizon, or D; and coniequently, they are the Vanifliing Points of the Diagonals, BG and CF, asA is of the Sides BF and CG. In this fingle Theorem, a foundation is laid for the whole Theory, in Vignola; and, indeed, for proieTing Objefls in all common Cafes, being parallel and per¬ pendicular to the Pidlure ; i. e. the Lines in the Objeds being fo fituated. And, for Figures which are obliquely fituated to the Pidure, they are determined by the fame means; that is, by drawing Lines, from every Angle, perpendicular to the Interfedion, or Bafe Line; and, feting oft its Diftance, on the Bafe Line, a Line is drawn to the Point of Diftance, cutlng the former in the Point fought. By this means, every Angle of the Figure is determined on the Pidure; and, being joined by Right Lines, produce the Figure without having recourfe to Accidental Points. ' The Theory of this Author is very copious, confiftingof forty-three Propofitious, fourteen of which are Problems; but the whole is Geometry rather than Per.'pec- tive; feveral of which are the fame as in Euclid, others are Ibmewhat varied; and, in o-eneral, judicioufly chofen. For inftance, the firft, from which there are feven or eight more, that might be Corollaries to it. The 17th. If there are feveral Triangles having a common Vertex, the Safes (or Sides oppofite) being equal and parallel; that whofe Bafe fubtends the greateft Angle has the leaft Sides. This is deduced from the 21ft B. i. of Euclid (the 14th of mine) from which I have deduced a Corollary nearly fimilar to this, entirely on account of its utility in Peri'pedive, which 1 frequently refer to. The 21ft is a very notable one, viz. If a Pyramid be cut by a Plane, parallel to its Bafe, the figure of the Sedion will be fimilar to the Bafe. This is a Corollary deduced from the 25th 11 Euclid (Theo. ift. B. 8. of mine) and is a moft excellent Leflbn in Perfpeftive; for the Pyramid of Vifual Rays, formed by any right lined Figure, or plane Solid, being cut by the Plane of the Pidure, produces the per- fpedive Reprefentation of the Figure, or Objed; and, being parallel to the Bafe of the Pyramid, i. e. perpendicular to the Axe of the Eye (which is alfo the Axis of the Pyramid) is the only true Pidure, being fimilar to the apparent Figure, or Objed; but being cut obliquely, the Sedion is diflimilar (of which, Vignola makes another Theorem, the 22d) that is, the more oblique the Sedion of the R.iys is made, by the Pidure, the more diftorted is the Reprefentation thereon. Theorem the 8th has fomething pertinent in it; viz. Whenever the Diftance is taken lefs than the height of the Eye, the gradated Sides of a Square (i. e. feen perfpedively) may be either equal to, greater, or lefs than the real Side; which is thus demonftrated. Let DF be a vertical Sedion of the Pidure, E the Eye and DE its Diftance. Fig. Y. If EA be drawn fo, that DG is greater than DE, the Diftance; then, becaufe DE is parallel to CF, the Triangles DEG, G A F'are fimilar; wherefore, FG:FA : : DG : DE. But DG is greater than DE, therefore, FG is greater than FA. Again; let EB be drawn fo, that DH is equal to DE; then, the Triangles DEH, HBF are fimilar, wherefore, FH is to FB, as DH to DE; i. e. equal. Laftly; let E C be drawn fo, that DI is lefs than DE; coufequently, from the reafoning above, FI is lefs than FC. But, if AF, BF, and CF, be confidered as the Sides of Squares, FG, FH, and FI, reprefent their relpcdive depths, or re- cedings on the Pidure, which are either greater, equal to, or lefs than the Originals; i. e. than the given Sides of the Squares, being parallel to the Pidure. The next Theorem (when the Diftance is either equal or greater than the height of the Eye, the receding Sides of the Square will rile lefs on the Pidure than the given Side) might be a Corollary to the foregoing; from which it is ealily deduced. All the reft are, merely. Theorems, or Problems, in Geometry, fave the 33d. the Figure for which is expreffive, and feems to indicate a true Idea of determining the Center of the Pidure, as the Vanlfhing Point of Lines which are perpendicular Sea. I. HISTORY OF PERSPECTIVE. to it. The Theorem itfelf is of no Confequence; it is, if a Figure be parallel to the Horizon, the Eye not being in the fame Pl.ine, it will appear gradated; which is exceptionable; for, the Eye may be in a Perpendicular to the Plane of the Figure, in its Center, in which cafe, it will not appear gradated, though parallel to the Horizon. It is alfo partial; for, if the Axe of the Eye be inclined to the Plane of the Figure, i. e. if the Figure be feen obliquely, however it be fituated to the Ho¬ rizon, it will appear gradated. Thefe Propofitions are preceded by twenty-feven Definitions, and twelve Suppo- fitions; the whole is illuftrated with copious Annotations, by Egnatio Danti. But what feems, to me, moft extraordinary is, that in the delineation of a Cube (hav¬ ing a Face parallel to the Pifture) the Points of Diftance are placed in the Vertical Line, as well as in the Horizontal, and a proper ufe is made of them; i. e. as Va- nilhing Points of Diagonals in the receding vertical Faces of the Cube. The Figure before it feems to indicate how they are determined, by a Radial Line drawn from the Eye, parallel to them; although, in the Defcription, it is not mentioned as fuch, nor, 1 believe, intended, (but to Ihew the optic Angle of the Pidlure) I think, there was no great Merit in determining, from thefe Figures, the Vanifhing Points of Lines in general; in which, the Excellence of Brook Taylor’s Perlpeflive chiefly confifts. Seeing that this Author has advanced fo far, towards determining Vanlfhino- Points, in general, geometrically, I am furprized that he did not proceed one Step further, and perfeft it; for, from the theoretic Diagrams, given in the Work, there feems to be nothing more wanting thereto, than drawing the diagonal Lines, from the Eye to the Points of Diftance; which being done, their parallelifm with the Originals was Idf-evident; and it was alfo as evident, that if the Diagonals de¬ viated from an Angie of 45 Degrees, whether more or lefs, that their Parallels from the Eye, would, neceffarily, determine their Vaniftiing Points. And it is ftill more aftonifliing, that, for fo long time after, none fhould hit on fo valuable an Expedient. Thus much for Vignola, in whofe Work, on Perfpeflive, there ara no ftrikino- Objefls, effeiSed with that unwearied labour, as in DeCaus; for he prefers the fecond Rule, the other being fo exceffive operofe. The moft extraordinary Plate, in the Work, is a horizontal Pifture, reprefenting a vile Piece of Architeftuie. and a round Temple (little better) which, by means of a Sefliori (not badly deviled) taking away one-fourth of the Building, exhibits both an e.xternal and internal View. But thefe being amongft the Notes (although the firft is a folio Plate, 13 Inches by 81) I am of opinion have been added, with the Frontifpiece, by Roffi. There are feveral more Plates of Arches and Arcades, parallel and perpendicular to the PiiSure, merely Outlines; in one of which, there is an attempt at an Entablature in the Tufean Order, but without Rules for, or Reference to it. Another Plate exhibits a Pedeftal, geometrically drawn, the Proportions of which, as well as the Mouldings, I can fay nothing in praife of; which (he being an Architefl:) is fome- what extraordinary; the wooden Prints that follow, of the Pedeftals, the Safes, and four Columns in Perfpeftive, are better proportioned; but the Prints of Capi¬ tals, compounded of the Ionic and Corinthian, are vile. After thefe are two Plates of double, winding Staircafes, both geometrically drawn, the laft is a geometrical btaircafe ; which, with another exhibiting the manner of conftrufling them (to no purpole, in Perfjjedlive) concludes the Book. I had omitted to mention, that, in the firft Part (In the Notes) are exhibited leveral Methods of drawing, mechanically, by Apparatus, all of which, fave one, are unworthy of notice; which (in a folio Plate) exhibits the horizontal and up¬ right Scale (See Fig. 14. Plate II.). It is a moft clumfey Conftruaion; the upright Scale is moved, to and again, by means of a Roller, having a Cord fi.xed, at both ends, to the bottom of the Scale (in the Groove it Aides in) and, paffing over a Pulley, at each end of the Groove, is wraped twice round the Roller, which the Perfon turns either way, at diferetion, with his Hand, and fo moves the Sliding Scale, to the Right Hand, or Left, at pleafure. The Divifions, on thefe Scales, are by Sea. I. HISTORY OF PERSPECTIVE. I Plate II. l>y fliort bits of fmall Wire, Ruck in the edges; wliich, for the large Divifions, 1 I approve on and recommend as the beft, being more obvious than (mall Lines, as i in common Scales; but, being divided fo, into fmall Diviliens. they would contule j the Eye, which could not dittinguifh one from the other. t Mr. Kirby is under a miftake when he fays, “ the Inftruments which have been a publilhed, of this kind, hav'e no Dlftance limited for the Eye-hole, which make ail 1 the Reprefentatlons that are drawn by an improj er Diftance raoft egregioufly falle, as it is demonftrated in what ive have faid, concerning the Dlftance of the Eye.” I know of no liir.ited Diftance, as the only true; nor is the Perfpedtive falfe, at any Diftance; it will bediftorted, when too little, but not falfe; and lurcly, when it is greater than is either proper or necefl'ary, he cannot fay it is. Of this more' hereafter, in the laft Seflion. After expatiating, fo largely, on the Work of Y^Ignola, to whom (though he was j not the Inventor of the Methods of Pradlice, which it treats on) we are indebted, 1 for handing them down to Pofterity in fo able a manner, it is fuperfluous to (hew I how fome others, before, or cotemporary with him, proceeded in their Operations,. in delineating Objefts perfpeclively. Nor (hould I think the Authors worthy of notice, but that the fame Method ftill prevails, and has, of late Years, been revived, by an Author, not undefervedly, in repute, in other Subjefls. The firft, we are ' acquainted with, who praflifed, or publilhed, this puerile and trifling Method is [ ' Jan Vredeman Frieze, a folio Work, in French; printed at the Hague in 1619, I which is fomewhat remarkable, being exadlly a Century, before the Art was j brought to Perfection, in the moft fcientific manner, by, and to the honour of ; our Countryman, Dr. Brook Taylor. This Method is by reticulating, perfpectively, the Ground, or Pavement, on which the Objefls intended to be delineated, are fuppofed to be feated ; as in the following Example. The dimeiifions of the Object being known, or de¬ termined on, fome equal part of it is taken, as a fcale of Meafure to work with. 1 Suppofe it required to draw a Block of ftone or other materials, which is 3 feet '■ long, 2 feet and a half wide, and 2 feet thick; fituated two feet and four inches to the right Hand, at one foot diftance beyond the Picture, having one of its Faces (2 feet, by 2I) parallel thereto, and feated on a Face which is 3 feet by two. 1 ' 1 F'g- 9 - height, and diftance of the Picture being determined, make B C (Fig. 9.) . equal to the height, and draw the parallel Lines AF and CD; in the laft of ; || which, make CD equal to the Diftance. Then, A a being taken for the mea- Di fure of a foot, fet off as many of thofe Divifions as are neceffary, a,b, &c. from Jj I all which draev Lines to C; from A, draw a line to D, curing them all; and j through the Interfections, draw the parallel Lines which complete the Squares. I ' i Bcf being equal to the fituation of the Object to the right hand; in dC, ag will reprefent a Side of the Object, and ab another, which is parallel to the Bafe I Line. On a, b, and g, draw Perpendiculars, and make ad equal to a^, which is I 2 feet and a half in that place; draw dC and cC; then draw ef, which com¬ pletes the Figure ; e being the interfection of the Perpendicular ge, by dC. At X is another Object of the fame Dimenfions, refting on the Face adeg, at the diftance of three feet, from the Picture, and almoft direct before the Fye; li i being the meafure of two feet and a half (equal At) in that place. The next who ufes this Method, that is who has publlllt’d it, was A. Boffe, a French Engraver of fome diftinction; printed in French, at Paris, entitled, The umverfal Method of Mr. Defargues Prahiice of Perfpehlive, by a fmall Scale, and publifhed in 1647; confidence, or rather effrontry', to aflert, that it ' is the fhorteft, the eafieft, and raoft exact method, not only, that had ever yet ] been publiftied, but that ever could be invented. What muft have been his Confufion, had he lived to fee, and to underftand the true Principles, on which 7 the I Sea. I. HISTORY OF PERSPECTIVE. >7 the Procefs is now performed ? which, with the utmoR Confidence, I affert, will never be excelled. 1 (hall give an Example, of an Objea in an oblique polition; Let A BCD be the Plan of a Pedeftal (Fig. to, No. i.) fituated as it^ is Fig. lo. intended to be drawn ; i. e. inclined to the Piaure in the given Angle ABF. 1 lie nioft ufual method was to take a meafure reprelenting a Foot, with which the Floor was reticulated, at random, without regarding how they cut the Objea; but, I would alk mv Friend Bofl'e, whether he thinks it is not better to enclole the given Plan in a Square, as here by EFGH ; and divide the Side ot the Square into Inch a number of equal parts, that the Angles, A, B, C, and D, may fall in one of them, or nearly, as here into five; it matters not what their meafure is, they will be in fome proportion to the given Side of the Pedeftal, AB. If the given Figure be not a Square, it may be circmfcribed by fome Reaangle or other. This Figure may be by any Scale, greater or lefs. IK being drawn, for the Ground Line, at the intended height of the Eye draw NL, parallel to IK ; in which take O for the Point of Sight; and on IK, take as m.-iny Divifions as you pleafe, as at f, t, 2, &c. in proportion to the in¬ tended Scale of the Drawdng (as at No. i, to the Plan ABCD) five are fufficient, from f to g. Having drawn Lines from each to O, he proceeds to gradate them, by a method peculiar to himfelf, at that time; by making, what he calls a per- fpeflive Scale; and which, to do him juftice, is an ufeful Expedient, often ufed now, though in a very different manner; but not at all neceflary, when the Dil- tance of the Pifture does not exceed the limits of the Drawing Board, or Canvas. KL being drawn, curing the Bafe Line and Horizontal Line at pleafure (it is Nb. 2; ufually drawn perpendicular, but that is by no means necelfary) take Kd at difcre- tion, and draw dL; then, make LM equal to as many times Kd as the diftanceof the Pifture is of the meafure I f, viz. fix times, and draw KM, curing dL at a; draw ab parallel to dK, and draw ^M, cuting dL at c ; continue this procefs as often as there is occafion, and from all the Iliterfedions, on dL, draw Lines parallel to IK, as yV, &c.; by which means, the Squares on the Floor are gradated, as is evident; for if eK be taken the full meafure of If, and LN be the full Diftance of the Picture, KN, being drawn, cuts e L at /a, which, being repeated, will be found to give the fame diminution of the Squares, as it necel- farily muft;; for it does not depend on the full meafure, but ou the ratio of one to the other (See Prob. 6. Stft. 4. B. dK is taken, here, half eK, confequently, LM is half LN. Any other Ratio of If, being taken, will effefl; the fame. The Reticulation of the Pavement, being elfefled, and B, the hither Angle of the Pedeftal (No. i.) being fuppofed to be in the Bafe Line, ati?; then it is obvious, that y/will reprefeiit .A, and C the Angle C ; f 5 reprefenting three, and f A two Divifions, anfvvering to F B and F A, in No. i ; at which Points, B, and C, draw the Perpendiculars AD, BE, and CH. Make equal to the known heiaht of the Cornice from the Floor, in proportion to the Divifions If, ft, &CC. (for the Perpendicular BE is in the Pifture) and ^ D muft be made equal to as many of the Divifions on the Line Ad, thus. Take fg equal to the height BE, and draw the dotted Line gO, cuting Ad at G; AG will be the true perfpeflive height of the Angle D. By the lame means CF h determined ; alio the height of the Plinth, at tii, n, and 0 ; which, being joined by right Lines, complete the Plinth, and the upper Fillet of the Cornice, D,E,F. The interior Square, or the three Points a,b, and c, which reprefent the Angles a,b,c. No. I, being determined, and perpendicular Lines being drawn from each, the mealures thereon muft be obtained as the other; for inftance. A Line, parallel to IK, being drawn tlirougb b, take the meafures of all the parts, from I or f, on IK, from all wdiieli Divifions draw lines to O, cuting the dotted Line yV in the perl'peclive mealures of be-, the other Corners of the Dado, ad, andey, being determined after the lame manner, and joined by right Lines tk, kl, &c. the folid part of the Object is completed. It is caly to conceive how the Fafcia, in the Cornice, and the fmall Fillets ra.iy be obtauitd, in like manner, from a perfpective Flan of each, on the Pavement; E but HISTORY OF PERSPECTIVE. l8 Sea. I. Plate II I perfuaded, that thofe Miniitias were taken by guefs, having obtained the principal parts; for it mull be an endlefs labour to projea the whole ftriflly true. Inrefpeftof curved Mouldings, as of the Torus, in the Bale of a Column on the Pedeftal, at df, thofe Rules could never effefl; it. Serlio made ufe of the fame method, of fquaring, or reticulating the Ground Plane, in order to determine the places and proportions of his Buildings ; the openings of Arches, and widths of the Piers, Doors, Windows, &c. were, luckily in thofe Days, fo proportioned, alfo Steps, as to be, always, fome aliquot part, or multiple of each other; no¬ thing could be determined but by Squares, and confequently, they muft, have had fome ftandard meafure, to which Artificers, of every Denomination,, were obliged to adapt the feveral Parts of every Building, or other ObjeiS, allb the Spaces between each, with the utmoft exadlnefs, without fradtional parts; which are now fo very common, that fcarce two parts of any Cbjefl, much lefs all the parts of an Objeff, which is multifarious in its parts, can be reduced to the fame common meafure, without Fradlions; and, confequently, cannot be readily de¬ lineated, perfpecSfivelv, by thofe means; therefore, this Method is now grown quite obfolete, and others have been contrived, or invented, of meer iieceffity, in compliance with the inaccuracy of the Artificers of thefe later Ages, who have no Idea of proportioning every thing to one, common, ftandard Meafure. I fliall therefore take my leave of Signior Serlio, and Motif. Boffe, to fhew tiie Method others have purfued, to accomplifli what was fo readily done heretofore, when Objedls were fo well adapted to theirs. It may not, I prefume, be thought impertinent, to fliew how an Objeft fo fitu- ated, as the Pedeftal, is delineated on the true Principles. The hither Angle of the Objeft being determined, at i?, the Ground Line (IK) and the Horizontal Line (NL) being drawn, and the Center of the Piifture fixed, at O, OP is drawn perpendicular to NL, and equal to the Diftance; then, PQ and PL are drawm, refpedlively parallel to AB and BC (No. i.) i. e. to the Sides of the Pedeftal, and the Angle LPQ being bifefted, or PN drawn parallel to BD (a Diagonal of the Square ABCD) the Vaniftiing Points Q and L, of the Sides, and N of the Diagonal, are determined. By means of the Vaniftiing Points Q^and L, it is obvious how exadl the Lines zfB, RC, &c. are drawn ; and, by the Vaniftiing Point, N, of the Diagonal, the perfpeftive proportions of the Mouldings are obtained, having fet up their heights on BE (See Ex. 17 and ig. B. ^.) How the Lines are proportioned, it is unneceflary to fhew here, at large, frequent Exam¬ ples are given in the Work; fuffice it to fay, that Bo being taken equal to the known meafure of a Side, at the Plinth, and QM being made equal to QP, OM, being drawn, cuts B Ci_at yf, giving for a Side in perfpeefive. After the fame manner BC may be obtained; or, drawing yfL and BN, the Angle T) is determined, and QDC will finifli the Square y^BCD; no regard being had to the Squares on the Ground, nor indeed to the Figure at No. i. its politioii to the Pidlure, i. e. the Angle ABF, with the true meafure of a Side being all that is necelfary. The difference of this Procefs, being compared with the tedious operation in the other (to lay nothing of the inaccuracy it is liable to) muft be obvious to every Reader, who has any pretenlions to knowledge m Peilpeclive. In the Y'ear 1642, a Parifian Jefuit publiflied a Quarto Work, in French; which was tranflated into Englifli, and publifhed by Robert Pricke, and thence, by fome, called Pricke’s Perfpeiftive, but more ufually the Jeluit’s, fometime about the Year 1685 or 6; and, again, by E. Chambers in 1726; a Work which is well known to every Painter and other Artift, and is gener.iliy cfteenicd as the moft ufeful Work extant, having gone through feveral Editions. On account of its fimplicity, I believe, this Work has furnilhed a greater Number with lome Ideas of the Subjefl, than any other; but the Ideas inculcated by it are limned and partial, which has prejudiced all, or the much greater part ot thole who ftudied from it; infomuch that, very few who, having imbibed thole Prejudices, can be reconciled to, or prevailed on, to make a fair trial of the method of Practice on the new Principles, and fewer ftill, who are ever divefted of their Prejudice, wholly. This Sea. I. HISTORY OF PERSPECTIVE. This Work was the firft, on the Subjea, that happened to fall into my Hands wdiich I ftudied with avidity ; being, at that time, a perfea Novice in the Art’ yet I entered into the Subjcd very readily; fo that, before I had gone throiinh half the Book, I had a clear Idea of the whole, which I was by no means fatfs- fied with, but vvanled conviaioii of the truth of the Rules prefcribed. In the pur- fuit of which, I fell, infenlibly, into the Method ufed by Sirigatti, by means of which, 1 found, that the determining a Point on the Piaure, by the Center andDiftance (as in the Jefuit) might be depended on, which evinces mv.igno¬ rance in Geometry, at the time. However, before I had gone through the'whoie I had the courage to attempt dra.wing the infide View of St. Martin’s Church’ which I completed, without other Inllrudlion than what I acquired from it I alfo drew the Portico, on which 1 bellowed more pains than on any Drawing fince, which has been much admired ; but, after I became acquainted with Brook Taylor, I found that I knew not what Perfpeaive meant, before; yet I improved the knowledge I gained from it, by my own Rudy and application ; of which I prefume, the Work 1 have produced is fome proof. ’ I lliall, here, take occafion to Riew the affinity between the Method of find¬ ing the reprefentatiou of a Point on the Pifture, according to the Jefuit, or to all the modern Writers, and Sirigatti or Vignola; or, how the truth of one is evinced by the other. Knowing how the Point is fituated, in refpea of the Piaure, and the Eye, its Reprelentation on the Piaure is thus determined ; e.g, Let A be a given Point, lo fituated to the Piaure, that a perpendicular Line Fin Y being drawn, from A, to the Piaure, cuts it at B, its diflance from the Piau-e ' being equal to AB ; C is the Center, or Point of Sight. Through C draw EC at pleafure, in which take CE equal to the Diftance the Eye is from the PicI ture; and, through B, draw BG parallel to EC ; having made Ba equal to B. 4 , draw BC, and aE, iiiterfeaing at a, the reprefentatiou of A, on the Piaure! (See Prob. 6, Sed. 4. B. 3.) Now, EC being confidercd as the Horizontal Line, and BD as the Bafe Line, the Procefs is the fame as in all the modern Authors; but they may as well be the Vaniffiing Line and Interfeaion of any other Plane, which is perpendicular to the Piaure ; for, if they had been drawn perpendicular, or any how inclined, being parallel, the effba,'that is, the Point a, will be found the lame. To prove the truth of this Procefs, by Sirigatti’s method, let DS be made equal to the difiance of the Piaure; then is S the Station Point, from which A is leen ; the Pidure may be fuppofed to Rand upright on BD ; then, AS, being drawn, cuts it at F; by which it is manifefl, that the Point A will appear on the Pitturc, at F ; that is, it will appear to be nearer the Station Line, SD, equal FD ; which the Perpendicular F^ evinces, feeing it cuts BC in the fame Point, Then, to prove that it will rife on the Piaure equal to Fa, make DG equal to AB, and draw EG, cuting CD (which may be confidered as a vertical Staion of the Piauie) at then it is manifeR, that D.^^ is the apparent height of the Point A, on the Piaure; for, the Piaure being perpendicular to the Plane in whicli the point A is feated, the Eye being diRant from it equal EC, and the given Point equal to AB, on the other fide (equal D G) confcquently, EG is a Vifual R.ay, from the Eye, at E, to the Point; and G will appear at A, above the Bafe Line, equal D^, 1. e. Fa, which the parallel Line Ja evinces. I am aware that this may not be entirely fatisfadlory, to the ungeometrlcal Reader; for the Eye is^ certainly farther diftant from the point h than EG; wherefore, at S, the point of Station, draw SO perpendicular to SA, and, at F, where it cuts the Picture, draw FI alio perpendicular; make SO equal to the height of the Eye (equal CD) and draw OA, curing F 1 at L Now. if the Fiiangle SOA be turned upon SA, till S O is perpendicular to the Ground 1 lane^;^ then it is jl.iin, that O will be in the true place of the Eye, and the Line FI will be in the Piaure; confcquently, the Vilual Ray OA will cut it at I, making F I equal to equal Fa, as before. Or, if CE be made equal 7 to Sea. I. HISTORY OF PERSPECTIVE, to S F, aud D G to A F, the dotted Line E G gives the fame point A, as before, ■ and EG, or O A, is a Vifual Ray in its true proportion. The geometrical Reader will readily perceive (by the fimilar Triangles, formed bv this Conftruaion) thatBa mull neceffarily have that proportion to rrC, as Ba (equal BA) to EC, i. e. asAB to SD ; as BF to FD, i. e. as AF : FS, or A 1 : lO. Thus it was eafy to prove, without Geometry, that the Method of determi¬ ning the reprefentation of a Point on the Piaure, truely geometrical, is true; and 1 was by thofe means, fully fatisfied, and convinced of it. The Method ufed by Vignola and Sirigatti is the moft fimple and conviaive of any, to thole who are unacquainted with Geometry, as it muft be obvious to all who coni,der the Procefs vvith attention; for it is performed on the moft fimple Principles poffible, and the eafieft to be conceived. . r j I don’t find that there is any thing particular m the Jefuit s method of proceed¬ ing the whole being performed as has been already lliewn, in refpea of a Point; for refpeaino plane Figures, the feveral Angles are determined, as above, and ioined by right Lines, in general; by which means, he determined the Vaniftiing Points of Lines, inclined to the Piaure, that is, to the Safe Line (for they had no Idea, at that time, of other Vanilhing Points but in the Horizontal Line) which they called Accidental Points, and they were truely fo called ; for they had no way of determining them, but by finding the two extremes; then, drawing the Line, they produced it to the Horizon, and found its Vanilhing Point; but, how to cut off any portion of an indefinite inclined Line, they had no other me¬ thod, than the foregoing, which, in lome Cafes, is impraaicable; when the length of the Line exceeds the bounds of the Piaure. . . This Work abounds with variety of Examples, but the fame thing is given over and over, with very little variety in fituation, which makes it tedious and trifling. The Rudiments are plain and fimple, fuch as they are, but it is fimple, indeed, to a degree of puerility; for inftance; in order to determine the Horizontal Line, there are no lefs than three Diagrams; in the firft is the figure of a Man elevated, on Steps; in the fecond the Figure is (landing; and in the third,^t is fiting on the Ground, and, through the Eye, a Line is drawn for the Horizon*; as if it was not fufficient to be told, that the Horizon, or Horizontal Line, is parallel to the Bale Line, and diftant from it, equal to the height of the Eye from the Ground whether we be fuppofed fiting, {landing, or elevated. Then, being told to let oft the I oints of Diftance, on the Florizontal Line, the whole of the Principles conlifts in deter- mining the reprefentation of a Point; for, in that only Precept is contained the whole Praaice, according to the Jefuit, and on that Principle every thing is done. Squares it abounds with, and Pavements of Squares; by which means, tne places of Obieas are determined, as in other antecedent Works. Arches, Arcades, and Groins, often repeated, with Steps and Staircafes, make up no Imall part of the Work In refpea of Mouldings, he has done foraething more than others wlio went before him; but it muft be obferved, that almoft every Objea has Line Face parallel to the Piaure ; fome are inclined to it in an Angle of 45 Degrees; lo that, being right angled, both Faces are equally inclined, which, of all other, is the leaft piaurelque; the Vanilhing Points of Lines parallel to the Horizon, are, in this cafe, the Points of Diftance, which, with the Point of Sight, are the only Viuiifh- ing Points, in general, ufed. There are Line trifling attempts at oblique Politions, by means of Accidental Points, but to little pirpofe ; as the method ot proceeding by them, being founded on no geometrical Principle, is tedious, and liable to Ei ror; fo that, there is not one interefting or ftriklng Example given. In fpeaklng of the pofition of Lines, he lays, fometimes Objefts are fo fitu-ite,., that the Lines run neither into the Point of Sight nor Diftance; but, as it lyere by accident, into fome other Point in the Florizontal Line; and lometimeo tiiey are » This Idea, with the very fame Diagrams, is taken from an old Work, printed at Pans in Frrn.h, in the Year I 576, entitled, “ Lejons Ue Perfpeaive poriuv»,_ par Jacques Androvet du Ce c.-»u, “Architeae;” of which, the Jelnit’s is fo clofe a Copy, that 1 did not think ,t neceffary to conneer it fcparaiely, Lmongft the old Authors, being fo little known; yet, a VV ork of fome Merit, m uhole I m.e^ Sea. I. HISTORY OF PERSPECTIVE. zi fo iiiCDiivenieiitly fituateJ, that they do not run into any Point in tlie Horizon, but cither above or below it. What trifling puerility is this; as if Objeds mull ne- ceflarily be fo fituated or placed, that the Lines lhall run into, or tend to certain ^ Points in the Horizon ; inflead of finding means to reprefent them, as they happen to be fituated, from the determined Station. Herein lies the excellence of Brook Taylor’s Principles, which, by pure Geometry, determines the Vanilhing Points of ,Lines in Objedts, however fituated; whether they tend to the Point of Sit'ht, or rDiftance, or elfewhere in the Horizon, or, whether they tend above or bdow it • witli equal facility. It is -remarkable, that the Jefuir, and other old Authors, call 'thofe Lines on-the Piaure which reprefent Lines perpendicular to it, and confe- quently vanifla in the Center of the Piaure. Vifuals, or Vifual Rays, which they are not, but indefinite Reprefentations of certaiirLines; Vifual Rays are Right Line’s imagined to be drawn hom any Point or Angle in the Objea t’o the Eye, wdiicli can only generate a Point on the Piaure, not a Line. ■ In refpea of Shadows, this Work is, in fome cafes, extremely erroneous, for he makes no other diiTerence, between Shadows projeaed by the Sun or a Torch, or Candle; although he tells us that they are parallel when projeaed by the Sun,'yet his Method is the fame in both; for he determines the Seat of the’ Luminary on : the Ground, is if it was not a hundred Yards diftant from the Piaure ; not confi- dering that its Diftance is infinite, to fenfe, and conlequently, that its Seat is always ill the Horizontal Line, whether it be on tins fide or the other fide of the Piaure; nay, when he intends (by the Shadows) that the Sun is on this fide, yet It appears in the Piaure, and its-Seat is on the Ground Plane, as if it were between the Piauie and the Objeas whofe Shadows are projeaed ; and, when they are projeaed parallel BO the Ground Line, that is, whenthe Luminary is in the Plane of the Piaure, he flill determines its Seat on the Ground Plane, oppofite the Objea, and confequently the Shadows muft diverge, which fhould be parallel; aMb, for every Objea, the Seat of the Luminary muft be changed. ’ ■In the Year 1647 he publilhed a fecond Part, which, in five Seaions, treats of the projeaioii of various-kinds of Solids; fuch as Prifms, Pyramids, Stars, Cylinders, Cones, &c. in various Pofitions, but ufually ftudled for cafe; fbme are hanging by Cords, fufpended, others laid inclined over Blocks, in which there is invenuity, although the Pofition is calculated for cafe, as much as may be. Here are*alfo the regular Solids, and feveral other curious Objefts ; but there is more to be learned from Infpeaiqn than Defeription. A third part of this Work was publilhed in 1649, which IS chiefly on horizontal Pidures, and projeaing on vaulted Ciclings; in which there is nothing ftriking or interefting; the horizontal Piaures are nu¬ merous, but they are plain and trivial, and moftly calculated to be feen from above, looking down, as if painted on a Floor. The latter part, in three Seaions, is wholly on Anammphqles and optical Liftortions, m which there is much Ingenuity dil- played. Thefe two Parts are bound up together; they are in French" and have .not yet been done into Englilh, a-nd I am of opinion will not foon, if ever; for I do not conceive, notwithftanding the ellimation the firft is undefervedly held iu, that it would repay the expence, as it abounds more with the curious than ufeful To the firft Part there is a Theory added, by J. Hodgfon, F. R. S. comprized m nine Theorems; of which, three or four, only, are effential. He gives three or four Specimens of SirigattTs Method; and others, from Maralois, which Pozzo has adopted; hut there-is nothing in the whole Book, excepting the abfurdity of his Shadows, that can be called original, Andrea Pozzo, an Italian, of the Society of Jefuits, publilhed a Work in Latin and Italian, intwo Volumes, folio; thefirft in 1693, the other in 1700, which is confidered, by many, as the bell, or moll valuable Work, of the kind, extant; becaufe it abounds with elegant Defigns, in pieces of Architeclure, feveral fuperb Alters, and magnificent Buildings, -finely engraved, at Rome; particularly fome Pieces, which are beautiful and grand, and appear to be corredlly drawn. ^ lie two Volumes differ, not only in^ the Defigns, but alfo, in the Method of -F -Drawing, 22 Sea.l. HISTORY OF PERSPECTIVE. Plate II Drawing, or projeflhig them perfpeftively, like Vignola’s two Rules; the Lift, in ‘ this Work, being the firft in the other; lo that, the Method which Vignola wholly difapproves, Pozzo prefers. The nth Figure exhibits the Method which Pozzo made ufe of, in delineating thofe elegant Defigns of Temples and Alters, in his firft Volume; the whole of which, has been re-engraved in England, by, and much to the Reputation of, John Sturt, who publilhcd the Work, in Latin and Englilh, in 1707. This Work is in great Eftimation by many, and indeed defervedly fo, in refped of the number of fine Plates it contains; there are, in the whole, 105, many of which are really ftriking Objeas; but they are, almoft, in general, regularly fituated, centrally, direa before the Eye, and parallel to the Piaure ; fo that, one Side is generally a Dupli¬ cate of the other, which is by no means pifturefque; but ftill worfe, being oblique. Indeed it would fcarce be poffible, by the Method he makes ufe of, to draw fuch Objefts, obliquely fituated to the Pifture, nor has he attempted it; it would be too complicated and operofe for human patience, to go through with, as it would require orthographical Projedlions of both Front and End, in the oblique Pofition firft ; and thofe to be projea’ed again, perfpeaively, in piano, before the folid Reprefentation can be effected; which will be better underftood in an Example. Fig. II. At No. I. is half the Plan of a Pedeftal, having one Side, AB, parallel to the Piaure; the Ground Line of which is DC. No. 2. is the Profile or Elevation of the Pedeftal, feen from E; DF is a vertical Seftion of the Piaure, and EF the Diftance. A perfpeaive Plan being drawn, at No. 3. by means of the Diagonal Line CF; which having been fo often deferibed, I fhall omit the Procefs of it, here, as the’dottedLines, fromthe.Plan, atNo. i. fufficieutly fliew how it is effeded. Any Point, as G, in the Horizontal Line, being taken, and Lines, parallel to the Horizon, being drawn from every Member of the Profile to Db, draw DG; and, from the perfpeaive Plan, at No. 3. produce all the Lines which are parallel to CD till they cut DG, at D, 2, 3. and 4; from each of which, perpendicular Lines being drawn, and others from all the Interfeaions on FD {b, c, ti, &c.) to G, curing the Perpendi¬ culars, by their Interfeaions, the perfpeaive Profile, at No. 4. is delineated. Being thus prepared, the Objea, at No. 5. is readily deferibed, thus. From the Angles a, b, c, d, e, and f, in the perfpeaive Plan (No. 3.) draw Lines perpendi¬ cular to CD; and, from the Angles b, c, d, e, Stc. of the perfpeaive Profile (No. 4.) draw Lines parallel to the Horizon, curing the Perpendiculars from a and b, at bb, ee\ alfo, thofe at d and e are cut at c, d, &c. from the correfpouding Angles in the perfpeaive Profile; and by the fame means, it is obvious, that, all the Fillets in the parallel Mouldings may be determined; and then, from the Angles b, c, &c. Lines being drawn to E, curing the Perpendiculars at c and f, in f, g, &c. the Pedeftal is completed. In refpea of the Mouldings of the Bafe of the Column, on the Pedeftal, the perfpeaive Profile is of no further ufe, than to determine how high each Member rifes; for it does not affift in deferibing the Curves. The Profile, at No. 2. being drawn, the perfpeaive Profile is wholly ufelefs; for, by drawing lines to E, from every Angle of the Profile, A, B, C, &c. their Interfeaions with FD determine the height of each Member, in the parallel Mouldings, by Vignola’s firft Rule, or by Sirigatti, exaaiy the fame; as it is obvious on infpeaion. And it is alfo obvi¬ ous, that the perfpeaive Profile may be made without the other, by feting up the heights of all the Mouldings on DF; the Profile, at No. 2. being of no other ufe here, for that Procefs, but as a given Defign, in refpea of the proportion of the Pedeftal, with the height and projeaure of its Mouldings. After this laborious manner, are all thofe fine Defigns in Pozzo’s firft Volume delineated in Perfpeaive; having correa Plans and Elevations firft drawn, geome¬ trical; and then, by making a perfpeaive Elevation of the whole, in piano; which is not neceffary if the Vanifhing Point E be ufed, as it is obfervable in this Pedeftal; but only the hither Profile of the Mouldings; but, if that be not ufed, then, lines parallel to the Horizon being drawn from each Angle (as g and h of the farther Profile, No. 4.) cut the Perpendiculars at c and f as before, by drawing lines to E, which is mote accurate. I have Seel. I. ^3 HISTORY OF PERSPECTIVE. I liave examineJ this Work with Attention, and (fave the Defigns which are really fine, and well executed) find nothing in it, which can recommend it to thofe who wifti to underftand Peripeelive; being well convinced that it cannot be ac¬ quired from this Work, not even the delineative part, in the moft common man¬ ner of drawing. Indeed the Publilher apologizes, in the Preface, for its deficiency, in refpeift of the Inllruilion which might reafonably be expedled from it, nearly in thefe Words. “ That no Perlbn may be difeouraged in attempting to learn, from the brevity, or filence of the Author; writing in a Country where the Principles, or Elements, of the Art are more generally cultivated and known, there was no need to infill, fo much, ou fuch matters as are necefl'ary to beginers;” &c. True but the Book may fall into the Hands of fome, who want to learn the firll Prin¬ ciples, and Rudiments, neither of which can be had from it; for Theory there is none, and the brevity of the introdudlory part is fuch, that very little Inflrudlion can be gained. It is fo very conche, that the whole may be read over, and tho¬ roughly digefted, in a few hours; twelve or fourteen of the firll Plates, with half a Page to fome of them, much lefs to others, contain the greatell part of what tends to inllrud; many of the fine Defigns, not having fix Lines (meerly deferiptive) without a fiugle Reference; w'ith three, four, or five preparatory Plates, refering to one another, but none for the Operation. Here are five or fix Plates tending to the improvement of Scenery, which feem as if fome Inllru£llon might be gained from them ; but they fill Ihort, like the foregoing, of what is necefiary for the purpofe. There is not any attempt at tlie projeftion of Shadows, nor the leall Inllrudlions for giving Eftedls, by means of leflefted Light on Objedls; although the Author mull have underllocid every re- quifite thereto, as is obvious from the Plates. One would be led to expedl, from the calling of a Jefuit, fomething more fcientific, rather than the fine produaions of an Artill, in Inch well executed Defigns. In Ihort, there would be almoll as much propriety, in binding together a parcel of perfpeaive Prints, and calling it a Book of Perfpeaive. Notwithllanding the great Expence which mull have attended the execution of fuch a Work, and the time fpent in deviling and making the Defigns, in the Original, it is now fold fo low as one Guinea, not half its value; yet it is a matter of doubt, if the firll Impreffion, of the Englilh Edition, has been fold off; for it is reafonable to fuppofe, that, if the firll Volume had met with encouragement, proportioned to the undertaking, the fecond would, ere this, have made its appearance, in Englilli. Although W'e are told, in the Title Page, that the method of Praftice is entirely new, it had been ufed almoll a Century before, by S. Maroiois; as appears from a folio Work printed at the Hague, in Latin, engraved and publilhed by Henry Hondius, in 1615, if we may credit Mr. Kirby; but I find it later, viz. in 1633; a Performance which, like many other, abounds more with the curious than ule- ful, yet ’tis not void of merit. The Method ufed by Pozzo, in his fecond Volume, is that which was pradifed by all the old Authors, as in Vignola’s firll Rule, ufually called Sirigatti's; performed by the Line of Interfeaion, which is an Abridgment of, and greatly preferable to the other, which is obvious; for, Hues being drawn to E, from every Angle, A, B, C, &c. of the geometrical Profile, No. 2. cuting DF, the height and proportion of the parallel Mouldings, in the Pedellal, are determined’ the fame as by the perfpeaive Profile, No. 4. and, having the whole Pedellal drawn, geometrical, the returning Mouldings may alfo be determined, without ufing E as a Vanilhiiig Point, but better with it. Therefore, the perfpeaive Profile, at No. 4. in which the imagined Excellence of that Method confills, Is wholly fuperfluous; nor Ihould I have dwelt fo long on it, but that, the Ellimatiou the Work is in, fo very undefervedly, induced me to enquire thus ftriaiy into its Merits, and to lay them, juft as they are, candidly before the impartial Public, that they may form fuch a Judgment of the Work as it really merits. At the end of Prob. 27. Sea. 3. P. 132. it is referred to the Appendix for another Specimen of the Method uled by the old Authors for projeaing plane Figures, in¬ clined to the Horizon; or plane Solids, relling on inclined Planes, any how fituated to the Piaure, and compared with the Method on Brook Taylor’s Principles, Let 2 + Plate II. Fig. 12. No. 3. No. 4. ■Sea. I. H I S T O R Y O F P E R S P E C T I V E. ■'Lttj'lBCD be the B.ife of an irregular Solid, bounded by fi.y Planes, which are all Trapezia; no two Faces, or Sides, being parallel, in the whole Solid. The Angle CAl (No. 2.) is the Inclination that I'ace is Ibppoled to have to the Hori¬ zon. No. 2. is the orthographic Elevation; the upper Face, EFGH, being in¬ clined to the Bafe is fomewhat feen. AE is a vertical Seftion of the PiRure, which cuts the Objedt, fo, that the folid Angle AFE projects through the Picture, E is the Center and EO its Diftance ; AI is its Interfection with the Ground Plane, and AE the height of the Eve; the Plan of the upper Face is thus determined, the Side DE being in a vertical Plane which is perpendicular to the Pidture. From all the Angles, E, F, G, and H, draw Lines perpendicular to AC, No. 2. as Ee, Ff, &c. make Ac, on the Sedlion AE, equal to Ae, where a Perpendicular from E cuts AC, and in like manner transfer Af, Ag, and Ah, to Af, Ag, and Ah. Draw eE parallel to A\, curing a Perpendicular from Z) at £ ; and, from e, f, and h, draw Lines alfo parallel to AI ; then, make EF and EH equal, re- fpedlively, to the known meafure of thole Sides, alfo FG and G H*, and join AE\ BG, and CH. The Angles B, C, and D, being tranfpofed to AC, by a reverie operation, let Perpendiculars be drawn from each, and Lorn all the Angles in the upper Face to AI, as FF, GG, Bb, &c. by means of which, and No. i. the Plan, or Seat of the Solid is formed on the Ground Plane, at No. 3. thus. At any diftance, at difcretion, draw eL parallel to AI, in which, trike a, in n perpendicular from A; and, from every Angle in No. 1. draw Lines perpendicu¬ lar to eL, curing it at a, e, K, and L. Now. becaule the Angles A anJ.E, in the Elevation, No. 2. are in the Interleftion AE, and eL being conhdered as the In- tcrfeffion of the Pufture with the Ground Plant, a, and e, are the Sears of A and E. Make af equal to AF, No. 2. Lg equal to AG, and Kh to -'if; and, joining the Points ef, fg, dec. the Seat of the upper Face is obtained. In like manner, make ed equal to Ad, K c to A I, and Lb to A b, which give the Seat of the Bafe, abed; then, joining the Angles a and f, b and g, c and h, the Scat is completed. The Seat on the Ground Plane being obrained (No. 3.) the perfpeibive Seat muft be next drawn. Let eL, produced, be conlidercd as the Bale Line, and, at the height of the Eye, draw DC for the Horizon; in which, take C for the Center, and CD (equal OE) for the Diftance of the Pidlure. I 3 raw CA perpendicular, futing the.Bafe Line, and take a Point A for the reprefentation of A, as far from that Perpendicular, as a (No. 3.) is from the Perpendicular A a. Make AE equal to ae ; and draw EC; and, Ea being made equal to de, aD is drawn, curing EC in D. After the fame manner, all the other Angles muft be feparately determined; for.af, bg, and ch, being inclined to the Bafe Line, do not vanilh in the Center. The Angle F, being on this Side tlie Pift-ure is projeifted, by drawing CF, through A; and making A a equal to af (No. 3.) Da, produced, gives F. Then, joining AB, ad , ef , fg , &c. the perfpeftive Plan is completed, as below at No. 4. Laftly, the Solid will be obtained, by drawing Perpendiculars from every Angle of the perfpeRive Plan, and making each equal, perl'peftively, to the height of tire Angle from its Seat, thus. For the angle_/; at a (where FD cuts the Bafe Line) draw af perpendicular, and equal to FE, No. 2. then, draw Df, till it cuts the Perpendicular from F t\tf. Ee is m.ide equal to AE, No. 2. becaufe it is in the Piflure; and the angle d, by feting up the height of that Angle (Dd, No. 2.) from E, to d, and drawing dC. The other Angles are determined in the lame manner, by drawing Lines through their Seats, from any Point, D, E, or C, in the Horizontal Line, curing the Bafe Line, where draw a Perpendicular; as Gh, equal to the height that Angle is irom its geometrical Seat, in No. 2. and, from h, draw a Line to the fame Point; from b, a Line is drawn to C, which cuts the Perpeudicukir Bb at b. The Angles being all obtained, and joined by right Lines, Bb, Af, Ad, de. Sic. as in the Figure, the Perlpeftive of the Solid is completed (No. 4.); and after this laborious manner, Objects, fo fituated, muft be drawn in Pertpeftive, according to the methods of Pradtice made ule of in the Jeluit, and other old Authors, on thofe limited Principles. * As the upper Face, EFGH is not parallel to the Bafe, the Lines G H, 8:c. are not the full mea- fufi s of thofe Sides, bur are lels, the more it is inclined; fur, the Side will be the Hypothenufe of a right ^nglcd Triangle, of which thofe Lines are the Bafes; the difference, here, is inconfiderable. 5 As Sea. I. A P P A R A T U S F 0 S. D R A W I N G, 2 As a P.irallel to this Figure, or rather to the manner of projeftirtg it, I refer the Reader, who is dtfirous to know how it may be projeacd on the new Principles, to Ex. 1. Sea. 12. Fig. I 51. where, a Parallelopipcd, whofe three dimenfions are dif¬ ferent from each other, is projeded ; which would have been Ibmevvhat lefs trouble to projea than the laft Figure, and that, would be more troublelome on the new Principles; as every Face would require a feparate Vanilhing Line, and evervLine a leparate Vanilhing Point, feeing that, no two Faces, or Sides are parallel; never- thelefs, the fiicility and accuracy of one, in comparifon of the other, is obvious, and performed from the known dimenhons of the Figure, and its lltuatioii to thePidure, without any previous operation, or geometrical projedion, whatever. Having flaewn, by various Methods, how Objeds mav be projeded, perfpedivelvi by Rule, 1 lliall now Ihew and explain the ufe and appjicaiion of an Apparatus, by which, the molt complicated or irregular Objeds. Landicape Views, &c; may be accurately drawn, without underftanding Perfpedive; the beft calculated for the purpofe of any I have feen or heard of; at the fame time, fimple, and eafy to be applied. I fpeak from Experience, having frequently made ulc of it, in drawing corapllc.ated Machines, and other Objeds, in which there were fcarce anv Right Lines, or none that were principal. The Apparatus confifts, chiefly, in a redaiigu- lar Frame, the length, in proportion to the width, about 3 to 2, is a good ftiape (See fig. 13. No. i.). This prime is reticulated by filken Threads, or it is better with fine iron Wire, in Squares, not exceeding half an Inch ; if fmaller, the Draw¬ ing may be more accurate. They are ufually done with Threads all of one fize, or thicknefs; but I advife larger, or thicker, at every fifth Square, begining from the middle, longitudinally; and, having made one (AB) for the Horizon, in common Cafes, let oil the other from that, breadthways. By means of this Apparatus, I firll began to draw from an Objed; and the firft I attempted was the Portico of St. Martin’s Church, of which I made a tolerable Drawing, at that time. The Situation was not the moll eligible, being at one End,' almoft in a Line with the Wall, from a Window in the fecond Story; fo that, the Floor role on the Pidure more than the Cieling appeared to defeend ; befides, it was too near the Building; the Columns in the Front receded inwardly, and confe- quently, the Pediment was not leen. Such as it appeared, I drew it; and, as I liudied the Shades from the Objed before me, it furnilhed me with general Ideas for lhading Mouldings, and other architedural Ornaments ; for which, I was fel- dom at a lofs, thereafter. This was not that Drawing of the Portico mentioned before, which was done by Rule (from the Jefuit) for, at that time (though not long before) I knew not that there were Rules for the purpofe; or at leall, I knew no more than, that certain Lines in the Objed tended to what is ufually called the Point of Sight; and in that, many imagine they know enough of Perfpedive; which is knowing nothing to the purpofe. It is a matter of lurprlze, to me, that ’though almoft every Artift knows how, by Reticulation, to reduce or enlarge Drawings from Prints or Pidures, yet are at a lofs to apply it in drawing from an Objed ; in which, there is only this difference, that in the latter, a Sight-hole, to keep the Eye to one Point, is neceffary; the application; for Landfeape Views, is as follows. Being provided with a Frame, reticulated as above (No. i.) in order to fix it, for ufe, a ttrong Staff (marked X) not much Id's than two inches thick, is necelTary ; for if it be too fmall, it will not be fteady enough, but fubjed to trembling, when ftuck in the Ground; for which purpofe, it rauft be pointed at the Bottom; and, at the other End, a crofs piece is fixed (G) about nine inches long, more or lefs, according to the fize of the Frame, for which, a Groove is made, in the upper edge, to fix it upright; it would be better if a Spirit level be fixed in it, to let it hori¬ zontal, which the Threads (hould be, cxadly. At G is a hole about an inch and a half wide, and f inch deep, for the Slider, D G, to be fixed in, fo that it may be fteady, yet free to Aide in or out, at diferetion, according as the Sight-hole, E, is required to be nearer to or farther from the Frame; which Sight-hole is raifed or lowered, as occafion requires, for a higher or lower Horizon, and is fixed by the G turn rTFcrpp APPARATUS FOR DRAWING. turn of a Screw, at D. The Staff may be about 4!- or 5 feet long, fo that, when fixed in the Ground, the Horizon, in the Frame, may be on a level with the Eye, which is at dilcictlon, either llanding, or fiting on a high Stool. 'i'he wliole of the Apparatus being lixed, for ule, at Fig. 13. the Sight-hole being on a level w ith the Thread AB (tlie Horizon) and diftant trom C, in the Center, about the length of the opening ot the Frame, the Landlcape, before it, will appear, on the '! breads, Irorn the Sight-hole, as a Drawing reticulated, or Iquared; which may be copied, on Paper, the lame as a Print or Drawing; but great care muft be taken, that the Sight-hole be not moved, after you have begun the Drawing, as the places of the Objeels, on tlie Threads, will be varied thereby. Let your Paper be jquared in the fime manner as the Frame, but in any proportion you pleafe; as here, at No. 2. by a larger Scale. Now', luppofe the Frame, at No. i. with the Land- icape on it, as it appears from the Sight-hole, and, at No. 2. is the Copy of it, on Paucr; in which, there is no more difficulty than In copying a Print, as the Lines in the Olijefts appear to be cut by the Threads, in the lame manner, as if the Squares were Lines ruled on a Print or Drawing. To deicribe the operation of Drawing tile Copy, at No. z. would be trifling, as it is evidently the fame as copying.a Pidlure, or Drawing of any kind. This method of Drawing fcenis to have originated from common obfervation, of feeing Objcdls through .1 Window; which, in thofe early times, W'hen this Inftrunient w,is contrived and firll ufed (for it is not of late invention) were not in Squares of two feet in height, but in Imall Divifions with Lead, which were almoll adapted to the purpole; inlbmuch that, there I'eems nothing left to con¬ trive, except a Sight-hole to fix the Eye ; as it was perceivable, that the Objefls varied in their apparent proportions to the Squares, on approaching to, or receding from the Window, (being iefs in the former cafe, and encreafing as we recede) fo that, it was not poffible to reduce it to praflice without that necelfary Expedient. The contrivance of a Frame was in order to make it portable ; and the dividing it into Squares, by means of Threads, or Wires, can fcarce be attributed to it as an invention, but an improvement; for, making them lefs feems an unavoidable con- Ibquence, which. Experience would loon render necefl'ary. . No. 3. is a Stand, with Notches in the two upright pieces, at F, F, to fix the reticulated Frame in, when it is to be uled on a Table, in order to draw any Model, or Machine; the Slider is fixed at G, and then it is ready for ufe as before; the Ob- je£l being placed before the Frame, which m.iy be fixed lengthw.ays or upright, as the figure of the Objefl: lhall require. Tliere is another Method of-taking Reprefentatlons of Objefls, from Nature ; which is, .by having a Plate of Glafs, well ground and poliffied, fixed in the Frame, iullead of Threads; which, being lightly Imeared over'with Gum diluted with water, andiwhen dry, may be drawn on-with a loft Pencil, or French chalk ; by that means, the Objedls may be traced on it (the Eye being fixed at the Sight-hole) and afterwards taken off, by tixicing the lame on Paper, oppofed to a ftrong Light, d < Fig. 14. is another .Apparatus for the fame purpofe, confifting of a horizontal and an upright Scale; by which, greater accuracy may be ufed,in taking the proportions of the Objects; but, it requires a better hand at Drawing, and is not fo well calcu- kted for Landlcape as’the reticulated Frame; it is thus ufed. The horizontal Scale ( W) fixed-in the Groove a b, (Fig. !§.) level, may be confidered as the Bale Line of tire Drawing, divided as a Scale, at dilcretion; having a Groove in the upper edge to receive the upright Scale, which is tongued, at the bottom, to fit the Groove fo, as to hide freely, to and again, yet Itand firm in any part of it. '’Tis not fo ealy to deferibe the manner of proceeding as by the Frame; but, fuppofuig the FTame, which ap¬ pears to be beliiud the Sc.aJe, was brought down, till the edge DE coincides with the tipper edge of tl-re Scale, and tben, imagine the Frame with the Squares taken away, leaving the Landlcape, only, as if it were the real Profpeft, as it appears through tlre-Sight-hole, which is alio jieceffary here. The upright Scale being moved, at dilcretion, till it appears, from the Sight-hole, in the direftioii of fome Objefl, or ... - - > ,.i - part Seel. II. OF MILITARY PERSPECTIVE. part of the Objea; then, noticing the Divifion in tlie horizontal Scale, at which It ftands, and mark the lame place on the Pape.- (which i.r divided in the fame manner, at the bottom Edge, and one of the Sides) wlrcre, draw a Line acrofs the Pape^ if neceflary; and having marked where anv part, or various parts of the Objeft, cuts the upright Scale, a parallel Line mult be drawn from the lame Divi- lon on the edge of the Paper, till it cuts the perpendicular Line; and thus as many i oints may be got as are iiecelTary to defciibe the apparent figure of the Obje-a. There is a fimple, portable Inllrumcnt, of a late Invention, for taklno- the per- fpeaive proportions of Objeds, by the very ingenious T. Sandby, Efq, IT A. c.alled Peilpeaive Compalles; which are well calculated tor the purpofe*. With thele Corapafles, the Angle, under which any Objefl, or the various parts of it are feen is taken, by means of a Sight-hole in the Center, or Joint, the Legs being feen through at, pointing to the parts of the Objeft; alfo, the Bearings of different Obiefts ma one another may be taken, with tolerable accuracy. This Inff.unieiit is intended only as an Expedient for taking a Sketch, with more truth than by Sight meerlv on this Principle Suppole the Joint of the Compallbs to be the Eve of a Spea[- tor, on which the Le^gs revolve, as the Radi, of a Sphere; the E^e being Jn its Center, which is fixed, whilft the Points move in its Surface, direds thei^ to the Objeas; and confequcntly, the mealures taken, are all in the Surface of a Sphere which IS proper; but then, it is not poflible to reduce it to a plane Surface, and’ therefore the Mealures fo taken cannot be applied. Or, granting they could it is evident, t wt there would not be any parallelifm in the whole Pidurc; for, whether perpendicular right Lines, they will necsirarily be projeaed into curved Lines tending to meet each other, and therefore, could not be applied to a regular Building. To remedy this, the Points are fq fixed, in the Legs, as to ilide out, at pkafure^ by which means. Drawings may be made of various proportions ; alfo, bv ap- pl.eat.on of a Right Angle (uUial y called a Square) the Tangent of the Angle may be taken, but that is attended with much lofs of time. To obviate which, 1 advifo a ^mmon Sedor to be ufed; then, the. mealure of the Angle being known almode of reprelentation. The Fig. zi. I t A a ° A '1! ’ w ^ ^ of View for ' I’irr^h Vertical Line, equal El in the Horizontal; it is deicribcd by means of the Square A B C D, on the Side AB, given. In this Fi¬ gure It IS obvious, that the Curves of the Hoops are flater, cominuallv, frmn The hither end of the Barrel to the other, zt a c i; the Ellipfis, of which, a 5 k the llthlPir^ "“"'"Pi’ 1 w Conjugate (c d) much lefs than the hither end, although, being in parallel Planes, they have the fame Vanilhing Line, E V ■ and coiilequeni >, diat Curve is defenbed by a much greater Diftance. ,2 1 ^ is the true Curve ot that End, being feen from the fame Point of View, E. The 25th Figure exhibits a Bell, as I have frequently feen it reprefented; in which ftre fame impropriety in the Curves is remarkable. The Vaniftiiiw Line of the The pPr!’ ^ Perfpeaive, m order to afeertain the Curve. The Beits, or Borders above, it may be obferved are flater, the farther they are removed from the Vaniftiing Line; and the Top appears as if the Eye was elevated MPerAlo’ 'pc appears as if the Bell (being made of foft Materials) was cruftied over towards the Eye; for the meafure, from the middle le Curve, at the Crown, to the hither edge of the Bottom, is much lefs than on the Hither fide ; which would ftill be lefs if reprefented true, owing to the figure of a Bell, Ipreading fo much at the Bottom. The dotted Curves (hew theiue curv.ture of the Belts, delcrlbed on the Diameters IK and T L. T US manner of repreienting round Objeds is almoft general, by which, the Genius ot the Artift ,s diicernable. I cannot conceive wLt the; cL alledge i^ exen e for it, being againft all Rules, and Reafon alfo, in Objeds whichire fo PPip!, " p ’ extraordinary, there are thofe who can delineate UiUan Figure, or other Animal, m various Attitudes, with facility, yet will never- Fig. Seel:. lil. . -OR THE APPEARANCES OF ROUND OBJECTS. Plate IV.be .greatly deficient, in Rich regular ObjeOs. Now, tbofe who repre- - feiit fuch Objefti after this manner, yet would ridicule, or treat with contempt, the -performance of another Perfon, who, beinglavifh.of his Genius, had exhibited both •'Ends of a Barrel, are equally,deferving of ridicule ;-for, although they have not . • fnewn both Ends, yet, I maintain that it is full as abfurd, which I fliall prove. Fig. 26. ■ The 26th Figure exhibits a Cylinder; the Vanifhing Line of the End, AB, is the "Vertical Line of the-Bell, and the Table belorv it, which divides them centrally. CD, EF, .&c. ore intended to repretent feveral Seflions of the Cylinder, at equal diftances, and parallel to the End, or Bafe; conlequently they all reprefent parallel Circles, and have the iarne Vanifhiiig Line. . Now, if-the. Curves ;gcaw flater as theyretede from the Vahidilng Line, the Sedlion CD, flater than the End, EF than CD, and the next fbill flater-than E-F; confequently, the Sedllon atiJL will •be a right Line; and what w'ill be the confequence beyond that.' why, ,it is evi- •dent, the Cnrves.muft take ,a contrary diredlion,.and then, it is manifeft, the other '■End will be feen, as at MN, ■ or PQ- But, according ta this Delineation, JLis the Vanifhing Line of all thofe Circles, from which, as they j'ecede, the Curves ■ are more convex; and,‘i-n{lead,of a convex Cylinder, it'exhibits a concave Surface; if the Light, be fpppofed oii the other fide it will appear fo; in. which cafe, both -Ends may be feen, internally; the Ellipfes being all upright, i. e. their tranfverfe A.xes are perpendituiar to the Axis of the Cylinder, indicates the Point of View, or Center of the'PIdlurc, to be at O. . Or, fuppofuig it to.he a convex Surface, the ■Objedt does not reprefent a ftreighf Cylinder, hut.one that is bowed, turning both •Ends'towards the Eye, being oppofite to the Point O. Now, what excufe caii be made by .thofe, Vvho, palling under, the denomination ■of Artifts, have fo little judgment, as to be capable oLluch iipproprieties as are unpardonable in a Boy, who has anypretenflons to the Art of Drawing? It cannot •avail them to fay they never made Perfp'edive their ftndy; for, although it is the Dafis of the art of Delineation, yet, ’tis not always neceflary to apply it-to every Objedb that is delineated; far furely, if they place any hollow i'eflel, or round Object before them, h is foon perceived, which-way the Curves are turned, and whether the upper or the lower parts are moft curved. I have feen Velfels of va¬ rious kinds, fuch ns Punch Bowls, Cup.s, Tankards, &c. reprefented, by thofe who ■arrogate t6 them'felves no fmall fliare of merit, and would highly refent a Truth being advanced, in Company, refpeflliig their Pertormances, in.the delineative part. •whole Tops wei'e below the Eye, yet the Bottoms reprefented by right. Lines or nearly approacliiiig thereto; with various other enormities equally as abfurd; fome ■of which are exhibited in the 27th Figure, where almoft every Obj.e£t is falfly drawn, ■cither in refpeft-of itfelf or of the reft. 1 In the the Table on which they-are, as' it repreftiits a Circle, is drawn ■with a higher Horizon than the things which are upon it; fo that, a greater breadth being feen than is proper, gives it the appearance, of being confiderably inclined, and the things ready to Aide off. The'PJates, refpedling themfelves, are true ; but, the Either Knife and Fork are proportioned to'the apparent breadth .of the Table, io-that they are prepofterous in refpeft of tiie Plate. The Tankard, on account of the Lid being rounder than the Bottom, appears crufhed on the hither, flde.;. the curves in the Lid are lame and imperfeH, as is the bott(-,ni of the farther Caiidle- IHck ; the Punch-Bowl, the.Bafon, Decanter, &c. are all more curved at their tops than the bottoms, which render fome of them very difigreeable to a judicious Eye. The Shadows-arc the only SubjeG that is done with truth; which, beiiig projedled bycwo Candles, is.fomewhat difficult; infome parts,'the Shadow.call, by one Candle, OF THE APPEARANCES OF ROUND OBJECTS. Sea. iir. 37 Tlie Claw-Table (Fig, 28.) with the Things on it, are all defcribed from one Fie 28 Station and Point ot View; m the former, almoft every Objed has a different one ‘ and lome of them nwe than one Point, the upper Curves being more convex than the Bottoms. The Elliphs which reprelents the Top is defcribed on the given Dia p ’f '1'" °f the Pidure is at O (in the Bell) and V is tL Vanilh- g o.ntof the Diagonal of the circumlcribmg Square, confequently, O V is the Dilfance ; by means of the point V, all the Curves are defcribed. Firft for the P ate; being fuppoled to be as near the Eye as the edge of the Table, and as the tTi f the Table, take a b, above the Interfedion of the Table (A B) equal to it, and on a b dcfcribe the e.xterior curve, of the Rim ■ then as the interior Curve is not in the fame Plane, but lower, take another Iiiterfed ion (cd) as much lower ; and, c d being its known Diameter, at its proper dif- tance, delcribe the inner Elliplis, which will be nearer to the outer one ^at the hither part, on account of the Rim flielving inward. Thefe two Ellipfes are all the deline.at.ve part; for, u.ilels dieEye was lower, or at a greater diftance, the bo.tom cannot be Ice.i or it is loft in the Shade. The Knife and Fork, are delermi.ied, in refped of length and breadth from their place on the Table ; the reft miift depend on the Hand, and Eye. At X is a Sea.oii of the Cup, from which the Curves m.ay all be deicnbed, in its determined place; as the dotted Lines llievv f.ifficientiv from the given Diameters a b, &c. The Ears, or Handles, may, by a troublefoine I rocefs, be detenbed; but more will depend on a judicious Eye and corred Hand. At Z IS a ^a.on of the Bowls, from which the meafures are taken, and the Curves dcfciibed. The contour of the external Curve is defcribed as the Torus of a Co¬ lumn; by deferring the Reprefentations of as many Circles as are neceff.ry - as o the Diameters at DE and EG. Take DE, above the Interfeaioi. of the Va- ble, equal to the height of the Bowl, and equal to its Diameter, from which draw Lines to O, and find the Diameter d e, in its proper place; its diftance from the edge of the Table IS equal to .E .7, and therefore, the diagonal Line of the Table 1 hkewife the Diagonal of the Bowl, by which the Curves are defcribed. For the Diame^r EG, take another Interlea.on, equal to its height, at EG, and de- oTtlL Rotto'r"at'r''''’r"’ ‘'Hb, defcrlbe the curve of the Bottom, at .6;, and over the extremes of the other, falling into that or la.her below it, at the extremes, the outline Contour .is defcribed^ The Curve ot the Liquor is the ower Diameter D E, allowing for the thicknefs of the Sides The other Bowl is ot the fanie height, but is larger in Diameter, as much as i/j ^cccds A C, its place on the Table being afcertained, it is defcribed as the former The hither Glafs has its upper Rim in the fame Plane with the Bouls; its place being determined, by obtaining the feat of its Axis, on the Table at s. the heipTic IS got die fame as the Cup ; the Curves of the top and bottom being defcribed, and the height of the Bowl, or Shank, obtained, the reft 13 eafily doiie by hand the figure being known. ^ cue. Claw-Feet of the Table rauft depend more on the Eye than Rule; but as detenrii.ie their places, and the juft proportions ot fome parts; and alfo refpeaing their heights, '"T ‘ being known, and K L being obtafned or the Diameter of a c.rcumfcnb.ng Circle, in its proper place, let the reprefen- tation of a Circle of that Diameter be defcribed, of which, O is the reprelentation of Its Center, and the Imall Circle is the Seat of the Pillar on the Flo^or, If the p ace of any one of the Feet be determined, as at M, in the Circumference, the other may be determined by the V anilhing Points of the Lines O M, O N, and , y ro . 4. e . j. B. 3.; and if perpendicular Lines are drawn from the two fnvrmTtfe Fl[™'‘ ^ Circle, at the Center, the height of the Claws, and the Mould- f I’le b ’ ""T defcribed as 0.1 a Cylinder, giving fome what more pro- jeauie to the curve at the Cup; but, iii fliort, uiilefs a Perfon has judgment in draw- ‘the Claws can never be effefted by Rule , neverthelefs, Rules may be greatly affiftant thereto ^ K Ill ^8 Plat Fig- Sea. 111. OF THE APPEARANCES OF ROUND OBJECTS. DV In drawhis an Objed of this kind, by fight, the judgment is blafed cor.fidera- 'r 'bly ■ for, on account of the height of the Eye, looking down on ihe Claws, it is remarkable how much the hither one is lengthened, and the farther one, at P full more contraded; which difproportion is not perceived m the Objed, m any 1 pint of View; wherefore, in aiming to reprefent it. as it appears, we are apt to run into areat error, in the Reprefentation; not confidering that it is referred to an upright Plane which occafions the apparent Diftortion in the parts, refpeding each other, vet, being reprefented as it appears, the whole Pidure would be more tinnatmal, tor the Center ot the Pi 61 :ure would be thrown down to the fmall part or the i u- kr below tlie Cup; in which part, the Horizon would be very improper, and by no’meaus judicioully determined on ; and yet, it would be the true polition of the Piiflure. la this and in various other Cafes then, it is manifeft, that the Obje^ is not reprefented as it appears, nor can it be fo repreiented on a plane Pidure ; but, all that is or can be done, by the Rules of Perfpedive, or by any other means, is, to give fuch a Reprefentation of the Objed, that, the Eye being m the true I oint of View, (hall be affeded in the lame manner as by the Objed, and confequeiitly It Will produce the fame Appearance. ^ ^ As a Scale of proportion for the Table and the Objeds on it, the Diameter of the Bowl CDE') is a Foot, the Diameter of the Table is fomewhat lefs than three feet, and the projedure of the Claws from the Center (O) about 13 inches; the heighc of the Eye is fomewhat more than four feet, Diftance about three feet four inches. -T-| Barrel CFig 20.) which is on the Plane of the Table, continued, is truly drawn by rule, by means of the fame Vanilhing Line, but not from the fame Point of View; although the Vertical Line, for the Table, is the Vanilhing Line ophe Eads of the Barrel, and the Center of that Pidure is the Vanilh ng^l o.nt of all horizontal Lines which are parallel to the Plane of the Ends; the v,enter of the Pidure for thisBarrel is nearS in the other. The circumfcribing Squares abed and aied of the two Ends, fhew how thole Curves are defenbed; tor which, the Line of In’terfedion is a m, which is above the Plane the Barrel refis on, on account of the great fwell in the middle, where the Barrel has a 1 ^-ger Diameter, and which may be thus obtained. Make ae equal to half the difference, between tire Dia- mernr of the Ends, and of the middle part, and draw Oe; produce the Diapiial c a, curing O e, produced, in f; draw f b perpendicular, 1. e. paralkl to a b, p™* duce db cuting it; then, draw Lines from f and b to the Vanilhing 1 oint of the Axis fAB) and make fg equal, perfpeaively, to the known diltance which it ex- preflbs, ot the Hoops; wheredraw a Perpendicular, which being cut by a Line fiom b to the Vanilhing Point, at h, gives gh, m 'ts F°per place, tor the Diamemr of the Hoops in the middle; on which, a Square (ghik) being defenbed, perfpeaively, the Carve efsL may be drawn. This Curve, with the contiguous one of the fame Diameter, being obtained, will determine the fwell of the Barrel; and the Curves of the other ploops may be defenbed from them, as m the k iguie , to fay more is unnecefliiry. Fig. 30. exhibits a Vafe as it is feen Ifanding on the Floor, below the Eye at 3 • the natural height, Ifanding, about five feet; No. i. is a geometrical Profile. AB L the Interfeafon of the Plane of the Plinth, and ab its width; the \Atnilh.ng Line of the Horizon is 1 V, the fiune as for the Table and Barrels; the &nter ot the Piaure, for the Vafe is at S, near the Center of the extreme end of the Barrel. The dilfance of the Plinth from the Piaute is Aa; the reprefentation of the Circle, whofe Diameter found thereon (ai) is by means of the Diagonals, fiom A and B ; the Curves of the Moulding above it muft be defenbed by m^ns of othei Intei- feaions, as in the Plate, on the Table. To defenbe the larg^e Circle of the Cover, taL the Interfealon CD, above AB, equal to 1,3, m T the Plinth ; and, from the Vertical Line (the Axis of the VafeJ fet ofFcC, and eD, each equal to half the Diameter, as at 3, 4, by which, the Curve ced is delcribed. Alfo, by means of the Interfeaion EF, the Curve of the Moulding at 2, 5, is drawn 39 Setl. HI. OF THE APPEARANCES OF ROUND OBJECTS. and by the fame means gh, below it, but the Interfcaiion is omitted, to avoid con- fufion ; and thus, by means of different Interfeaions, the Curves of the Mouldings around the Vafe^ alio of the Top, or Cover, may be defcribed, each in its proper Plane, tdklng the height and Diameter of each from the Profile; nor is the pro- cefs fo very laborious, as may be imagined ; at leaft a few Curves of the principal parts of the Vafe, five tor the Cover, two on the body of the Vafe, one at the Shank, and two at the bottom, in all ten, by which it may be accurately defcribed ; the reft, which are contiguous, may be drawn corredl enough by hand, dircfted with judgement, but without that, ’tis in vain to attempt it. The places and the height of the Handles may be nearly afcertained; but their figure, and the ornamental part of the Vafe, muft be drawn by hand, as it is not poffible to lay down Rules by which they may be effedled. This Figure has, I prefume, the true appearance of a Vafe, below the Eye, on the Floor; feen at the Diftance S V, oppofite the Center S ; in which it is ob- lervable, that the Curves are flateft at the Top, and grow more convex, the far¬ ther they are removed from their Vanifhing Line; the curve of the Bottom, on the Plinth, is the roundeft, and yet it feems to ftand firm enough on it. If I had had room on the Plate, I would have given the figure of one, b}' the very ingenious Mr. Waldron, Drawing Mafler for Orna.ment, &c. in the .Academy of Dublin, which may be feen, during the Summer, on a Chimney Board, in Mr. Wilfon’s Shop, Bookfeller, on the Pavement, Dame Street; in which, the Curve at the Top, in the greateft Swell, is not above a third part fo much bowed as it fhould he; and below it, the Curve of the ornamental part, in the middle is nearly a rivht Line, and at the bottom entirely fo, although the top of the Plinth is feen; and the receding Lines in it, which fhould tend to the Center of the Pidlure, tend to the Moulding on the Shank, the firft from the Bottom, and confequently it is the height of the Eye ; and therefore, the Curves at the top would be bowed the con¬ trary way, nor could the whole Circle be feen, but only the hither part. It is, tame, aftonifhing, how a Perfon who has any pretenfions to the appella¬ tion of an Artift, can luffer fuch a Performance to be exhibited to public View, and pretend to teach others; I do not mean to teach Perfpeclive, but Drawing; for furely, he is unfit to handle, or to ufe a Pencil, who has neither Eyes nor Judgment to direft him better ; which every one who pretends to dr.aw, from an Objear, ought to have. If an Objedl be placed before us, in the pofition we would with to reprefent it, we can, furely, fee whether the right Lines in it feem to tend upward or downward, whether they appear converging or diverging, and towards what part of the Pidlure they do tend and converge. Or, if the Objefl: be round, it is eafy to fee and determine, whether the Curves bow upward or downward, to the right hand or to the left, or whether they grow more or lefs curved ; if not, why would a Perfon attempt to draw, at all, feeing he has not the firft neceflary qualifications of an Artift, a judicious Eye, to difeern, critically, ths tendency or direftion of the Lines, and a correft Hand to delineate what he fees. To be per- fe£l is not human ; but, if Rules can be deduced from a Theory which is fo, is it not incumbent on every Artift to make himfelf acquainted with them (if he has a Capacity to learn) before he attempts drawing from Nature, or from an Objedf? iiiiy, without learning the Rules, to conceive, clearly, the nature and the meaning of Perfpeftive, in rationale, will infenfibly correft the Judgment, and renderthe Eye more competent, to judge of what it fees, in order to give a proper Reprefentation. "37 SECTION 1f 40 S.d; IV. OF SCENOGRAPHY, SECTION IV. Of SCENOGRAPHY; Or the Application of PERSPECTIVE to SCENERY. I N the application of the Rules of Perfpeftive to emhelliOi the Theatre there IS, indeed, a much larger Field than can, with propriety, be comprehended in an Appendix, even iuppole it contained nothing elfe ; for, to treat it fully would make a Volume, of itfelt. I fhall, however, give an Abftraa of what 1 have in Idea, which thole who underftand the Rules of Perfpeaive, thoroiio-hly may ea lily apply toufe; and lome may probably find their account in it” who perhaps will grudge the trifling expence of the Work, to obtain it. ^ Much has been faid, by Mr. Hamilton, relpeaing the declivity of the Stage the Point of Contraaion, &c. to very little purpofe; leeing that, it would be very im- improper to raile the Stage above a certain Pitch ; as it would, by inclining it too much, be attended with great inconvenience to the Aaors; who, undoubtedly would prefer a level Floor, to one inclined at all, being more certain of their Hep's’ Wheretore, as there is a kind of necellity that it fhould rile, as it recedes and as It muft ablolutely be fi.xed, I lhall leave that Point to the Adors, who are accuV- tomed to tread the Stage, they are the meft competent Judges; not, as it conduces to alliil the Peifpeftive; but how much declivity is convenient to adf on, the Per- Ipeflive mull; be adapted accordingly. I am of opinion, to rife one foot, in ten feet length, would be fenfibly perceived by the Adors; neverthelefs, it may be necefliiry in reprefentiiig a great length, to rile more, unlefs the Stage be of fufficient extent • otherwife, the height of the Eye miift be varied. For, according to the length which can be allowed, in the Theatre, for the Reprefentation of anv given leiwth (the height of the Eye being determined) the Floor ought to rife in'proportion.” I lhall fuppofe it fi.xed, to the declivity which one foot, in twelve, gives. The prefent Conftriiaion of the theatres is Rich, that ’tis fc’aice pradicable to reprefent a real Building, with propriety. For, according to its length, the Point of Contraaion, of the whole Perfpeaive, will be at a greater or lefs Diftaiice; and the Side Scenes mull be ipaced as the Subjed requires; whereas, they are fixed, and cannot be varied at all. How judicioufly they are fi.xed, I (hall enquire; as nei¬ ther Pozzo nor Hamilton, have given Rules for fpacinv them. In the Theatres Royal, and in the Opera-Houfe, they are fpaced-equally Ac¬ cording to Pozzo they are nearly equal; in Mr. Hamilton’s Schemes they a're wider affunder, as they recede ; m Mr. Kirby’s they are equal, fave the firft two wlilch are clofer together. As Ks is but an Abftraa from Hamilton (he candidly ac¬ knowledging, that “ ’tis irapoffible for him to treat it better than Mr. Hamilton has done, before him”), I lliall fuppofe that it was intended to be the fame. Why Mr. Hamilton makes the fpaces continually wider, I am at a lofs to devife, as he does not determine them by any Rule. ’ On the firft thought of this matter, it feems reafonable to conclude that they lliould reprelent equal Spaces; confequently, being in Pcifpedive, they o’uvht to be nearer together, as they recede. Mr. Hamilton tells us, that the firft Pair repre¬ lent a Space, there laid down ; and the reft, other Spaces, which have no deter¬ minate ratio to each Other, from any Defign, or Scale whatever ; but are continu¬ ally larger, conhderably, feeing they are ftill fo in Pei-fpedive. In Kirby, they are equally fpaced ; and, according to the Point of contradlon of the Sta-e ’wlftch he gives, the fourth Space repreibnts, nearly, double the firft ; what reafon can be afilgned lor this, I cannot devile; for it is inconfiftent and ab'urd in the hio-heft degree; unlels certain Spaces had been given, in order to be fo reprefeuted. ’ Much Sea. IV. OP SCENOGRAPHY. 41 Can any reafon be affigned, why the feveral parts of an elegant Building, in¬ ternally, Ihould be, in every part, equally fpaced? or all fall in the fame line of Diredlion ? as they always do in the Theatres, where one Wing is generally (if not always) a duplicate or likenels of another; that is, they are all the fame, in figure, and frequently in dimenfions, too; whichj if they were geometrically fpaced, on a level Plane, would be right; but, being intended to reprefent a much greater length than the Stage can poffibly admit of, it is moft grofsiy abfurd to bo equal in proportion, as I am well -informed they generally are ; fo that, each anlwers for the other, being taken promifcuoully; which prevents miftakes of the Scenes-men, and which, otherwile, they would be liable to. Undoubtedly a Sett of Scenes; which are full of work, with the affiftance of Colours and Gilding (although it is but the fame thing repeated, one after another, to a confiderable diftance) will appear very bufy, and may pleafe the Eye of an injudicious Speaator; but, where is the propriety of it.? as the Infides of elegant Struaures (fit for reprefenting in Theatres) are feldom fo conftruaed; one%rt being more fpacious and open than others; the Piers and Columns; varioudv dif- pofed, iupporting coved or vaulted Roofs, Domes, or other Superftuaures." To reprefent which, in a proper manner, fo, as to give each Scene its true place, and proportion, and cohneaing them fo together, above, that the Dome or vaulted Roof, horizontal Cieliiigs, &c. lhall appear to bear on the Columns, or other Supporters; each Pair of Scenes fo difpofed as to appear adually eonneaed with the next, is a real difficulty, a mailer piece in Perfpeaive, not eafy to be defcribed; neither is it worth the attempt, as fo very few will be benifited by it; yet I ffiall endeavour to do fomewhat towards it. There is not one Author, extant, who has treated this Subjea (at leaft, which has fallen in my way) has given a Defign to be reprefented on the'Scenes, which, to me, IS unaccountable; that lo many Ihould attempt a Subjea of that importance, without touching on the part, by which, the whole machinery of the Stagei muft be regulated; furely, it is as neceffary here, as for a firnple, plane Piaure, 1 ind in¬ finitely more fo ; for, without It, what does all they have done mean, or tend to 1 in reality, I don’t perceive that one of them has done any thing, to any piirpofe*’: and therefore, I ffiall do what they have omitted, or had not the requifites for. In the firlf place then, it is necellary, whether it be a real Building to be repre¬ fented, or a Defign, exiftiug only in Idea, to have a correft Plan and Seaion of the Building; and to determine, what part of it ffiall be reprefented, on each Wing, &c. The Defign ffiould be fo contrived as to have various breaks, particularly at each Column or Pier, which is intended to begin a feparate Wing. For, to reprefent, on various detached Planes, a continued Entablature, &c. is not poffible, fo, as to appear tolerable out of the true Point of View, Wherefore, in order to be a good Scene- Painter and Defigner, the Artill ought to be a tolerable Architea. Though fome imagine it very eafy to arrange Columns and Arches, and vary them at pleafure, like ringing Changes on a Sett of Bells; true, yet, how few do fo with propriety, (and produce Harmony) Is but too obvious, to a judicious Eye. The firft Figure, Plate V. is a longitudinal Seaion of the Theatre; ai is the Fig. i.' Stage, with the determined declivity, and E is the Point of View.' AB is the Sec¬ tion of the Curtain, where the Stage ufually begins to afcend; but, as what is re- prelented on it, ferves only as a Frontifpiece, or Frame, to what is reprefented be¬ yond it (with which it has no connexion) I think it needlefs to begin the affient before the firfl Scene (at a) as there wnll, by that means, be more level Stage for the Adors (called the Prolcene) beyond which, ’tis leldom that any thing remark¬ able is perlomed; lb that, the remainder of the Stage may afcend as much as is requifite for the Perlpeftive. * I except, here, a Work by a French Author, Gabriel, jVfartin Durnont; printed and publlllied at Pans, in the Year 1763 ; vvhicii, refpedling Defigns for Theatres (fonie of which were ercdled, abroad, under his immediate Infpeclion) appears to be a very valuable and mafterly Performance, and bnely en¬ graved. It iiiay, not improperly, he called Theatrical Architeflure ; as it refpefts, only, the general, architectural Conltruaion of the Houfe; but in no wife regards the Scenery, either in (heir arrangement, er in what is to be reprefented on them. L The 4 -! Sea. IV. OF S C E N O G R A P H Y. Plate V. general Point of View being fixed (at about the Diflance of the Front Boxes, I’ic. I. fomevvhat forwarder) as at Ef, draw EC, horizontal, and produce it till it cuts the Stage (ai) produced to O. It is then manifeft, as the Stage is intended to re- prefent level Ground, that aO reprelents infinity of Diftance thereon; and confe- quently, it is the general Point of Coiitraaion of the whole Scenery. Now, if iL be the End of the Theatre, and ai the utmoft length of the Stage, then, according to that length, the whole of a grand Scene (for a Proceffion, &c.) muft be adapted; and in doing that, properly, confifts the whole Art of Scenery. Suppofe then, zF to reprefeut the whole geometrical length of a Building to be reprefented. Draw EE' curing the Stage at f, which reprefcnts F thereon. But, the Theatre will admit of a greater length; fo that, the Stage need not be lb much inclined, to reprefent the length aF, the Inclination a/being lufficlent; In which cafe, the Point of Contraftion will be at a greater Diftance; and confequently, the whole Reprefentation will be nearer to the geometrical Proportion of the Original. Hence it is manifeft, that, according to what length is, or can be allowed, on the Stage, for the reprefentation of any determinate length, the declivity of the Stage Ihouid be adapted to it. For, I can by no means allow of much latitude for the Eye, or general Point of View, which, I lay down as an infallible Rule to be on a level with the Eye of the Adtors, at a medium, at the hither End of the Stage. Since then, the afcent of the Stage is fixed, alfo the Point of View, and Con- traffion of the Scenes; elfe, by raifing the Eye, to E, the Point F will appear at i, at the farther end of the Stage; but fuch a height for the Eye, would be produftive of very difagreeable Reprefentations, to thofe below; for which part of the Houfe, the whole ought to be particularly adapted. Wherefore, in order to occupy the whole Stage, either a greater length may be imagined, or the Scale of proportion enlarged, from aF to twice aF, or more; then, ai is iuppoled to reprefent the whole length, geometrical, of what is intended on the Stage. Neverthelels, as much length as is required may be reprefented on iL, the flat Scene, which clofes the View. Suppofe aF to reprefent, geometrically, as much of the infide of a Buiidiiig as is intended to be reprefented, on the detached Side Scenes; and, let B, C, D, &c. re¬ prefent certain Diftances of Columns, or other Objefts, to be reprefented ; not ne- ceflarily at equal Diftances, but according to their true place in the Building, in refpeft of their diftances from the Interfcflion, at a. Draw EB, EC, &c. curing ai, at b, c, &c. which reprefent, in their true places, on the Stage, the Points B, C, &c. conlequently, a being the place of the firft Scene, the fecond will be at b, the third at c, &c. which it is obvious are not equally fpaced, nor in any regular gradation whatever, but muft neceflarily be in thole places, and no other; feeing it is impoftlble to reprefent, truly, and with propriety, Objefts ftanding on B, C, &c. fo, that, all the parts, reprelented thereon, lhall be properly connedled with the other, unlefs the Scenes ftand in the very places, a, b, &c. as it is evident. For, fuppofe any one (as at c) removed, fo, as to make the fpaces ab and be equal, or otherwile. Now, the Scene, at c, not ftanding in its true place, in refpeft of the reft, will be cut by EC at the point c, above the Stage; confequently the point c is not on the Floor, but above it; and cannot, therefore, appear in a Line with the other Scenes, where they cut the Stage. y In the middle of the Front Roxes, projefting forward, into the Pit (as at No. 2.) their Majefties Seat, with an elegant Canopy over it, being fixed, would add, greatly, to the magnificence of the Theatre, At prefent, 'tis in the very worft part of the Houfe ; I grant it is the bell, for the Audience to fee their Maje- llies ; but I think it paying too great a Compliment to the People, to have the worft place for no other rcafon. In the Front of his Majefty’s Box, a Sight-hole might be fixed occafionally, of about an Inch in Diameter; which fhould govern every Piece of Scenery, of any confequence ; and make it (as it certainly ought to be) the principal Situation, The greateft pleafure rcfalting from theatrical performances, is the Deception; which gives, in a great meafure, reality to the whole. Then, certainly, the Deception is the leaft, where the whole Scenery is loft, or has no Effedl; where the Actors are feen ready to come on, as they are wanted, to perform their fevcral parts; the Prompter, the Scene-Shifters, &c, being in fight, and the nakednefs of the Houfe expofed to view; the glare of Lamps full in their Faces (which, alfo, produces a moft hideous effcdl on the features of the Aflors) all which concur, to tender that Ctuation the leaft eligible plaec in the Houfe. Hence Sea. IV. 43 OF SCENOGRAPHY. Hence appears the necelEty of having the places of the Side Scenes mbveahle, at pleafure, as well as the Flatt, at the far End; all but the firft, which may be fixed. How far this is prafticable I leave to the Managers, or to the Scenes-Men, who are acquainted with the Machinery ; I think there would be no great difficulty in it. At the lame time, it is not neceflary to ffiift their places for every different Reprefentation; becaufe, for common performances, a proper gradation may be determined on, to which the Defign might generally be adapted. Having determined the Dift.ance of each Side Scene, from the Curtain, and from each other, their places in refpeft of their fituation and diftance, muft alfo be con- fidered, from a Right Line (S P) down the middle of the Stage. In Theatres, as the whole Place is uniformly regular, on this Side of the Cur¬ tain, fo ought the Scenery to appear on the other; and confequently, all Grand Scenes, reprefenting a great length, either internal or external, Ihould be fo regu¬ larly difpofed, that one Side is a perfedt Duplicate of the other. For, as it is in lome meafure real, though a Deception on the whole, it would be highly abfurd to take the Station towards either Side (except for very particular reaions) or, to fuppofe the Building inclined to the Curtain ; iiifomuch that, all attempts at mak¬ ing it more pidurefque, by inclining both Sides of an Objeft, as in a Pidlure, are ridiculous. Detached Objefts on the large Scene, external, and having no connec¬ tion with the Side Scenes, may be difpofed at difcretion, as they belt pleafe the Eye, In all Grand Scenes, intended for Proceflions, or Banqueting, &c. on the Stage, they ought to be fo conftrufled, as to have a fpacious Area at the hither End, where the Adtors affemble together; but may be contradled further on, at difcretion. The fecond Figure is the Plan of a Building to be reprefented, internally. A Sec- Fig. 2. tion muft be made, and the Building laid open, beyond the firft Columns (at X, X) elfe, the Stage will be incommoded, in Front. From the Seflion of the Scenes above, produce the Lines which reprefent the Sedtions of each pair of Wings, through the Stage, indefinite. Draw S A, SB, &c. cuting them, refpedlively, at A, b, c, &c. which give the place of each Column, &c. at the Plinth of the Pedeftal; and determine alfo the apparent width of each Face, and projedlures of the Mouldings. But, becaufe of the inclination of the Stage, being fo near a level, and the Eye not being raifed above the natural height, the Vifual Rays E B, &c. cut it fo very oblique, that the true Interfedlion is not eafily determinable. Wherefore, if, from the Eye, a Perpendicular be drawn to S, and from O to P, in the central Line of the Plan; P will be the Point of Contradlion, and S the Station Point, by which, the true places of the Scenes may be determined with greater accuracy. A being the place of the firft Scene, applied clofe to the firft Column, intended to be reprefented, draw A P, which is the general Line of Contradlion, of the Scenes, on the Stage. Then, drawing SB, SC, &c. cuting A P, at b, c, &c. the true place of each Scene, refpedlively; but it does not abfolutely limit their extremes on the Stage, as is feen by the Figure ; which projedt more or Ids thereon, accord¬ ing as the Objedls require. Right Lines, from each Objedl, to the Station at S, determine the true place and proportion of each, on its proper Scene *. The true places of the Scenes being thus determined, according to the Original Defign, there remains nothing more, but to delineate on them (by the Rules fuffi- ciently defcribed, and enforced by Examples, in the foregoing Work) whatever be¬ longs to each Scene; taking particular care, not to delineate on the next Scene (as at b) the fame Column, or Pier, &c. which is already drawn on the Scene A ; but, all which falls between that and the other, which is out of fight from the general Point of View; but muft, neverthelefs, be drawn, as a continuation of that Pidlure, in order to fill up the Space, which would otherwife leave a vacancy, to the Spedla- tors on either Side; of which, care muft be taken, that each Scene is wide enough to cover in, from all the moft confpicuous parts of the Houfe. * This Procefs, it is obvious, is nothing more than the application of Sirigatti’s Method of Delineating, or determining the perfpediive proportions of Objedfs; and which, every Perfon who knows any thing of Dirtd Vifion, would pucfue, without ever having heard of Sirigatti, or his Method, 5 Herein 44 Seft iV. O F S C E N O G R A P H Y. P.'ate V, Plereui lies tlie greateft Art, in delineating on each Scene what properly belong* to it; and to diipole it as to appear to be connedted with the other, in fome degree, to all the Speflators; though it can be perfedlly fo, only in the general and true Point of View for the whole. In this particular Inftance, a deviation from fbe ftridt Suies of Perfpediive, may be difpenfed with, difcretionady ; that is, to have more than one Point of View for the fame Picture, or pair of Side Scenes. For, thofe parts,' which can be feen only from either Side, may be fo delineated, as to appear the moft agreeable from that Station; but, as another Point can no where be fixed, abfoutely, it rauft depend tntii-ely on the Artift's Judgment and Difcretion. The Diftance ufed for delineating each pair of Side Scenes is, refpedlively; E r, for the firft pair, E 2, for the fecond, &c. and the meafures of the Objedts or the ratios of them, are applied to the Interfedlion, or Ground Line of each, as in all common cafes whatever; each fingle Scene being conlidered as an oblique front View, of Columns, &c. having one Face parallel to the Pidlure. Notwithftanding 1 have, in the foregoing Work, made many objcdlions to this kind of Projeaioii; yet, in this Cafe, I maintain, that, to give them an inclined polition to the Piflure, is a moll palpable abfurdity, or to have the Point of View out of the middle. Fig. 3. Figure 3. is a Seftion, fhewing part of the Defign, of the inlide of the Building, to be teprclentcd. From the Plan it is obvious, that the left hand fide, from the Door, is the counterpart of the Right, from A to B, which it was therefore un- iiecoliary to repeat. On the right hand, the Building is fuppofed to be continued ; the part from B to D is again repeated, or rather inverted, leaving a Space between (as at C) with Windows, where are Recefles for fepar.ate places of Entertainment, three on each lide ; beyond which a Dome is imagined, lupported bv eight Piers, each coropofed of two-Columns with an entire Pilafter in the Angle (as at X and Z, in the Plan, No. 2.) fomewhat novel, and I believe unprecedented. Fig. 4. F‘g' 4- reprefents a latitudinal Sedbion through the Plan, on the Line KL, in which, the receding part, wdth the Door and circular Window over it, above the Cornice, alfo the Nich, and up fo the SofEt, under the Architrave, reprefents the far End, feen through the raiddre Avenue, and between the Columns, as at Y (in the Plan) but on the other Side; the Window at W is over the Columns at Y. From X to Z, in the Plan, is one large and fpacious Area, which is reprefented in the Front of the Stage, begining beyond X; over which is an elliptical Lanthorn, the bottom of which appears in the Sedtions, at V and U. The Secllons being well underllood, from the Plan, which reprefents the oppo- Ilte Side, and the places of all the Scenes determined, in the Plan, by Lines drawn from all the parts of the Building, continued, as at B, C, D, E, and F, to S, for which, a Right Line, (CF continued) is fufBcient, feting off the meaftires only, which give their repreientative Places on AP. I is the place of the Flatts*; as there is a large Space, acrofs the Dome, to be reprefented on them, confequently, a much larger Space is neceflary, between it and the laft Scene, at h. As it mull be obvious, that if the Plan was entire, the otlicr Side being but a Duplicate of this, the pofition of the Scenes on the left hand, will be the fame as thofe on the Right, inverted; therefore, it was unncceffary to repeat them. Fig. 5. F'g- 5- reprefents the whole Sett, on the fame fide, from the middle, according to their geometrical proportions and places, prepared ready for the Painter. Fig. 6. At the bottom of the Plate (Fig. 6.) is a complete Sett of Scenes, finifficd, by a larger' Scale (as 6 to 5, nearly.) The place of the firft, to the right hand (No. i.) is at A a, Fig. 2. the place of the fecond (No. 2.) is at b; No. 3. at c; and No. 4. at d, aulwei ing to the fame Number in the Elevation, at the top of the Plate; which is the firft P.dr that requires a hanging Scene which unites the two Wings, acrofs the Stage, as one Piflure. On it, a part of the Cieling is reprefented, coved at the Sides, and horizontal in the middle; containing about half the Ellipfis, which The large fliJins Scenes which crofs the S-age, at the farther End, on which is reprefented all that is net taken in on the Side-Scene?, In order to clofc the View, are ufually called a Pair of Flatts. I reprefents Sea. IV. OF S C E N O G R A P H Y. reprefents the Bafe of the Lanthorn; and, being cut out, at the lower edge, e, f, g it ■will fall in with the next (No. 5.) at e,f, g. This Scene (No. 5.) may be either in two, as a pair of Flatts, or as two Wings, and a hanging Scene, on which is deline¬ ated the coved deling, all that is above the Cornice; being cut out, whether in two or three pieces, as in the Figure. No. 6. follows next, which will be bell in two pieces; or it may have a hanging piece, containing the Arch only, falling oil the Cornice at both fides. On account of the View being now contrafted, there is no need for much breadth of deling to be reprefented; but may be left as in the Figure, unlimited. The yth Scene being alnioft perfedly firhilar to the laft, by a iels Scale; that is, it muft have the very fame Subjedl reprefented On it, by a greater Diftance, viz. as E7 to E6, Fig. i. it was therefore unnecelTary to be given; and another reafon is, that there was no room for it in the Plate. Thefe are the only two which have lo near a refemblance of each other; all the reft differ both in Figure and Proportion; the firft and the fourth have the fame Subjeift, exclufive of the hanging Scene, as is obvious, in the Plan; all the reft have different Subjects, in great part; in fome parts the fame; in ftiort, each has the part allotted to it from the Building. No. 8. has its place at h, and the Flatt (No. 9.) which clofes the View, is at i; between which, and the laft Scene, there is a much greater Space than any of the other, to be reprefented on it, equal to the width of the whole Flan; fome- what more than half of which,-a fquare Area (over which is a Dome, fupported oii eight femicircular Arches) is exhibited on the two, with a Recels beyond it, to the Door; equal to the fpace from the front Angle of the Pilafter to the Wall, in the Seftion (Fig. 4.) or from the outer Corner^ at X, to the Wall, in the Plan (Fig. 2.) Thefe nine Scenes, with their counter parts, being truly drawn by the ftridl; Rules of PerlpeiSive, and properly lhaded; the firft eight having their Profiles cut out, and the parts cut open, of the four next to the Flatts, as m the Plate; and being truly placed, as in Fig. 2. on a larger Scale, proportioned to them, the Stage beino- inclined, according to Fig. i. they will exhibit, in the true Point of View, a juft Appearance of a real Building, according to the Defigii given; in which, every Scene, from the firft, fhall truly coincide with the next. The Curve ab, in the fecond will exaflly fall in with ah in the third; cd in the third, with cd in the fourth; and efg in that, with efg in the fifth; the reft do not coincide in any particular part, but the Mouldings; in the Cornices, &c. will all fall into the fame line of Direiftion, and the proportion of the parts of each Scene, will fo harmonize with the reft, as if the Building itfelf was before the Eye, expofed to view, intern.tlly, ereifted on the Plan, at No. 2. and feen from the Station S, at the height SE*. The Horizon is marked on each, paffing through the middle of the Bales of the Columns, and the Center for each Pair, and of the Flat, is alfo marked at C; the Diftance for each relpedlively is Ei, Ea, E3, &c. in the Seftion, Fig. u that is, in that proportion, by a Scale adapted to the Scenes, as before-mentioned. I have obferved, that what properly belongs to one Scene muft not be drawn on another. It is obfervable that each Scene muft neceflarily begin with a Column, or fome other Break in the Building; and all the part, which is between that Column and the hither one, may be drawn on it, if neceffary; to cover in with the Scene ftanding immediately before it, from the Side Boxes, or fo much as is thought pro¬ per ; for, from the hither Boxes it is not poflible; efpecially from his Majefty’s Bo.x, on the Stage, from which, the View is ahnoft diredt on the Edges of the hither Scenes; and confequently; the beauty and effeift of the whole Scenery is deftroved and loft, to all the Spedlators from that part of the Houfe. Hence it is evident,"that it is neceffary to draw more on each Scene than can be feen from the true Point of * The Author, has Models of two Setts of Scenes, one external, the other internal, of the fsine Build¬ ing. In the interior Scene, there are nine detached Pieces, at different diftances; fix of wliich, bcfides the Flatt, arc very different in figure, and conffruftion, from each other; yet, fo calculated as to form one elegant Defign ; each appearing properly conneaed with the next; forming, altogether, a complete Build¬ ing, with ftveral Avenues. TheCieling appears in fome parts horizontal, in others cylindrical, and coved; a Dome appears in one Place, and Cupola in another; all which appears conneaed, and properly fup¬ ported from below, with Columns, &c. as they would appear in the real Building, from the determined S.ation or Point of View. O F S C E N O G R A P H Y, 46 Sea. IV. Plate V. View ; for iiiftance, the third Scene has the whole Door (at K) reprefented on If which cannot be ieen from the Station S, clear of the hither Column; as it is otv fervable by applying a Rule to the point S and the edge of the Column, at a, the line of the Door is cut at !>. It is alfo reprefented wider on the Scene than it appears, m the Point ot View ; becaufeas it can be wholly leen, only towards the Sides of the_Houle, it will conlquently appear wider. In which inftance (as I have before oblerved) a deviation from the true Point of View may be difpcnled with, in the lame Pifture; as in the Flatt, No. 9. in which, the returning Mouldings at AB which are parallel to thole at D, in the Original, and Ihoiild vanifli at C, tend to’ another Point in the Horizon, to the left hand; where a Perpendicular from the Itye ot a Spectator, on a level with it, and where it can be feen, wmuld cut the Plane of the Flatt; and confquently, from that Station, the Lines in the Original would take a different direflion, and the Face AB, with the Arch over it, will appear wider, than from the middle. Therefore, what could not be difpenfed with, on any account, in a Pidlure which is wholly taken into the Optic Angle, from the truC'Point of View, is warrantable, and julHliable in this Cafe; because, it can¬ not be wholly leen from any fingle Point of View, and therefore, may be confi- dercd as three feparate and diftindl Piiftures, thougli united in one. On the hanging Scenes it may be obferved, that there are fome parts reprefented on two Scenes, which cannot be avoided, with propriety,; for inftance, the Curve ab, in No. 2. coincides with ai in the next; and cd in that, with ctf in the fourth, fo that, the lame Border is on both, the hither one hiding the next, in the true Point of View; but, from the Pit, the edge of the hither one will be feen more under, and the nearer to the Orcheftra the more; in which fituation the farther Scene would appear naked, and deficient, if the Border was net repeated. So, in No. 5. all the part above e/g-, is alfo reprefented on the fourth ; for, otherwile, the hither one being removed, as here, or feen under, which is nearl5' the fame thing, it is obvi¬ ous that No. 5. would appear very naked without it. How much ought to be drawn on each, fo as to cover in, from any particular Situation in the Houfe may be de¬ termined fiom the firft Figure : as for .Example. Let AB be the height of the opening of the Curtain ; from the height of the Eye, at F, near the Orcheftra, draw FB, and produce it to the firft Scene, cutiiig it at a, which determines the utmoft height requilite for that Wing, for, from any other part of the Houle, a cannot be feen; from E, the general Point of View, that Wing IS leen no higher than 6 , the next to c, and the third to d; from the Pit they W'lll require a greater height, d D reprelents the height of the hanging Scene, No. 4. at ef, then, if from F, a I.uic be drawn through D, themext Scene is cut at e, which Ihews, what height is necelLry thereon. From E, a Line being drawn through S, paffes allb through D to e, fomewhat lower than before, from F. G is the height of the opening of the Arch, in No. 5. from which, a Line being drawn to P, gives the height ot the three following, being all eqoal in the Originals; and ■.if through G, H, and I, Lines are drawn from F, the heights which are necelTary for painting the next are determined, at f, g, h, and for the Flatt, at /; L is the height of the Arch, as it muft be drawn on the Flatts. It is almoll fuperfluous to fay more, on this Subjea:, to fuch as are at all ac- .quainted with the Conftruaion of a Theatre, and underftand the Rules given in the Work. To treat fully on it, and go through the whole Procefs of one Set of Scenes, would far exceed the bounds preferibed for this Appendix; which has orher Mat¬ ters yet to treat of. If what is laid be clearly tmderflood, there needs no more; as each Perfon’s own Judgment, with proper application, will Iboneft make him a Proficient, and enable him to improve on the hints I have given, .In refpebf oi the polition of the Side-Scenes, it is ufelefs to expatiate; for, to Tuppofe them in.any other pofition, than parallel to the Curtain, is a grofs abfurdity, and can anlwer no ufeful purpofe, whatever. I .cannot, conceive what Ihould induce ■the Italians (according to Pozzo) to prefer the inclined Pofition; as he feems to be very little acquainted with the .delineation. of Gbjebls inclined to the Pi6tiire ; iu -this Cafe, they are two inclined Pi.dures, in the place of one, parallel; which can neyer Seel. IV, S C E N O G R A P H Y. 47 O F never appear tolerable, but in the true Point of View; in fome parts of the Houfe, moft intolerable. Beficles, in interior Views, where there is a neceffitv for haiw- ang Scenes to unite each pair, as one Piaure, on which, the Roof or Cieling is re- prefented, it would be the moft abfurd thing imaginable; which every one of judgment, muft acquiefee in. _ Yet, in fome Circumftances, inclined Scenes may be ufed to great advantage VIZ. in reprelenting a long Street, of Houfes in Right Lines, which can never be done, properly, in the common way, on feveral parallel pieces *. But to draw the Objeds, properly, on inclined Scenes, there are but very few who are duly qualified. The Method of drawing Scenes by Reticulation is puerile and tedious, and lia¬ ble to great Error ; which is done, by drawing a true Perlpedtive of the whole, on ail entire Pidlure, in the place of tlie firft Side-Scenes ; then reticulating the whole 1 ifture, the. Squares are projected to the feveral detached Scenes. Mr. Kirby ima¬ gines that he has done fomething extraordinary, in attempting a Method, whillt hnnfelf knew-not how to apply it to pradice. It is manifeft, that as they diverge, they are continually encrealing; from which It IS evident, that, in order to appear equal to the reprefentation on the entire Piaure ^emg beyond it) the parts muft neceflirily be larger, as they recede farther back. But, to be at the trouble firft to delineate one entire Scene, and to reticulate the ..others from it, will be attended with great lofs of time uniieceflarily. Befides they muft not be reticuhited as Mr. Kirby has done them, lefs and lefs as they recede, but larger and larger; elfe, how is poflible that they can appear equal to the fame Kepreleutation on the entire Piaure. Mr. Kirby leems to imagine, like others, that each Wing is to be a duplicate of the other, on a fmaller Scale, as they recede, by fquaring them all alike, which IS not the Cafe; for, they ought to be fo reticulated as to appear, in the Point of -View, as an entire Piaure ; confequently, each part on the entire Piaure, muft be projeded forward to the detached Scenes, and fill the correfponding Squares on them. But, as the Profiles cannot poffibly be cut out before they are drawn, fome parts will fall on the hither Scene, which fliould be projeded to the next. Having done the whole by this Method they will be greatly defedive, and only fit to be been, from the true Point of View ; as there will require additional parts to each Side Scene, except the firft pair; .allb on the Flatts, which could not be reprelented, on the entire Pidure; which, if the Artift be not well acquainted with ireripeciive, he will find difficulty in filling up, properly. In reality, it is a bungling and very imperfea method of proceeding, fit only for .fuch as know but little of Perfpedive; who imagine, from a Print, or Drawing m Peripeaive, they can form a Sett of Scenes. But I am afraid they will find themleives miftaken, if they are not acquainted with its Rules, for to do it, with .fuGcefs, requires both_ judgment, and knowledge in Perfpedive. ’Tis a very dif¬ ferent Cafe, to that of copying Prints or Drawings entire, by a larger or fmaller Scale (except what belongs to a pair of Flatts, only, which is the lame thing, in every relped) 1 mean, from one entire Drawing of the whole, to perfed a com- pleat Sett ot Scenes; as thofe who have tried it muft have experienced. To form a Sett of Landicape Scenes, requires little knowledge in Perfpedive. The feveral parts, as Trees, Hills, Rivers, &c. are not delineated by its Rules, but by.the Judgment of the Artift; and although a Building be here and there in¬ troduced^, yet, they are generally fuch as require but little knowledge of Lines; except the View be a-Garden, or other Ground Plot, regularly laid out, with Build¬ ings, &c. mterfperfed, fome of which are principal Objeds. X,* Thofe who eboofe to be convinced of the trnth of this offertion, may have ocular conviaion; as I -have a Model, by me, of a Sett of Scenes, reprelenting a local View, on an entire new Plan ; which everyone, who has leen it, affirms to be the moft juft and natural Reprefentation, of a real Place, they have ever feen repreftnted j in which, every Perfon (whofc Habitation is on the Place) ftallknow his thing never yet done on the Stage. One or two principal -Objeas, to charaaerize the Place, being thought fuff.ciem ; the reft, if natural in any Point of View, ■s all confu ion and ablurdity m every other, p.irticularly towards the Sides of the Theatre ; whereas, this appears reai every wherej or as much fo as can be, on plane Surfaces, 1 Yet Sea. V. OF THE APPLICATION OF PERSPECTIVE, Yet fuch is the miftakeii notion of the Managers, that it is a queftion if they ever looked further into the Merits of a Scene Painter, than, that he was a good Landfcape Painter; vvhich was the firft, and perhaps the only recommendation; whereas, a thorough knowledge of Lines, in Geometry and Perfpedlive, is the chief, and ablbl'utely heceflary qualification. In fliort, he Ihould underliand the whole Conftrudlion of the Scenes and Theatre. Painters of Landfcape may always he found to execute what is requifite in that Walk; when, perhaps, a Century does not produce five Perfons, fufficiently qualified for the diredlion and management of the Scenery, in general. SECTION V. Of the Application of PERSPECTIVE to a SHIP, S OMETIME about twenty Years ago, I remember to have feeii a Work, which was publifhed about that time, called Naval Perfpedlive ; which implies no¬ thing more than the application of the Rules of Perfpedlive to the delineation of 3 Ship ; than which, there is. not a more beautiful Objedl; and, being properly de¬ lineated, is.a mofl pleafing Figure, which, I am of opinion^ very few take the pains to delineate by Piule ; indeed but few are capable of it, who make Ship-paint¬ ing their more immediate Study. I am forry that I cannot fpeak of that Work, relpedting its Merit dr Deficiency ; for, with all my affiduity, I have not been able to meet with or hear of it; and I cannot, from memory, fay any thing concern¬ ing it, nor Can I learii who was the Author. In vifiting the Royal Dock-Yards, feveml Draftfmen there, feemed much to with that 1 had given, amongft the variety of other Subjedls, a Ship, by the Rules of Perfpedlive ; lome of whom I made fenfible, that if they were well acquainted with the Rulcsj and underftood the Subjedl, clearly, with the knowledge they had of the geometrical Conftrudlion of a Ship, which I had not (and therefore did not choofe to attempt it, perfpedlively) they might apply it as well to that Objedl, as feveral other in the Work. For, although there are few or no Right Lines in its conftrudlion, that are principal in it, yet it is eafy to Imagine Lines or Cords ftretched from one part to another, fore and aft, horizontal and parallel, or otherwife, at pleafure; alfo latltudinally, from any Part to its oppofite; by which means, as many Points may be afeertained, in any Curve, as are fufficient to deferibe it with accuracy; and that is all which can be done, by Perfpedlive. Speaking of this to a Perfon of great Abilities and Genius in Ship-painting, he fliewed me a Book on Ship Building, by Mungo Murray, Shipwright; in his Ma- jefty’s Yard, at Deptford ; publifhed in 1754, which I find to be not a fuperficial, or meerly an ingenious produdlion, but in which is difplayed a depth of reafoning on the Subjedl, beyond what I expedled from it; and, furely, the Subjedl requires it, being, in my opinion, the moft wonderful and extraordinary Conftrudlion in the World. 1 beftowed a little time on it, to make myfelf fo far acquainted with the external form, as was neceflary for its Delineation, for which the outward Fi¬ gure, only, is needful; the mechanical Conftrudlion being, in order thereto, nearly of the fame ufe, as the Anatomy of the Human Body to the delineation thereof. Indeed; anatomical Dilfedlions of a Human Body cannot in any wife conduce to its Delineation, in the variety of Attitudes, that are given to it; but, in the other Cafe, the Anatomy of a Ship may be conducive to it; at leaft, by means of va¬ rious latitudinal Sedlions, the true Contour of a Ship may be deferibed, in any At¬ titude, or Polition. Although by ftrength of Genius, and having a thorough knowledge.of, or ra¬ ther, being well acquainted with the outward form of a Ship, by a familiarity with it, it is poffible to delineate it in all the variety of pofitions it can exhibit; yet, where Sea. V. TO THE DELINEATION OF A SHIP. v.here Dch Genius is fpontaneous, how much perfpeaive would contribute W ards greater accuracy ,s lo evident, that >tis needlcfs to ufe many Lrd. to enforce If. However^ as I have no where feen ^PYr#'nf in u ^• attempt to lay down Rules for the Proceis they are more eVr "f :;a;s » iHa r a- figure of the lower part, can only be defcribed. ^ ‘ Pro^iaioforfhTshrerWaneTtfo'wIvfoS'^ jea.on on the Floor Plane; and at No , i a M I ^ at Its greateft Swell ; this is called the Body Plafe rwhich'a 1 th' are projefted ; on the left hand the Sedions of ^h’. P a ^ S^flions frirs otr “““ s=a£xr.,s Plan,, whid,*,,,„i,,„i„5;i*“ the Interfeaion ; and DC is its D tonc O G °f/'h‘ch, A V is on the Floor Plane, at right angles with th? IlZ’ o/d? Sh' pT' being produced to the Piaure, |,ve the interfeafor R fT ^h-ch mlhmg Point of horizontal Linfs parallel to tlw Sheet Plane^-’the^th^ V ‘ Po.nt(of the horizontal Lines of'lhe Seaions) runs oS of\ e Preliminaries being fettled, which ir miiR „k„- • ricrure. 1 hele Objea, we now proceed to the perfpeaive Plane*°^^ Pe^'eSicHars^fol^ffeidry Pon:ts'3 ttin ?ouSf 71^'"’’ various Points elevated to Lrtain heigts l^^’hrGliS^n^^irr rf b7a 7ft irnoi,! Oper^mi ^ ^ Ship, ^uUi IlKift^^. ft7 wludl'^;irr7a7etf°77^ L ^"Sn^.Sn t7 wi7;;ireirr7^:7r'.:“77£ other, being propeilv applied ■ as when the Fvp ' U *^he exemplified in the Work. ^ -ontal Line, as it is frequently P.aurt\n?c^7the the P.aure being determined a C fe’t off t 7 d"ft°'''' Center of of Lines parallel to th7 Vanifoing Point V. i-mes par.Uclto the Keel, equal, or in any other proportion toCV, Fig z ^ ^Ai 49 . . Plate VI 1. e. Its Fig.,. Fig. 2. Fig. 5 = Sea. V. OF THE APPLICATION OF PERSPECTIVE, Plate VI. Scale of this Drawing is double of the other, t.ake C V equal twice C V, Fiu- 2- the Vertical Line, CD, being drawn, fet off DA^ equal to twice AC, Fig. 2. and draw A V. Find the places, a, b, c, &c. of all the Sefllons, perfpec- lively, on A V. (Prob. 8. Sefl. 4. B. 3.) through which, draw Lines to the Vanilh- iiig Point of horizontal Lines in thofe Seaions (which are at right angles with the Keel, i. e. perpendicular to the Sheer Plane) which runs out of the Piaure, by Prob. 13. Seft. 3. and, on thofe Lines deferibe, perfpeftively, the leveral Sedions at No. 3 ; the half Seaion, on this fide the Keel-IJne is fufficient, as the larboard Side of the Ship, only is feen; fave at the Bow, where the SeiSion mud be entire; the Seflions, at No. 3, being numbered, according to their order, in regular fuc- ceflion, Ihew which is the Original of each perfpeiSlive Seftion. The fird only is entire, and expreffes the Curve marked i, in No. 3, on both fides ; the two next exprefs thofe on the fore Body, Inverted. The Line HP, Fig. 2. being in the greateft fwell, is the Seaion of the Body-Plane, and is the lame on both fides, at No. 3.; the other two, towards the Stern, arc exhibited as if the Stern was to¬ wards us, which, in thePerfpeaive recede; but the Curves are the lame, and the SeTions follow as above. It is aimed fuperfluousto Ihew how thofe Seaions are defcrlbed, being the fame as deferibing any irregular curved Figure, by means of its proper Vanilhing Line; which mud be drawn through the Vanilhing Point on the left hand (which is out of the Piaure) perpendicular. For the midlhip Seaion proceeds thus. At the interfeaing Point (S) of the Line P H draw a Perpendicular; on which fet up, from S, the feveral heights, from No. 3. that is double; and having determined the perfpeaive Seat of each, at a, b, c, and d, and Perpendiculars being dr.awii thereon, draw lines from all the meafures on ST, to the Vanilhing Point, on the Left, curing them, at e,f,g, and h, through which the Curve may be defcrlbed, as in the Figure ; and, after this manner, all the other Seaions may be defenbed. But if the interfeaing Point be not within compafs, the fame Perpendicular, at S, may ferve for any other; by drawing a Line from S, through the Seat of any perpendicular Line in the Seaion, to the Horizon, as Sj, and, from T, draw a- nother Line to the fame Point, E, which gives the height of the Gunwale at d. By the fame means, any other height, in any of the Seaions, may be obtained ; alfo, any other Perpendicular, on the Ground Line, will anfwerthe famepurpofe. Thefe Seaions being obtained, a fair curve Line paffing through tlie correfpond- iug Points of each, will reprefent the feveral Lines in the Wales or Borders on the Sides of the Ship, Mouldings, &c-; the Curves of which vary according to the fituation of the Eye; and as they are not plane Curves, they cannot be defcrlbed as other plane Figures, by means of a peculiar Vanilhing Line. The Draughts¬ men, who can lay down, in Plano, the true Seaion of every part, could probably determine a Sedion parallel to the Piaure, at the Bow, where a right line from D, the Station, touches it, at E, which, if the Eye was on a level with it, would be the apparent Contour at the Bow; but, as the Eye is elevated, in this Piaure, it would not, as the fwelling of the Bow, beyond it, would be feen over it. From the Stern, the apparent Contour is deferibed over the bend of the leveral Seaions, down to the Bottom; and by no other means does it appear, to me, praaicablc, or polfible to be deferibed, with any degree of accuracy. The curves of the Mouldings, on the Gunwale, &c. being obtained on the hither Side, the oppofite being feen, may be deferibed, thus. From the Points a,b, &c. draw lines to the Vanilhing Point on the left hand, and determine their apparent lengths, from their known meafures, as at Fig. 2 ; by wliich means, as many Points may be obtained, in the Curves as are neceflkry to deferibe them._ The Lines on the Decks alfo, where they are feen, muft be obtained after the lame manner, from a geometrical Seflion by the Sheer Plane, as at No. 4. The Water Line, 1 , m, n, o, is in a horizontal Plane; its geometrical figure being determined, on the Floor Plane, the perfpedive figure may be found, by means of the horizontal Vanilhing Line, in the fame manner as the general Plan on the Floor Plane. Or it may be determined by the Seaions; for, it cd, No. 3, be fuppofed Sea. V. TO THE DELINEATION OF A SHIP. 5* fuppofeci thefurface of the Water; then where it cuts the feveral Seaions, at 1,2, &c. perpendiculars being drawn to the Floor, determine the diftance of each, from the Sc-aion of the Sheer Plane; and being all of equal height, they are readily transferred to the perl'pedive Sedions, as the other meafures thereon. To determine the Gun-Ports, with accuracy, would be rather a troublefome Ope¬ ration; nor do I fee any other way to effea it, than by defcribing the Curve of the Deck they are on, which is not a Plane Floor, or rather the Curve of the Line they are in, at the proper height above the Deck; which, on account of the Sides battering, or bending inward, in this part of the Ship, will fall within the line of the Deck ; which being defcribed, and their places determined in it geometrically as at B, &c. No. 2; then, determining their places on the perfpeaive Floor Plane, (the curve Lines being drawn on the Side of the Ship, for the top and bot¬ tom Lines) Perpendiculars from them, will cut the Curves in their proper places. In the fourth Figure, the Ship is reprefented as feen from an Eminence, as on the fore or main Top, &c. of another Ship, or from a Cliff, on Shore ; or it may be fuppofed, that, the Sea being violently agitated, the Ship is defcending to¬ wards us, on a large Billow; as the Effea would be nearly the fame, and, in an Objea of this kind, the difference would fcarce be difcernable; in a right lined Objeff, it would be very obvious; for, the Horizontal Line would croft the Ob¬ jea, which IS now elevated above it, and all perpendicular Lines, in the Objea would tend to a Point at a diftance below the Horizon, which, in this cafe, will be perpendicular, and confequently, parallel amongft themlelves; but, as’there are no perpendicular Lines, on the outfide of a Ship, and thofe on the Deck are fo very fliort, comparatively, it would not be difcernable whether tliey tend to a diftant Point, or are parallel to one another. C V. Fig. 4. being the Horizon, at the intended height of the Eye, above the Ship, take AB for the Interfeaion, anfwering to the Ground Line in the other- and having drawn the Vertical Line, CD, fct off DA as above, equal twice A c’ Fig. 2. and draw A V, for the reprefentation of a horizontal Seaioii of the Sheer plane. Let the Interleaion be fuppofed to pafs through the hither Ano-le of the Beak-head, near the Cat-head; then, imagining horizontal right Lines,°or Cords ftretched, from each Angle, parallel to the Sheer Plane, irlarking the place where F e cuts iheedgeof the Gunwale, (Fig. i.) orthe Floor Plane, No. 2. which are alfo exprefled by the dotted Lines Fe, and Eh, in Fig. 2. the iiiterfeaing Point of the firlt being obtained, making AG equal to AF (twice A F Fig. 2.) draw FV and G V, indefinite, and make Fe reprefent its proper length (twice Fe Fig i or 2 j the Vanifhing Point on the Left, curing the other at alio FE being drawn to the fame Vanifhing Point, £/a fF reprefents the Reaangle Eheb Fig. 2 ; and after the fame manner, any number of Points on the edge of tpe Gunwale, and Rails, may be obtained, as are necelTary for defcribing the Curve Fn^c.i'ey with accuracy; as for Example. To obtain the reprefentations of the points c and k. Fig. 2. Draw Fc parallel 4 - twice AF Fig. 2. on both fides, making A a and Ab equal, at which Points a and b, draw fhort perpendicular Lines, below the Interiedlion ; and make ad and be each equal to the height of the Line Fe Fig. I. above the edge of the Gunwale, at c, and draw c V and d V; then, making Fe reprefent, perfpeaively, twice Fc, Fig. 2. and drawing a Line from c to thi Vanifh.ng Point, on the Left, curing dV at ^ the Points r and ^ are obtained. The Points b and d deviate fo little out of the Line F c, and are fo nearly on a level with It, that tis needlefs to take any other means to obtain them, than by determining their diitances on the Line Fc and transfering them to the other fide. ^ 1 determined after the fame manner, drawing a Line from f paral¬ lel to AB (Fig. 2.) curing the Pidure at n; then, making Ae and Af, Fig 4 each equal twice An Fig. 2. at which Points, e and f, let Perpendiculars be drawn, .above the Iiiterleflion, and make fg and eh equal to twice fg Fig. i • from g and h draw lines to V, and make g/reprefent twice n f, Fig. 2 ;’ from /darw / g to its Vanilhing Point, and thus, any number of Points may be obtained. 3 Fig- 4- The 52 Sea. V. OF THE APPLICATION OF PERSPECTIVE, Plate VI.. The Seaioiis,_ by which the Curves of the Wales, with the Contour of the Fig. 4. Bottom, are defcribed, muft ne.xt be determined; as for Example; the Seaioii cHq, of the Midfliip, from the outer Curve of the Body Plane (No. 3). Draw H o parallel to AB, Fig. 2. cuting the Pidure at o; then, making A j, Fig. 4. equal to twice Ao, Fig. 2. draw the Perpendicular jn below the Interfeclion ; in which, take the lengths of the feveral Perpendiculars, from the Line AB (No. 3) to the Curve, and apply each twice, on jn, from j, to k,l, m, and n, from all whidi draw- lines to V i and having made j i equal to twice the height of A B from the Gunwale, draw i V, cuting kc produced, at C, where draw a perpendicular, cuting k V, 1 V, &c. at o,Ar, p, andq; from C, determine the Points, 1,2,3, on ck (the per- fpedive meafures of thofe Numbers, at No. 3) from all which, draw Perpendi¬ culars; and from o, p, and q, draw Lines to the Vanifhing Point, on the left hand, cuting them in the Points 0,/, and y, refpedively ; through all which, a Curve, being defcribed, will reprefent a peripedive Sedion of the Midlhip. The point H, being in the greateft fwell, is in the Perpendicular. All the other Sedions, at F, G, /, &c. may be obtained after the fame manner; but as the operative Lines in this, cannot be rubbed out, as in drawing (being only pencel’d Lines) the operation of another, would render them both confufed ; and ’tis eafy to apply the very fame operation to the reft as to this; however, by mak¬ ing another, towards the Bow, in dotted Lines, the Proceis may be traced out, by the former Defcription ; a repetition of it would be ufelefs, confequently uupleafing. Having defcribed as many Sedions as are deemed neceflary, the Curves of the Wales and Mouldings may be drawn with a careful Hand; but, beingfurnilhed with variety of curved Rulers, they may be done much neater, and tire Curves truer. R lie Contour of the Bottom is defcribed over the bendings of the Sedions, which being carefully drawn, forms a fine, and fair Curve ; which, with a low Horizon; and the Ship being confiderably more in profile, would be be loft infenfibly, towards the Stern, as well as in both thefe, towards the Bow; owing to the Sedions being ftiarper, or not bulging fo much as in the Midlhip. 1 he Head, with the Harpins and Rails, it would be a moft troublefome Procefs, to delineate by Rule, therefore I lhall not attempt it, but the Cutter, or Cutwater, being a plane Figure may be done; but ’tis not neceffary to be at the trouble, ex¬ cept to determine its projedure, and the height of the Bow, at the Head. Here, the whole of it is projeded, as, in Fig. 2. it projeds on this fide the Pidure. Pro¬ duce the middle Line (V A) indefinite, and make AB, perfpedively, equal to its projedure; draw BD and AA perpendicular, and make AA equal to its height, twice Aa, Fig. i. draw YA cuting the perpendicular, BD, at D, in the middle of the Bow; which being obtained, the whole Figure may, from the geometrical form, be drawn by hand, accurate enough ; or as many Points may be obtained, after the fame manner, as is required; as, at i and 2. The Cat-Heads may be thus defcribed, perfpedively, in their proper places. At Fig. 2. it is obfervable that the hither one, on the larboard Side, projeds through the Pidure, as the Cutwater, and muft be projeded to it; in Fig. i. is fhewn the raking, and inclination to the Horizon, though not truly, being confiderably fore- Ihortened. In Fig. 2. a Line being drawn, from one extreme to the other, as rs, the Pidure is cut at t; make Ar, Fig. 4. equal twice At, Fig. 2. and, at r, draw a Perpendicular; make rs equal to the height of the ends, above the Interfedion (twice the meafure at Fig. i.) and through s, draw a Line to the Vanifhing Point on the Left, indefinite. Make sr, and sr perfpedively, equal to twice tr, and ts. Fig. 2. then, find the Point u, which reprefents u, in the Floor-Plane (Fig. 2.) tvhere the Cat-Heads, being continued, would meet, on the Deck, or eli'ewhere, and draw rw, and Kr ; notin parallel Lines, but allowing, difcretionallv, for their re¬ ceding, as tending to their refpedive Vanifhing Points; which, if required, may be found, by Prob. 4. and 5. Sed 3. Book 3. The Chains to which the Shrouds are faftened, as at X, Y, and Z, Fig. 2. may be determined on the Pidure, by drawing lines, from D, to the extreme of each, cuting the Interfedion, at x, y, and z; the places of which may be transferred to 7 the Plate TI (‘y7//. / \ \ 1 1 L ^0^' ^ '’■ _ As»=jr s □ D -1 in n ? 'J fH □ n D n "H®, s k s z ■; Im'K iPm ^\:l U]\ J Sea. V. TO THE DELINEATION OF A SHIR ^ the Piaure, having already defcribed the Curve, on the Side of the Ship, in which they are; making each, from A, Fig. 4. double the meafure from A, Fig. 2. at X, T, and Z; otherwife, their places riiay be found in the Curve, by drawing perpen¬ dicular, or other parallel Lines, to the Interfeaion, AV, and transferring them to the Piaure; then, drawing Lines to the Center, or other Vanilhing Point, cuting the Curves, in their proper places, perfpeaively. Other Minutias, with the Orna¬ ments, &c. may be drawn by hand, either from a real Ship or Model; but when that cannot be had, their places may be afcertained, and drawn corredl enough, by a Perfon who has judgment in drawing. Thefe Figures, w'ere projedled in Per- fpeftive, entirely from the geometrical Drawings, at Fig. i. without the affiftance of either. The Gun Ports, though determined by rule, in Fig. 3. may be obtained, perhaps more accurately, by the fame means as the Chains, above; and fo indeed may all the parts of the Figure, projefted on the Floor-Plane, at Fig. 2. as in Vignola’s firfl Rule. The interior parts, on the Deck, which are feen, with the Quarter Deck, and other Ereflions, as they are regular, and moftly right lined, thefe is nothing pecu¬ liar in their projeiSions on the Pidlure; therefore, I fhall fay nothing more refpec- ting them, than that, their true places being obtained, Rules fufBcient have been given for projefting them. The places of the Marts being given, in Fig. 2. and indeed, of every other Objeift, on the Decks, may be bcft obtained by the above method, and with accuracy, refpefting their apparent magnitudes and places, to¬ wards the right hand, or the Left; alfo, by a proper Elevation, their heights on the Pifture may be had; and with the aflirt:.ance of Vanifhing Points, for the direc¬ tion of certain Lines, it is perhaps the beft calculated for fuch Objefts. From what .has been done, and laid, it is evident, that the Rules of Perfpeftive may be applied to the projeding, or delineating a Ship; yet, I am far from fup- poling, that a Ship-painter would be at the trouble of drawing every Ship he paints, by thofe Rules; by no means, but this I would advife him, to go through the Procefs in one, or two, in different politions; by which he would acquire a greater facility in deferibing the variety of Curves, which corapofe a Ship ; as his judgment in them (being thus truly projedted) would be much improved, his Eye would be more competent in judging of their various appearances, in different pofitions, and, in many refpedls, he would find great advantage, to his natural Genius, refult fiom it. As in every Pidure there is always fome principal Objefl, I would alfo advife him not to trull wholly to his Eye in delineating them, but make ule'of Rules, to ' give the general form and proportion of the p.irts to each other; and witli this Advice I Ihrdl beg leave to conclude this Sedlion; for if 1 w-as difpofed to treat the Subject ever lb fully, all that could be laid or.done, more, wotflj not make it bet¬ ter underftood. At Figure 5. is given another Ship, with its Stern towards the Eye, fomewh.at Fig. more inclined to the Pifture, floating; an account of the height of the Stern, and the Eye being on a level with it, nearly in the middle, very little of the Deck is feen; the Contour of the Bow, in this pofition," is a graceful form, when tnilv defcribed. In relpcft of the Rigging, but little’can be done by Rule, except in giving the heights and proportions of tlie Mails,-^c. but even in that refpeifl, as, in Sea-pieces, the Diftaiice is generally conliderahlei the projiortibn of tiie'parts to each otner, is nearly geometrical, the perlpeftive gradation affccls them very'little, at fuch Diftances. 1 he Right Line JM, Fig. 2. is the pofitioti of the Pia'dro rcrpcaihp- the Ship in this View; the Cc-nCer is at C, and the Dirtance i± inches, double "the other, but drawn to a lels Scale. - -No. 5. is the geometrical proportion of tht Stern, to which it is drawn. ' ’ ' i ■ ■ i - I ii, t ■ il ■ ' ■ -0" i-rt - ■ i'-.d: b;: ., . ■' - njjiia'l , ■ • r . \i ~o ; : .' . 1 , t'"' • ' O SECTION r PlateVII f Fig. t. SECTION VI. of the Utility of PERSPECTIVE in LANDSCAPE-PAINTING. I N this Seftion, I Intend to fliew, in what refpefts Perfpedtive may be ufeful to the Landfcape-Painter; which is more fo than many may imagine. Refpe£t:ing the general Defign, if it be a Portrait, there are certain Preliminaries neceflary to be fettled, according to Rule, before he can begin drawing, which cannot be dif- penfed with. In the firft place, the Station muft be fixed on, and the height of the Eye determined, from which he muft never deviate, in the leaft; he muft ne.xt de¬ termine, what extent he intends to take in, which (hould not be more than can be feen diftindlly, at one View; I do not mean, without moving the Eye, for that would be but a very fmall compafs, but without moving the Head, not exceeding an Angle of 50 degrees at the moft, if but 40, the better; for determining which, the perfpeiSive Compaffes, mentioned in the 27th Page (which, by means of an Arc of a Circle, properly gradated, fhews the Angle) are conveniently adapted. Then, having determined the height of the Horizon of his Piece, the Center being in the middle of the Piflure, he muft note particularly, what Objedt, or what part of the View will fall there, which may alfo be determined by the Compafl'es; fixing them at half the Angle of the whole extent, and then, applying one Point to either extreme of the View, mark where the other Leg diredls, and that will be the Center of the View. Having proceeded thus far, a Ground Line fhould be drawn on his Paper, in pro¬ portion to the height of his Eye, from the level of the Ground where he luppofes his Pidlure or tranfparent Plane placed; and in this, I am perfuaded, many Artifts err greatly, by taking into the Pidture all the Ground they fee, even to the place where they ftand, which would be infinite on the Pidture; when, properly, no more than what is beyond the Pidlure fhould be introduced; but, occafionally, more may be added, with Diferetion. The height of the Eye, i. e. the Diftance between the Ground Line and the Horizon, on the Pidlure, (hould be in proportion to the Dif¬ tance of the Pidlure, and confequently to Its width or length. To make this better underftood; fuppofe I intend to take into the Pidlure all the Ground I fee beyond the diftance of 30 feet, from D, the place where I ftand, and there, fuppofe a tran¬ fparent Plane, eredl, large enough to take in the whole View; the Diftance (CD) being 30 feet, and the Optic Angle fuppofed 50 deg. the width of the Pidlure (AB) will be nearly 28 feet, for which, the height of the Eye is 5 feet. Now, fuppofe the Pic¬ ture brought nearer the Eye, to the diftance of 10 feet; confequently, the width of the Pidlure (ab) neceflary to take in the fame extent of View, will be about 9 feet 4 inches, for which, the height of the Horizon will be but 20 inches; which height of the Eye, for a Pidlure of that width, would be rather too little, and if the Ground be level would not rife fufficiently on the Pidlure; in which cafe more Ground may be added, below the Ground Line, or it would be too flat, and the Buildings be low in the Pidlure. Thefe neceflary Preliminaries being fettled, with judgment, the Artift may then proceed to the delineation of the Objedls and Landfeape before him; notwlthftanding which, if he has not fome knowledge in the Principles, and perfpedllve proportions of Objedls, ’tis a great chance if he produces either a natu- tural Portrait of the Place, or a judicious Pidlure. In Compofitions, a knowledge of, or fome judgment in Perfpedllve is ftill more neceflary ; for here, the proportions of the Objedls and the parts of the Pidlure to each other, muft depend wholly on his judgment, not having the Objedls before his Eye to draw from. In the former Cafe, the Artift having taken his Sketch by fight, and though he fuppofes that he has delineated the Objedls as they appeared to him ; or if from Fancy only the Defign be produced, we are, in either Cafe, very liable to be impofed on, in judging of their proportions, thinking them very 4 corrtdl; Sea. VI. OF LANDSCAPE PAINTING. correa; when, being tried by the Touchftone of Perfpeaive, they may be found very imperfea This I experienced, myfelf, in the Coinpofition of the Landi'cape exhibited rn the yth Plate; for, after the Sketch was made, and appeared tolerable refpeamg the Cottage, the Bridge, and Figures, it is fcarce credible how imperfea they were, before 1 correaed them by Rule. perrect This being the cafe, it may be alked, of what confequence, then, is Perfpeaive feeing that it is not eafily perceived whether it be truly delineated or not ? I Lfwer’ that although It may appear pafliible, in the laft inftance, not being accurately mined; yet, when truly drawn, the difference can fcarce be imagined; of which I fhall give an Example, hereafter, from the Performance of an Artift of the firft ClaE. In lefpea of Trees, except when they are regularly planted, Perfpeaive can be of no ufe in delineating them; and then, it can only afcertain their places, but in no wife their Figure or true Dimenfions ; yet are they not wholly eLmpted from Is Jur.fdiaion The irregular courfe and windings of Rivers, the unevLnefs of the Ground, and irregular dimenfions of Hills, and Mountains, &c. of which Lanl fcape is compofed are Subjeas, to which Perfpeaive is not applicable, fo as to be dehne.ated by Its Rules But, when Buildings, of any kind, L introduced and more efpecially when the Building is principal, in the fore Ground, as the Cottage m the 7th PHte It is then that Perfpeaive will be found abfolutely necefliiry and cannot be d.fpenfed with, if the Artift has any regard for his ReLtatlon It ^ al o effential in proportioning Figures, human or brute, both in refpea of other Objeas and to 01^ another; which are frequently very difproportionate and par ticularly in refpea of their fituation and diftance."^ F P . par- rudrRuild'hw^iT“’ although a rude Building, the parts muft be proportioned to each other in fome degree; and the Lines which compofe It, though not abfolutely Right Lines, are meL as fuch and their tendency to fome particular Point in the^ Horizon, or elfewhere is^ftill dilcernable; and, although there are none which are really parallel, yer thofe which we know are underftood to be fo, it is but reafonafale that we fhould tr^ them as if they were really fo; though not with that fcrupulous exaftnefs as in a regular piece of Architeaure becaufe it is not iieceffary, in an Objeft of this kind Shadows alfo, and the EfTefts of Light on Objeas; are Subjeas which can¬ not be wholly negleaed, in this branch of Painting; the former lies immediatelv within the Province of Linear Perfpeaive-; the latter is wholly Aerial ■ which tme"° which'” invariable Laws'of Na- theh elr^y ftudy! denomination, who are ftiled Artifts, thould make t'i ■kV'I down a few Rules, from the firft Elements of praaical Perfpec- nve, by which the Landfcape Painter may correa and regulate his Piece on^the Canvas from the Sketch he has taken by fight, or compofed ■ for it is nor nnffll I to confine the volatile Ideas of an Artift" to® Rfoes, i"gRi 4 ’ortaLr^^^^^^^ hi fom/d^‘^''“’ to Paper, m.ay be correaed^and reduced to Rule’ m fome degree ; and that, by a Perfon who is poflelTed of but a fmall Sliare of knowledge 111 Perfpeaive ; and which, being fo eafily attainable, muft rLiderth? hi " fr T""'- “ -f'“ o tend towards the lame Point; in confequence of this Lawf in Vifion all Rfobt Lines, m Objeas, which are not parallel to the Piaure, aaually do for ftiouldl tend It iieceliary. This, every pretender to fome knowledge in Perfpeaive does know and in that les all their knowledge, frequently; yet, ftranve to te 1 thev dn even apply that knowledge to praaice, as I foall (hew hereafter. In’ confcqucnL which'’ '' {but it is alfo demonftrable) that alF Lin‘es vv hich aie parallel to the Horizon, and not to the Piaure, tend to fome point in the Horizon, then, having drawn the Horizontal Line cf the Piaure-(QV) apply a Ruler .“8. cy, being made equal to Lt, gives the Vanilhing Point of its Image, ft/. ^ & 'i the™ai? BC FC if fis pa’rticularly exemplified in the Rails of tne t_liair, BD, EC, &c. reflefted on the Mirrour W; Fig. 53. Plate 48. Third; when the Mirrour is inclined to the Pifture, and to the Horizon. Fig. 20. „ Let A B he the given Line, in a horizontal Plane, whofe Vaniftiing Point is V; C is the Center of the ^^rire, G D is the Interfeaion of the Mirrour, with the Plane the Line AB is in, and GH its Iiiterfedlion with the Piflure. CE perpendicular, equal to the Diftance of the Raure, and draw DE • make DEF a Right Angie, F is the Vanifhing Point of Lines perpendicular to G d! Then, bec.iufe D is the Vamftuig Point of a Line in the Mirrour, and GH itslnter- ff M-t mV’ L, par. to G H, is the Vanifhing Line of f f Through C, drawKL, perpendicular to JI, and find L, the Vanilhing Point of Lines perpendicular to the Mirrour; a Right Line drawn Birongh F perpendicular to the Horizon, will aPo pafs through L; for it is the FFf’” u Piaure, in the Angle CED, equal Etc. Make FE, in the Horizontal Line, equal to FE, and draw EL- nike the An^e LE M equal L£ F, and M will be the Vanifhing Point of refleaed Lines, on the Ground Plane, perpendicular to GD. DrawAFand AL, alfo BFand BL- and, from the Pointsji and b where AF and BF cut GD, draw aU and , 5 M, cut¬ ing AL and BL at and B; a Right Line JB is the refleaed Image of AB. Or, Its Vanifhing Point, F, may be afcertained, thus; which is more accurate. FI L, the Vaniflung Point of Perpendiculars to the Mirrour, and V being the Vanifhmg Point of AB, draw VL, the Vanifhing Line of a Plane per¬ pendicular to the Mirrour, and pafling through AB; in which will be found the Vanifhmg Point of its refleaed Image; for, the Line .and its Image arc both in a Plane which is perpendicular to the Mirrour. . Dlftn”"' ‘'““"S ‘t at N, and make NO equal to its Diftance (equal EE) draw OV and 01 , and make the Angle lOEequal to lOV- P IS’ the Vanifhing 1 oint fought. For, I being the Interfbaion of the V3ni(hin<^ Luie^ JI (of the Mirrour) and VL, it is therefore the Vanifhing Point of the Seat r ni’ 5 '■vhich IS the common Interfeaion of the Mirtour, and of a Plane paffing through AB, perpendicular to it, that is, AABB; and, becaufe the refleaed Image appears to be as far behind the Mirrour, as the Line, or Objea IS before it, on this fide; therefore, the Angle I OE was made equal toTOV on the contrary fide of I, the Vanifhing Point of the Seat of AB. Produce BA, to die Interfeaion GD; draw GF, and AL, BL c-ating it at ^ fn F-’ ^ “"8 B L at a and b ; a b is the Seat of AB on the Mirrour, and Its rcflecS^ed Image,-as before. •J- Agam. Let P B be a Line inclined to the Horizon, as well as to the Mifrour and Piaure, and let AB be its indefinite Seat, on any Plane perpendicular fo the Piaure. From any Point in BP draw a Perpendicular, PQ, eating AB at Qj draw 3 Sea. viL OF REFLECTION, ON MIRROURS. PL and QL; and through q, where QL cut GD, draw a Line from the I'O . ' o: Interledion of the Vaniflaing Line of the Mirrour (JI) and of a verti- c I Pl.i.e pafliiig through PQ, perpendicular to the Mirrour (which pafles through P, perpendicular to the Horizon) cuting PL at p; pq is the Scat of PQ on the Mirrour, and bp of BP ; make pP reprefent a rneafure equal to tlie diftance of P from the Mirrour, that is, to what Pp reprefents, and draw P B the reflefted Image of PB. Or the Vanlfliing Point of P.® may be determined; having made FP equal to FE, and drawn a Line from E to the Vanilhing Point of its Seat on the Mir- •’ tending to it. Draw £ J perpendicular, tliat is parallel to IQ, Its R.adidl (being parallel to the Piffure); make the Angle R£S equal _RPJ; £ S vyill cut the vertical Vanidiing Line pafling through M, L, and F in the Vanifliing Point ot P^ If Q P be produced, and qp, its Seat on the Mirrour, meeting at T (the Point in which QP cuts the Mirrouf) &P tends to the lame Point. Then, drawing GT, and producing B P cuting it, at U the loint 111 which it cuts the Mirrour, BP, its Image, and bp, its Seat on the Mir- rour, tend to the fame Point; for, GT is the InteiTeffion of the plane Triaiwle BPQ with the Mirrour, and confequently, the refle£led Image of each Line B*P BQ, and Q P, tend to the fame Point,-in GT. ’ ’ _ In Fig. 21, the Mirrour inclines to the Horizon on the other fide; that is It reclines from the Eye, as, in the former, it inclines towards the Eye. _ It IS unneceflary to be minute, in defcribiiig the Procefs, in this Cafe which is but the reverfe ot the former; excepting that, in this, the Vaniniing Point of the inclined Line (AB) given, at V, is made ufe of, to determine its Image on the Mirrour; and, it inclines to the Horizon the contrary way, or reclines from the Piaure, and does not, immediately, cut the Plane Z. C is the Center of the Piflure, and GD the Interfedtion of the Mirrour with a horizontal Plane; or of any Plane perpendicular to the Piliture, of which, FH IS the Vaiunimg L>i>e J I, the Vaiiiihing Line of the Mirrour, being given, its Interfeaion wiA the P.aure is not neceffiry ; KL, pafling through C, perpendicu- lai to J I, cuts F M (perpendicular to FH) in the Vanifliing Point of Lines perpen¬ dicular to the Mirrour, as before (F being the Vanifliing Point of Lines perpendicular to G D) ; and, E E being made equal to F E, the Angle LEM, equal L £ F. detcr- minesye Vamftiiig Point of the refleaed Images of the Lines, P a, &c. perpendicu- i" Letters of Reference indicate the remaining Procefs, as by dielaft Figure ; I fliall here Ihew how it is effeaed. by means of the Vaiiifliiiw roint, only, which is the mofl accurate, moft concife and mafterly. ^ V being the Vanifliing Point of AB, the given Line, and L of Lines perpen¬ dicular to the Mirrouiy, VL, being drawn, is the Vanifliing Line of a Plane perpendicular to the Mirrour, pafling through A B. Find its Center, N, and Dif- NO (CE being the Dillaiice of the Piaure) drawing CO perpendicular of the Eye, in that Plane, draw O Valid OR, and make the Angle'RON equal ROV; N is the Vanifliing Point of the, refleaed,Image of A B, as R is of its. Seat on the Mirrour ; being the interftaing Point of the Vanifliing Line of the Mirrour with V L, as above a'J' -r y '^himfliiiig Point of the Seat of P Q, on the Mirrour, and Li of Its refleaed Image, m the Vanifliing Line H L. which anfwcrs to V L iii_ tlie former CaL;_ V being the Vanifliing Point of the Seat (Q B) of the inclined Line, as heie PQ is the Seat, and H the Vanifhing Point. G T is the InterTeaion of the Plane PABQ with the Mirrour, T being de- former Cafe ; A P, being produced, cuts it at S, and B A at U; D IS Its Interfeaion with tlie Plane Z, the reft is obvious. ■ ' I have nmy, I think, made ample amends for the brevity I had ufeft in treeing this Subjea, in the Work, which 1 own I had not, then, confidered fufficieiitly; Sreater length than I intended, here, but finding the Subjea fo very uiterefting, 1 was unwilling to leave it imperfed; and have, therefore. 79 ffg- 2l. Sea. IX. A PARALLEL OP VARIOUS AUTHORS. 8'j therefore, taken Iti all the variety of Cafes and pofitions of Lines to the Mirrour, and of the Minoiir to the I’iaure; to dwell longer on it would be to protraft it unneceflarily, as there cannot poffibly be conceived a Circuraftance, wherein the Lines, which deferibe the Object, do not fall within fome of the Cafes I have given. And, although I am far from imagining, that any Perfon will be at the trouble of projecting the reflected Image of every ObjeCt by thofe Rules, yet I think it neceflirry that they Ihould be imderftood, as it would prevent many grofs abfurditles wlrich are dally practiced, by Artills, in this part of their Studies. SECTION IX. Containing a P A R A L L. E L of the English Authors, on Perspective; with Remarks on W. J.’s Gravesande, F.R.S. who was Cotemporary with fome of them, publifhed in the begin- ing of this Century; alfo, on Guidus Ubaldus. I N this Section, I have propofed to draw a Parallel of all the Englifh Authors who have wrote oii PerfpeCtive; but, having already exceeded the Bounds I had preferibed, as an Appendix, 1 am obliged to abridge it, and omit the greater number, having nothing in them either interefting or worthy of notice ; and therefore, hope my Readers will be fatisfied with my Remarks on thofe, only, who have been and are Rill in repute; as my Criticifms on a Work, but little known, or its Author, could not be very entertaining; unlefs it tended to bring an Author, who had been hitherto unknown, into Reputation, which is not likely to be the cafe. However, I fliall be candid in my Remarks on thofe I do take into confideratlon ; to be otlierwife I am not difpofed, ’tis not my Incli¬ nation ; I (hall be as ready to point out their Excellencies, as to expofe their Er¬ rors, and fhevv their DefeCts; Humanity diCIates the former, what the latter is hard to fay. Yet furely, a candid Difqulfition cannot be charged with Spleen, as fome may mifeonRrue it, unlefs the Author w as living, and there was fome degree of rivalRiip between the Author and the Critic, which, I prefum.e there is not; neither can it be attributed to Envy, unlefs he either really excelled, or was reputed to do fo, in his Works. Let others attribute it to what motive they pleafe,- there may perhaps be fome Vanity gratified in it. I have fpent much time and Rudy on the SubjeCf, and think I,h.we acquired a kind of right to de- teCl Errors in it, wherever I find them; as the falfe Opinions advanced by thofe who are in Repute, are the more dangerous, and being once imbibed are not eqfily erafed, where there is not Rrength of Judgment to perceive the Ertor. There¬ fore I mean, by a RriCl Scrutiny, to bring each Production to a fair'trial, before the impartial Public, and prefume I fliall be juflified in fo doing, although fome favourite Author .fliould lofe part of the Reputation he had undefervedly been held in. In the RrR Section, I have given my Sentiments on all the old Authors on PerfpeCtive, which had fallen within my cognizance ; but, fince it was printed off, another, of fuperib'r merit,, to fome of them, was put into my hands; by Guidus Ubaldus, a folio Wo'rk, in Latin, in fix Books or Chapters, publiflied in the Year 1600; which, for that early period, is an extraordinary Production; where it was printed is uncertain, but, the Diagrams (all cut in Wood) are fo badly devifed, that thofe who were not already clear in the SubjeCt, would find fome difficulty to invefligate'the Propofitibns by them, and for that reafon, chiefly, 1 am of opinion, the Author is but jltfle known.' The'fitfl Book is mofily theoretic, in 36 Propofitions, which contain more ge¬ neral Principles'than thofe who wrote before him, or any fihee, within the laft Century; which is' evident to thofe w'ho can enter into the conRruClion of his j S'-'' ■ Diagrams. Plate IX A//. // /a/. /6. St a. IX. REMARKS ON GUIDUS UBALDUS. Diagrams. After fome preceding Propofitioiis, raeerly optic.al, he plainly fliews, that Lines being parallel to the Piaure are reprefented by parallel Lines; and have that proportion to the Originals, as the Diftaiice of the Reprefentation to the Diftance of the Original. He (hews, that all Lines in horizontal Planes (for he does not venture beyond that) being parallel, tend to the fame Point, on the Pidure, of equal height with the Eye; and that, whether they are fituated on this fide, or on the other fide of the Pidure, and projeded to it; whether they are at right angles with, or inclined to the Sedion Line; whether they are below or above-the Eye, and whether they are in the fame Plane or not. He alfo fliews how the finite parts are determined, by Vifual Rays; alfo, that Lines from the Eye, parallel to the Originals, determine the Points on the Pidure, to which they appear to tend; and make, at the Eye, the fame Angle with each other as the Originals. Yet, he does not (eem to have any notion of a Horizontal Line, ei¬ ther in the Theory or in Pradice, and of placing the Diftance of the Eye therein. His method of Pradice is fiugular, and I verily believe it is original, as 1 have not feen an attempt at the fame Method in any other Work ; I am grieved that it did not fall in my way fooner, when I (hould have had more leifure, and more inclination to perufe, and to have given a fuller account of it, in the proper place. However, as it is not now too late, 1 cannot pafs over fo valuable a Work without giving a Specimen of his various Methods, and of his extraordinary Abilities; for, in the Defeription he gives, there is an eLgant fimpllcity and perfpicuity, without prolixity, of which, the following is a Specimen, in determining the Reprefenta¬ tion of a given finite Line. In this Example, S is the Station Point, which he Fig. 22. ^ calls the Point of Diftance; BC is the Interfedion of the Pidure, or Ground Line, and DE the given Line, in the Ground Plane ; the height of the Eye is S A. DE is produced to the Sedion Line, at F, and from the Points D, E, at plea- fnre, the Lines DG, EC, are drawn, parallel to each other, which agree with BC, in the Points G, C; but, from the Point S, SB is drawn, parallel to DG, EC, and SH parallel to FE; and now, imagine B, F, G, H, C, to be in the Pidure, and alfo in the Ground Plane (as we fiiid alfo, in the preceding) ; now, let the Plane be taken for the Pidure, and BV, HX are drawn perpendicular to BC, which are made equal to AS, and FX is joined, and GV, CV drawn, which cut FX in LK. Wherefore, beeaufe V is the Point of concurrence of DG, EC, the Lines DG, EC will appear in G V, C V, as it was laid in the preceding; in like manner, when X is the concurring Point of FE, then the Line FE will appear in FX. From whence it follows, the Point D appears in L, but the Point E in K, and therefore LK will be a Line appearing in the Pidure. Which indeed is manifeft, if the Pidure is confidered iu the lame Plane with the Lines BV, HX, FX, GV, CV, perpendicular to the Ground Plane, and likewife, AS will be over S, perpendi¬ cular to the fame Plane. Therefore, the Line LK is deferibed, appearing in the Pidure; which was required to be done. This is, nearly, a literal tranllation of the Example from the third Problem iu the Second Book, which begins the Pradice; which may ferve to fhew, how well the Author was acquainted with his Snbjed, and how clearly he treats it. In which, the Affinity with the prefent Method, on the new Principles, is obfervable; CB being the Interfedion of the Pidure with the Ground Plane; a Line, DE, is given therein, and produced to its Interfeding Point, F; and the Lines D G, EC, are drawn at pleafure, but parallel between themfelves; then, S being the Station Point (or it may be conlidered as the Eye) SH is drawn, parallel to the given Line, and SB to EC and DG; conlequently, being raifed up to the height o( the Eye, equal SA, the Point X will be the Vanifhing Point of the given Line, and V of the two Lines, EC and DG. Wherefore, the Indefinite reprefentation, FX, being drawn, and CV, G V, from the interfeding Points of the two other Lines, the Reprefen- tations of the Points D and E are in the Points K and L, of their mutual luter- fedions ; as is evident, in the Figure. In this Example may be clearly feen the true Principles of Perfpedive, applied to Pradice ; which, excepting that Brook Taylor has both Interfedion and Va- X nlftiing Sea. IX. REMARKS ON GUIDUS UBALDUS. Plate X. Line; and the given Line, with the place of the Eye, being inverted, in bis Elliiy, ’tis the very fame thing as the 2nd Problem, Fig. 7, of the firlt part. Fig. 6, of the fecond, refpeaing the defcribing of the Line, and determining its Vanifhing Point; which, here, is called Point of Concurrence; but here, the given Line and the Station Point are in their true places, in refpea of each other and of the Pidure, at CB, according to Vignola and other old Authors ; which is the mod; rational and eaficft to conceive, at fird. In this Example, the Vaniih- ing Line would not be of the laft ufe ; but when he has three Vanifhing Points as in fome other Examples, being of equal height, it is furprizing that he fliould not draw a Line, to determine their height, above the Sedlion Line, and yet there are lome inftances, in which he does draw the Vanifliing Line, as in Prob. ^5, the laft of the fecond Book, which, for its merit, I fhall inlert, as follows. Propofition 34 is previoufly neceft'ary to the 35th in thefe Words. A given Line appearing in an upright Pidlure, to draw another Line, which, with the given Line, fhall appear to a given Eye (in refpeft of place) to reprefent a certain Angle. The 35th fays only, to find the fame without the Objeft:. The Station, S, the height of the Eye, AS, the Line of Seftion, DE, are as before, and K is the given Angle; BC is the given Line, in the Pidlure, with which the Angle is required, which fhall appear equal to K. Pi j- The Line F G is drawn, parallel to DE, which is diftant from DE according to the length of SA. And then, BC is produced, which cuts FG at F; and from the Point F, a Line, F D, is drawn, perpendicular to DE, and DS is joined. After which, the Angle DSE is made equal to the Angle K, and EG is drawn perpendicular to DE, and from the Point C, CH is drawn, which tends to G. Doubtlefs, the Angle BCH will appear equal to the Angle DSE, therefore equal to K; if indeed BC, CH reprefent Lines parallel to SD, SE, which of courfe conftitute an Angle equal to K. Which was required to be done. But this muft be noted ; if SE was parallel to DE, the Line CH alfo fhould be parallel to DE. And, in like manner, if BC had been parallel to DE, then. DS will be parallel to DE. And in thefe Cafes, the E.xample is done, tuning to the other Point, only. If any Perfon will be at the Trouble to compare this Propofition with the 12th of the ift part of Brook Taylor, he will find it [the fame thing; DSE being in¬ verted, and DE coinciding wdth FG. In this fecond Book are no lefs than 23 different Methods of determining the reprefentation of a given Triangle, each of which has a Problem preceding the Example (more theoretic than problem.atic) with a theoretic Diagram to each. Fig. 24. exhibits the firft method, viz. by means of the Vanifhing and Inter- rig. 24. feftiiig Points, as by Brook Taylor. I fhall not defcribe the Procefs, here, it being fufficient to obferve, that CED is the giveir Triangle, F B the Line of Sec¬ tion, S the Station Point, and SA the height of the Eye; which is, in general, greater than the Diftance. The Sides of the Triangle, DC, &c. are produced to their Interfefling Points, G, H, and K, and from S is drawn SB, SF, and SO, refpedlively parallel to them; Perpendiculars being drawn from B, F, and O, equal to SA, the height of the Eye, give V, X, and Y for their refpeftive Vanifhing Points; then, drawing GV, HY, and KX, the reprefentation, LMN, is deter¬ mined, on the Pidlure, by their Interfedlions. In this (ingle Procefs may be feen the whole of Brook Taylor’s Principles, and as much as he has done towards determining the Reprefentations of Figures; which arc always given, by him, in the geometrical Plane, reverfed; but the Procefs is the fame, in every refpedl, nor has he done any thing more than apply it gene¬ rally. From this Author, then, it can fcarce be doubted that the Dodlor, and his Cotemporary, Gravefande, have borrowed fome of their Ideas of the Subjedl, for much may be acquired from it, by thofe who had already fome knowledge of it, and, being able Mathematicians, it was eafy to extend it further. There is a great deal of Ingenuity difplayed in the various Methods he has given; fome of which are according to Vignola, and Sirigatti; in others, he de¬ termines Sea. IX. REMARKS ON GUIDUS UBALDUS. termines the Angles varioufly ; in one place (Prob. 20.) by drawing Perpendiculars from each, to the Interfcaion, as at No. 2; in which, the Triangle is inverted, as here ; then, B being the Point, where a Perpendicular from S cuts the Interfeaion, BD is drawn perpendicular, equal to the height of the Eye, and DE, parallel to FG, equal to the Diftance; Fa is made equal to FA, and Gi equal to GC, and FD, GD drawn, which are cut by cE and hF in a and c, the reprefentations of A and C; and, the Angle B being in the Interfeclion, drawing aB, Be, and ac completes the Figure. . , In the 1 ith (No. 3.) from the Angles, A and C, of the Triangle ABC, Lines are drawn at dilcretion, as CD, CE, and SE, SF, .refpedlively parallel to them ; FG and EH, being drawn perpendicular, and equal to the height of the Eye, CJ and FI are the Vanilhing Points of CE and CD, refpeftively; alio of Ae and Ad, being parallel to the former. Then, drawing EG and DH, allb eG and dH, the Angles a and c are determined on the Pifture, by their Interfeftions, at a and c. In both thefe, it is obvious, that this Author had a clear Idea of Vanilhing Points, which he determines geometrically, as by Brook Taylor. I lhall give another In- Ihnce of his Abilities, and geometrical Knowledge, in the 25th Problem, and con¬ clude ; as 1 think it will be manifeft, that they are equal to what I have faid of him, in the Introdudlion. BCD (No. 4.) is the given Triangle, S the Station, andEF the Line of feflion. SC, SD being drawn curing EF (as by Sirigatti) and Ec, Fd drawn perpendicu¬ lar, it is manifefl:, that the Points C and D will appear, on the Pidture, fomewhere in thole Perpendiculars; to determine where, he proceeds thus. SA is drawn per¬ pendicular to SD, alio FG; and, S.A being made equal to the height of the Eye, AD is drawn, giving FG, to which Fd is made equal; and confequehtly, the Point d will appear at d, on the Picture ; which is obvious, if the Triangle SAD be fup- pofed turned up on SD, till SA is perpendicular to the Ground Plane; thep SA is a Vifual Ray, from the Eye to D, which mull necelTarily cut the Pidlure at d, making Fd (equal FG) to SA, as FD is to SD, as he preferibes, in the preceding, and Ihews, here, how it is effedled. But, if SB had been drawn perpendicular to EF, and equal to SA ; then, drawing BD, the Point d is obtained the litme. Af¬ ter the fame manner, c, the reprefentation of c is obtained, and B being in the Pic¬ ture, Be, Bd, and cd being joined completes the Figure Bed, reprefenting BCD, according to the Premifesgiven. The next dilfersonly, in.S^ being parallel to EF. Thus, I have given a more circumftantial account of this Author, and his Methods of Pradlice, than I, at firft, intended, rel'pedling Plane Figures, in the fecond Book; indeed I had lain it alide, not being difpoled to look further into it, or to fay any thing- more of it, than the firft general account I have given ; when, on another inlpec- tion, and pcrufing fome of the Premifes, I perceived more merit in his methods of PrafHce than I had imagined; inlbmuch that, I thought they deferved to be re¬ vived, and handed down to Pofterity, in the manner I have done, a Juflice due to the Author. To proceed further, in a Difquifition of the four remaining Books, I am not at all difpofed, nor is it necellary; as a judgment of the Author may be formed, fufficiently, from what I have done. In the third Book he treats of Solids, Parallelopipeds and other Prifms, only; the 16th Propoiition fays, if a Pyramid be cut by a Plane, parallel to its Bale, the Figure, in the Seftion, will be fimilar to the Bafe, and alike polited. After the 19th Propofition, he gives a Cube, having the Vanilhing Points of the Diago¬ nals determined, both in the horizontal and vertical Vahilhing Lines, the fame as in Vignola; and he has alfo a vertical Interleflion, which, by turning the Figure, ferves as a Bafe Line. After this, he treats on inclined Planes, in nine Propofitions, which I have not leifure to enter into. The 2gth is the very lame as the aift- Method, B. 2. although he imagines it to be a quite different Cafe. 30 and 31, propoles to deferibe Figures on the feveral furfaces of Prifms ; on cylindrical and irregular Surfaces, with other Curiofities, in the three following; the 37th is on horizontal Pidlures; the remainder of this Seftion, to 45 Propofitions, is for deli¬ neating on concave, conical, cylindrical, and fpherical Surfaces. 4 The bed. iX. REMARKS ON BERNARD LAMY. The ftjirth Book treats of various kiiida ef Solids, friiftrums of Pyramids, &c. their Coiiftruflion, tlieir Seftioiis, and hiGlination of rlieir Faces, &c. of the re¬ gular Solids, or platonic Bodies ; their orthographical Projcftiotis, Altitudes, &c. from one Angle to its oppofite, but not of their perlpccfive Projedfions. The re¬ mainder, from the 19th to 39 Propofitions, is on the perlpctiive projedtions of Citcles and the Sphere; with the application to Arches, &c. Tire method he ufes for the Circle is ingenious, and nearly the lame as Brook Tavlor’sfirft method. The fifth Book, in 15 Propofitions, is wholly on Shadows, projected on a hori¬ zontal Plane, by a luminous Point (as a Torch) at a fhort Diltanee; of which I can fay little, nor does it promife much; firve the laft, of a concave Hemifphere, which is very ingenious. The fixth Book treats wholly on Scenery, not in Pro¬ pofitions ; but the Prints are vile, and promife little fatisfadlion to the inquifitive Reader, fo that there is no inducement to attempt an Inveftigation of it. IN thefecond Year of this Century, lyo-i^a fmall odiavo Work on Perfpedtive, in French, by Bernard L,amy, was printed at Paris, which is difpofed in ten Chapters. Tlie firll is rather prefatory, treating on the excellence of Per- fpedlive, as laying the foundation of a great Painter; the fecond defines a few common Terms, Inch as the Geometrical Plane, the Pidiure, the Points of View and Diftance, the Horizontal and Bale Lines, Accidental Points, &c. in nine De¬ finitions; the reft is optical, in which is a Figure, from which, B. Taylor has copied the firft, of his fecond Part, but he has added the Pidlure. I don’t men¬ tion this as tending to depreciate, as the thought is neither new nor extraordinary; another is copied by Mr. Hamilton, refpedling Villon, how performed by two Eyes. The third contains 12 Propofitions in Geometry, from nth of Euclid. The fourth is theoretic, in 19 Theorems, in all which I do not find any thing either lingular or ftriking, as being eflential in the Science ; that, the Perlpedlive of Lines parallel to the Ground Line are parallel to the Originals ; but he confines k to the Gr. Plane wholly, and makes another Theorem of perpendicular Lines ; as if they were not fubjedled to the fame Law; and that, if they are parallel to the principal Ray, confcquently perpendicular to the Pidlure, their Reprelen tat ions, being produced, will pals through the Point of View. That the Perfpedlive of all Lines in the geometrical Plane, not parallel to the Pidluie, being continued, cut the Horizontal Line; and that, being parallel, they tend to the fame Point in it; that the Perfpedlive of every Figure, which is parallel to the Pidlure, is fimilar to the Original Figure ; that Lines parallel to the Pidlure, being any how divided, are in the ratio of the Originals; that the parts of Lines, which are perpendicular to the Pidlure (being equally divided) are unequal In Perfpedlive, &c. Of fuch like, common-place, matter is the whole Theory compofed; for illuftration of which, the Diagrams (neatly cut in Wood) are not badly deviled. Some few per¬ tinent Corollaries, of the fame ftamp, are deduced. To the 6th Theorem (that parallel Lines, in the Ground Plane, tend to the fame Point in the Horizontal Line) is added a Problem, to find the Accidental Point; which is, to find the Re- prefentation of one Line, and produce it to the Horizon ; then, all the other Lines will tend to the fame Point. This puerile Method, lo liable to Error, was pradliced by all the old Authors; fo that, the Point was properly called Accidental, The fifth is preliminary to the Pradlice; of the fituation of the Objedls to be reprefented, of the pofition of the Pidlure, the Point of View, &c. The fixth contains the Pradlice, on upright Pidlures, which is not worthy of notice, fave the firft Figure, which is theoretic ; Ihewing, that the diftance of the Eye being fee off on the Horizontal Line, and the diftance of a Point in the Ground Plane, 011 the Ground Line, will give the fame Point on the Pidlure, as a Vifual Ray from the Eye to the Point, in its true place beyond the Pidlure. The feventh is on inclined and horizontal Pidlures, which are peer indeed ; of Anamorphofes, and drawing on a fpherical concave Surface, by means of a Candle, projedling the Shadow of an Objedl thereon. The eighth contains Rules for colouring, as de¬ pendant on Perfpedlive; Clair Obfeure, &c. The ninth, general Obfervations for Sefl. IX. 85 REMARKS ON W. J. ’S GRAVESANDE. for projefling Shadows, not worth notice; and the tenth is a Converfation betweeii Socrates and Pyrrhus, and with Cliton; the firft an excellent Painter, the other an able Sculptor. W. J.’s GaAvESANDE, LP. D. Prof. Math, and Aftr. at Leyden, and F.R. S. at London, publilhed an Efl’ay in rpii ; which was tranflated into Englifh, and publilbed by E. Stone, in 1724, dedicated to Mr. W. Kent, Architedt. The Ori¬ ginal of this Work, which was printed at the Hague, in French (as above) ap¬ peared four years before Dr. Brook Taylor publilhed his firft Effay, the Tranf- lation is nine Years after. It is tar from my Intention, nor have I a wifh to lefleii the Merits of my own Countryman, Dr. Taylor; I had much rather attri¬ bute to him the foie invention of the new Principles, could it be done with can¬ dour; but, ’tis my determination to give the praile due to the Author, where- ever I find occafion. In this Work it is manifeft, that a foundation is laid for thofe univerial Principles, which are to be found in no Author before Brook Taylor; the Theory is concife, the whole being comprized in fix Theorems (the Subftance of which may be comprehended in thre^ with ten Corollaries, three or four, of which, may be difpenfed with, as ufelefs. Although the Original of this Work was wrote in 1707, as we are informed in his Works, it is remarkable, that he begins his Prefate with apologizing to the Public, for obtruding on them a Subjetl which was already fo much hackneyed, that the very Term, Perfpetlive, feems unpleafant to the Ears of the public Enemies of Repetition ; whofe Cenlure he defires may be fufpended till he has given the reafons which induced him to publifh his Work. Amongft which are the confined and limited Ideas, which the generality of Books, on the Sub- jefl, inculcate; forae contenting themfelves with the bare explication of the Theory, without Ihewiug the application of it; but that, very few have given a new turn to the pradVical part, in which, he believes he may be able (though he knows himfelf .to be much inferior to feveral who have wrote on the Subjedl) to treat the Art after another manner; and fo, repay with Intereft, what he may be inferior to them, by his Diligence ; and, becaufe he is perfuaded, that more learned Perfons than himfelf, will not take the trouble on them, he has ven¬ tured to expofe his Work to the tafte of the learned World. He candidly acknowledges that he is indebted to fome of the Authors who have diltinguifhed themfelves amongft the Crowd, having looked over the beft part of them, who have treated on the Subjedl. What would he think, did he live in thofe Days, to the Numbers which this Century has already produced, in England, only? more, in my opinion, than the preceding Century, in all Europe, befide. In defining, he makes ufe of the fame conftrudlion of the elementary Planes, as Brook Taylor, excepting only the Diredling Plane, which he has not; yet he makes frequent ufe of the Diredling Line, which he calls the Geometrical Line ; the Station Point, and Line, allb, the Vertical Plane and Line, are properly defined; and indeed, there feems only wanting a general Idea of Vanifh- ing Lines; for, Vanifhing Points he determines, of Lines however fituated, with propriety, yet he calls them Accidental Points, like the old Authors. In his firft Definition, he fays, the Perfpedlive, Reprefentation, and Appearance of an Objedl (for thefe three Terms are fynonimous) is the Figure which the Rays form, in paffing through the tranfparent Plane; in which it is obfervable, that he confounds the Appearance with the Reprefentation of an Objedl, and he makes ufe of the Terms promifeuoufly. The firft and fecond Theorem are contained in the ninth of mine, viz. that the Reprefentation of a Line which is parallel to the Pidlure is parallel to the Original ; and has the fame proportion to the Original, as the Diftance of the Pidlure to the Diftance of a Plane paffing through the Line, parallel to the Pic¬ ture. But, inftead of thefe words, in the latter part, his fecond Theorem fays, that the Reprefentation of a Figure, parallel to the perfpedlive Plane, is fimilar to the faid Figure; and the Sides of the faid Figure are, &c. as above; in which Y the 86 Seft.IX. REMARKS ON W. J. ’ S GRAVESANDE. Plate X. the fimilarity of the Figures is firft proved; whereas, it is obvious, if the paral- lelifm and analogy of the correfponding Sides are proved, the equality of the Angles, and, confequently, the fimilarity of the Figures neceffarily follow. The third Theorem follows from the fecond; viz. that a Line, parallel to the Pic¬ ture, being feen by two Eyes, both being in a Plane parallel to the Piaure (i. e. in the Direding Plane) the reprefentations of the faid Line will be equal (See Cor. 3, Theo. 9.) The fourth Theorem is in thefe Words. If a Right Line being continued, meets the perfpeaive Plane, in one Point, the Appearance thereof will be a part of the Line drawn from the faid Point in the perfpeaive Plane to another Point, whereat a right Line drawn from the Eye, parallel to the pro- pofed Line, terminates. The fenfe of this Theorem is raanifeftly the fiime as the 12th of mine (the firft of the ill Part, or 3d of the 2d of B. Taylor) there IS indeed a redundancy of words, and the laft (terminates) means, cuts tire Pic¬ ture. Three Corollaries deduced from this Theorem, are as follow; ill. All Lines parallel between themfelves, &c. have Reprefentations, which being pro¬ duced, will all concur in one point. And this point is called their Accidental Point (Def. 17. P. 10.) 2. Two or more parallel Lines, &c. parallel to the Geo¬ metrical Plane (i. e. the Ground Plane) have their accidental Points in the Hori¬ zontal Line. 3. The Reprefentations of all Lines, parallel to the Station Line, concur in the Point of Sight, i. e. all Lines which are perpendicular to the Pic¬ ture (Cor. Theo. 4.) The fourth is vague and ufelefs, and, as it is exprefs’d, erroneous. Theorem ^ is ufelefs as a Theorem (See Cor. 5. Theo. 12.) The fixth, as it Hands in this Work, means little or nothing ; but the fubftaiice of id is, that the Radials of two Lines, producing their Vaniihing Points, make the fame Angle at the Eye, as the original Lines make with each other. This is the whole of the Theory, in which may be perceived the EHence of Brook Taylor’s Elfay; there wants the moft eflential one, for pradice (See Theo. 13.) which teaches how to proportion Lines, peffpedively drawn, indefinite, on the Piaure, In the praaical part of this Work, to determine the Reprefentation of a Point, IS varioufly and judicioufly performed. He alfo fliews, that there is no neceflity for taking the whole Diftance; but when it is remote, any portion of it may be ufed, taking the fame portion of the difiance of the original Point. He gives the Method of performing it by Tangents; alfo, by means of the Di- reaing Line, very judicioufly; and, by another Method peculiar to himfelf, which is very ingenious, infomuch that I think it deferves to be communicated. Let IB (Fig. Z. PI. II.) be the Bafe Line, A a given Point, and E the Eye, diftant from the Bafe Line, or Interfeftion, equal to the Diftance of the Pifture, added to the height of the Eye; as in Brook Taylor, the Vanifliing Line (HD) not being neceflary in this Operation; C is its Center. ' Through E, draw F G parallel to IB ; make E F equal to the height of the Eye, and EG equal to its diftance. Draw AE, and AF cuting IB, at B; then, draw BG, cuting AE in a, the reprefentation of A. For proof of this Procefs, a Conftrudlion is made, by drawing G I perpendi¬ cular to IB, and EC parallel to AF; then, through C, draw HD parallel to the Bafe Line; or if HD be confidered as the Vanifliing Line, of whatever Plane the given Point is in, then, where it is cut by BG, (atC) draw CE, from that Point to the Eye, which will be parallel to AF. DEM. BecaufeHCis parallel to IB, the Triangles GBI, GCH are fimilar; wherefore, GC:GB;:GH iGI; But GE zz; G H, and G F zz: G I; conlequently, as GC:GB;;GE :GF; therefore, EC is parallel to AF, and confequently, C is the Vanifliing Point of AB ; and EA is a Vifual Ray from the Eye to the given Point. And therefore, the Triangles AaB, EaC are fimilar; confequently, a is the Reprefentation of A, on the Principles of B. Taylor ; for Ba : aC ;; AB: EC. SCHOL. From this Demonftration, it is evident, that if EF and EG are in the tatio of the height and diftance of the Eye, though not the real meafure, the Point a will be produced the fame. Alfo, if any other Line be drawn through E, not parallel to IB, as fg, and any Point f, or g, be taken at pleafure; e. g. draw fb, at Sea. ]X. 87 REMARKS ON W. J. ’ S GRAVESANDE. at dlfcretion, curing the Interfeflion, at b, and draw Ed parallel to fb; then draw bd, and produce it to g. Or, if bg be firft drawn, at pleafure, curing the Vanilh- ing Line at d; then, Ed being drawn, and bf parallel to it, the Points f and g may be ufed as F and G. For, becaufe dE is parallel to bf, o-d • gb •• gE - ef- and conlequently, any other Line, gB, being drawn, it will flill be, gC : gB gE. gt, as before; theiefore, the Point a will be determined the fame Without determining the height or diftance of the Eye, a Line, fg, maybe drawn, and three Points, f, E, and g, taken at pleafure, by which we may proceed - and, 111 order to know what the height and diftance is, draw f B and E K, perpen- being drawn, cuting EK, at C; then, C is the Center, EC the dillance or the Piaure, and CK the height of the Eye. In this Diagram there feems to be the whole of the true Principles for Prac¬ tice, as by Brook Taylor, which does not depend on the real raeafures being ap¬ plied, but on the ratio of the parts to each other, as it is obvious here ; fothat had this Author advanced but one Step further, and applied his Principles to Planes Ill ail Politions, refpeaing the Horizon (which one would imagine, from what he has done, there could be no myftery in) he had left very little for the Other to invent. But he falls off, furprizingly, in the application of them to Lines and bigures, m ti,e tollowing Chapters. Of Lines he gives but two Ex¬ amples ; VIZ. a Line parallel and another' inclined to the Bafe Line. The incli¬ ned Line is produced to its interfeaing Point, audits Van ilhing Point is deter¬ mined ; then, the indefinite Reprelentation is drawn, and two Vifiial Rays de¬ termine the finite Part as in Brook Taylor; but, as the Rays are drawn from the Eye, in Its place, to the Line, it is frequently impracticable; yet, neither here nor in B Taylor is it fiiewn how to tranfpofe the Eye to the Vanifhing Line, or the mealure of the Line, to the InterfeClion, as in Prob. ly. SeCl. V. Here IS given a method of dividing a Line into any number of parts, equal or unequal, vvhich I do not remember to have feen ellevvhere. and is very ingenious • the given Line IS AB, and ah its reprefentation, any Point, as D, being afl'umed’ between the original Line and the Interfeaion (or it may be taken beyond It) and Its reprefentationy being determined; Lines drawn through D, from the Divifions A, B, and C, cuting the Interfeaion at a, b, c, and from them Lines drawn through d, give the perfpeaive Divifions on ac. ° He gives but three E.xamples of plane Figures, a Pentagon, firft, a Reaangle, and a Circle. The I entagoa has its hither Side parallel to ihe Interfeaion; he makes ufe of but one Vauilhing Point, although it is obvious, that another would greatly facilitate the Procefs. The Reaangle is obliquely fituated to the Inter- leaion. and is divided into Icflbr Reaangles; the Eye Point is above the Vanifii- ing Line, from which, the Vanifhing Points of the Sides are judicioufty deter- miii^ed; and, the Lines, m the Figure, being produced to the Interfeaion, the perfpeaive Figuie is effected. By means of a Reaangle thus reticulated, he fays, any kind ot Figure may be defcrlbed, viz. by circumfcrlbing the Original Figure w-ith a Reaangle, as 111 Boffe, a puerile and trifling Method. The reprefentation of a Circle is determined by drawing feveral parallel Lines through it, to the In- terleaion, and their Vamflimg Point, as in the firft Method by B. Taylor - or finding the tranlverfe and conjugate Axes of the Ellipfis which reprefents it/ but U mult be feeu direct, fo that the tranlverfe Axe is parallel to the Bafe Line. To find the reprefentation of a Point, elevated above the Ground Plane his method of proceeding is meerly mechanical, by means of the Station Point’ and Directing Line; this is preparatory to the reprefenting a Pyramid, and Cone. To determine the vilible part of the Bafe of a Cone is really ingenious, the reft is tritling. After thele, he proceeds to determine the repreleutations of Lines per- pendicular to the Ground Plane which he performs varioufly, but by round about Methods; which fhew that he had no Idea of ufiug any other Interleaion but the Bale Line; although the laft Figure points it out, clearly (Fig. ac.) he feems de¬ termined not to make a proper ule of it, but applies the given meafure to the Bafe Line, iiiftead ot a perpendicular Line, at the lame Point; and demonftrates, that ^ the Fig. Z. S8 Sea. TX. REMARKS ON W. J.’S GRAVESANDE. tlie perfpcaive height is truly found on the Ground Plane, from which it is trans¬ ferred to the Perpendicular. I lhall pals over the reprefentations of Prifms (in which he makes not the lead ule of Vanilhing Points, but finds the Angles in the upper Face, as points elevated above the Ground Plane) and Cylinders; but his Method of projeaiug a Sphere, in Perfpeaive, is worthy of notice; although, in the Prefiice, he fays, it is very difficult, if not Inapoffible, to throw a Sphere into Perlpeftive, by means of general Problems, and the Torus of a Column is ftill more difficult; fo that, he is obliged to have recourfe to particular Methods for the folutlon of them; yet the Sphere is truly projected, by means of the tranfverfe and conjugate Axes of its Reprefenta- tlon. Of the Torus he makes a perplexed affair, for which, he gives a loi g, alge¬ braic Demonftration; yet, the reprefentation given is vile, and the Method he pre- feribes, for projedling it, imprafticable. For Lines inclined to the Horizon as well as to the Picture, he determines the Vanifhlng Point with great propriety, and lays down its Diflance on a Line pa¬ rallel to the Horizon, in order to proportion the indefinite Line to its perlpedtive length, in the moft judicious manner; which, one would imagine, had been much caller applied to Lines in the Ground Plane, in the preceding Problems, where there is not the leaft attempt at It. In reality, one would be led to imagine from the 36th Figure, that he was thoroughly acquainted with every requlfite for a general and univerfal Theory; but, in many refpefis, his Pr.aflice is deficient; and, although the Diagrams feem to point out the ufe of other Vanifhing Lines, yet it does not appear that he has the leaf! notion of any but the Irorizontal. Here follows a Chapter in which is nothing remarkable, containing four Prob¬ lems, for finding the Reprefentations of Figures when the Diftance of the Eye is fuch, that its place cannot be denoted above the Horizontal Line, nor laid down thereon ; or, when the Objedt is fituated very oblique, fo that the Center, or Point of Sight, is confiderably out of the Piflure; (an abfurdity for which no Expedient was neceflary) alfo, for finding the Reprefentation, when the Pidture is fituated above the Eye, yet vertical. The folution, in the former Cafe, is fuch as one might expedl, from his firft Problem; viz. by taking any portion of the Diftance, at dif- cretion; but, having found two Angles of the Figure, the reft are determined from them; after which (Chap. 5.) he treats of the inclined Pidlure. This Chapter con¬ tains fome Problems, for finding the Vanifhing Points of Lines perpendicular, or inclined to the Ground Plane, on an inclined Pidlure, as elegantly conftrudled, as fully and briefly demonftrated as any in B. Taylor; in which, the Diftance of the Vaniflrlng Point is laid down, and the Lines proportioned truly geometrical; in- fomuch that, there feems to be nothing wanting for a perfedlTheory, or, but little left for his Cotemporary to do, in order to perfedl it. In the next Chapter, for horizontal Pidlures, he feems to have loft fight of the Principles he has hitherto proceeded on ; for, in refpedl of Lines perpendicular to the Pidlure, the operation, though ingenious, feems to have no Affinity with the foregoing, in a fimilarCafe; and he calls the Center, or Point of Sight, their accidental Point, as for Lines in¬ clined, to the Pidlure. Refpedllng Shadows, which are the Subjedl of the 7th Chapter, (the whole of which is contained in five Problems and as many Pages) this Author has done little or nothing, to any purpofe. The 8th, is wholly mechanical, intended to fhorten Operations in Perfpedtive, by means of Rulers and Threads, on the Principle of Fig. Z, Plate II. Fixing the edge of a ftreight Ruler, by a Pin, at one end, in the Point G; then, a Thread being fixed in the Point F, which, after being put through a fine Hole, near the Point of a Needle, is carried round a Pin, fixed in E, with a fmall Plummet to keep it tight. Then, A being a given Point to be reprefented, he puts the point of the Needle at A; the Thread Aiding freely through the Eye, and over the Pin at E, by means of the Plummet, the Thread forms the two right Lines, AF and AE; the edge of the Ruler being brought to B, where AF cuts the Bafe Line, he marks the Point in which it crofles AE (at a) which is the reprefen- tation fought; and thus every Angle of any right lined Figure may be obtained. Sea. IX. REMARKS ON H. DITTO N. 89 This is indeed a wonderful Expedient; giving all the merit due to the conftruaidii of the Figure, which is really ingenious, feeing that there are but three Lines to be drawn, in the Procefs, or but one (AE) a Ruler applied to A and F gives B, and again, to B and G, marking where it cuts AE, the bufinefs is effeded; fo that, it is not worth while to fix fo much tackle to effea it. _ , There are more Apparatus of a fimilar nature; one of which, on the principle of Prob. 28. Sea. 5. B. 3. on the praaice of Perfpcaive, by means of the Direaing Plane is really ingenious; but they anfwerno ufeful purpofe, becaufe, all that can be effeaed by fuch Apparatus is, merely, to find the reprefentation of a Point, bv which means, plane Figures may be reprefented; but they are as readily, and vvith greater accuracy performed by Rule. Solids of the fimpleft conllruaion could not then be deferibed by them; becaufe they knew not the ufe and application of aiw other'Geometrical Plane, but the horizontal; and, for any thing_complicated or ornamental they are totally ufelefs. The ninth, and laft. Chapter is on the ufe of Perfpeflive in Dialling; after which is a Defeription, with the Theory and Ufe of the Camera Obfeura, of which there are two different Conftru£l:ions; all which are foreign to my Plan. ^ ^ . Thus I have given a candid and impartial Account of this Elfay, in which I have bee’n more circumftantial, as it far excels every antecedent Work, in refped of Theory and Principle; but contains no ftriking Examples to fet it off, yet more real knowledge of the Subjeft than is contained in them all. THE firft EnglllE Author I have met with, in any degree of Reputation, is Humphry Ditton, Matter of the New Mathematical School, ChrifPs-Hofpltal, who publKhed a fmall oTavo TraR in the Year 1712; but one Year after Grave- faude vvith whom had he been acquainted, he certainly might have made a much better Work of it, being greatly inferior, yet ’tis not void of Merit; and indeed, more may be attributed to him on that account. Yet, as thofe Gentlemen (between whom, generally, fubfifts a fettled Envy) have the earlieft Intelligence of each others Produflions, ’tis not improbable that he had feen it. Sometime ago, on a curfory furvey of this Tra£t, I conceived a much higher opinion of it, than 1 find, on a clofer Infpedhon, it deferves. He fets off on a rather extraordinary Hypothefis, after the laft Definition, of which there are twenty and two ■ feme abfurd, feme redundant, others pertinent, yet frequently exceptionable and 'partial. The firft fays “ Perfpedlive is an Art which teacheth how to delineate the true Appearances of Objefts,” &c. Gravefande fays, Reprefentations. The Dif- tance of any Point in the Ground Plane (the 9th) from the Table (the PiSlure') is partial; DireSi Parallel Lines, Oblique Parallels, and Pranfverfe Lines (in the three followi'ng) are fuperfluous, or exceptionable, as there is no ufe in the term Parallel, in the two firft ; fave that, in the firft cafe, all diredl Lines would be parallel; but not according to his Definition, which, he fays, “ are fuch as cut the Ground Line at right Angles.” Now, Lines may be perpendicular to the Ground Line in every direftion in Planes to which it is perpendicular. By tranfverfe Lines, he means only fuch as are parallel to the Piaure, but, partially, in the Ground Plane. The 12th is in thefe Words; “ Radial Lines, I call all fuch as run up from any Points in the ground Line, to any Perfpeaive Focus, whether the Point of Sight, or acci¬ dental Point,” &c. In the firft place, Radial Lines is an improper Term, for inde¬ finite Reprefentations; Perfpeaive Focus is too general, to take in every Vanilh- ing Point ; as it c.annot, with propriety, be applied to any but the Point of View, i. e. the Ce'nter of the PiTure. In the 15th he fays, “ The Accidental Point is a Point which bears the fame Relation to fuch Parallels as are oblique to the Ground Line, as the Point of Sight does to thofe which are perpendicular to it,” dec. It fliould have been Accidental Points, in the plural (that is, Vaniftiing Points) unlefs he had laid of a Line; but why to thofe Parallels, only, that are oblique to the Ground Line? what has the Ground Line to do in the Cafe? befides, Lines perpendicular to the Ground Line, may be very oblique to the Plifture, and confequently have Z Accidental Humph. Dittos. 1712. 90 Sea. IX. A PARALLEL, Plate X. Accidental Points; but furely. Lines in other horizontal Planes may be in¬ clined, as well as m the Ground Plane, in which he means to confine them, wholly, in his Definition. By point of Incidence, in the 17th, he means the Seat of a Point on the Piaure; but ftill on the Ground Plane, to which he is uimecefliirily partial. The 22d defines the Optic Angle; after which, he makes this curious Remark “ According as this Angle is bigger or lefs, fo we commonly fuppofe things to ap- pear bigger or lefs to us. And it is moft certainly true, that they do (o, in Varie¬ ties of Cafes; But that they do fo in all Cafes, is as certainly falfe,” &c. In the Inftance he brings to prove this alfertion, I think he is by no means juftifi'able; for 1 can fcarce admit it to pafs under the denomination ol Things, for all Subllantives are not Things; as Time, Space, Diflance, &c. I lhall give his own Example as follows. ^ ’ Fig. 26. Let AB be a Speaator, the Eye at A, and BD a continued level Surfiice ■ let BC be equal to AB, and ABC a Right Angle ; then, BAC, ACB are e.ach half Right; wherefore, if AD be drawn, to any diflance in BD, coufequently, the An¬ gle CAD IS lefs than BAC, (for if AE be parallel to BD, the Angle E AC is equal to BAC) yet the Space, or Diflance, CD appears greater than BC; bur, if the Diflance does, I prefume he will not fay, that the Line (which is a Thing) does; I doubt not the Diflance will appear greater, although the Angle is really lei's; but of that, the Eye is not competent, but forms a judgment from Experience, only. The firfl Propofition is this: “The farther Parallel Lines are produced from the Sight, the nearer they feem to approach to each other ; provided the Eye be placed any where, between the faid Parallels;” and then he adds, “ This is true whether the Eye be in the fame Plane with the Parallels, or whether it be raifed above or deprefled below them;” but the third is mofl extraordinary, viz, ‘‘ If the Eye be fituated any where without the Parallels, they will feem to go farther from each other (or the Intervals to widen) to a certain term of Diflance; and after that continually to approach each other." This very extraordinary Paradox he proves thus! Fig. 27. Let AI and BK be parallel Lines, and let the Eye be fituated at E; let FH be drawn between AI and BK, equidiflant from and parallel to them; draw EF per¬ pendicular to FH, and on F, radius EF, defcribe an Arc, ECD, curing the Paral¬ lels; alfo, take any Point, as G, on both fides F, on each of which, with the Ra¬ dius EG, defcribe the Arks EAB, EIK. Then, becaufe the Centers are all in the Right Line FH; AB, CD, and IK will be equal Chords, in unequal Circles; wherefore, if EA, EB, EC,&c. be drawn, feeing that E is in each Arc, and ECD has the leafl Radius (EF) confequently, the Angle CED is greater than AEB or IE K, which (if FG, on one fide, be equal to FG on the other) are equal; and therefore, the Lines AI and BK, appear wider afunder at CD, and converge'both ways, towards AB .and IK. It is obfervable, that, to the firfl Propofition, he fays, this is true, &c. as above- and here, the Premifes are, if the Eye be feated without the Parallels, &c. But he does not feem to confider, that, the Eye being in the fame Plane with them they appear but one Line, in the latter Cafe particularly, fo that there can be no Idea of Parallelifm in the Cafe; and in the former, although they are twodiflina Lines, being produced, they appear to approach direftly towards each other; and would, being continued, appear to fall into and conftitute one Right Line. But however it is certain, that if the Eye (in the latter Cafe) was raifed fomewhat out of the Plane, the EfFeft would be nearly'the fame; and is indeed a fingular Circumflance, that the Lines, being parallel, fhould appear wider afunder where they are farther diflant from the Eye. But this can only be the Cafe when the Eye is very near the Plane the Lines are in, and not poflible to take into the Optic Angle any portion of them, being extended on the other fide EF. The fourth is trifling and puerile; viz. “ All Planes above the Eye feem to link the more downwards, the further they are produced : Thofe that are below the Eye feem to rile upwards; thofe on the right hand to approach to the left, and thofe Sea. IX. OF THE ENGLISH AUTHORS. thofe on the left to the right.” I am at a lofs to know what is propofed in this ; H.Ditton ’tis obvious, to fight, that it is fo, and needs not a formal Demonftration. Here are deduced from it no lefs than ten Corollaries, as trivial and childilh as the Source they are derived fromj particularly the fecond, which is moft unaccountable ; it is too long to infert, but the fubftance is, that, for the reafons in the Propofition, in Churches, e. g. the Pavement from the Door, towards the Altar, need not be raifed, in reality; becaufe, as there is an Afcent, from the Principles of Optics, it ought not to be made more fo aaually, for various reafons, as abfurd as can poffibly be conceived. The fifth is, that the Reprefentations of plane Figures, parallel to the Pidure, are fimilar to their Originals. The fixth, that all the Conic Sedtions are only the perfpedive Reprefentations of the Bafe. The two next mean but little. The ninth fays, that, “ The Perfpedives of all Lines which are pa¬ rallel one to another, and not to the Ground Line, do run up into one and the fame Point on the Table.” After which he fays, “ This is the main and gi'eat Propofition in this Science.”It feems indeed, as if the greater number of Artifts gave him full credit for it. But he feems to have no notion of their riming down as well as up. Perfpedive is a poor Science if this be the grand Arcanum ; yet it is an eflential of it. There are no lefs than twelve Corollaries follow this Propo¬ fition ; the feventh propofes a Method, for determining where Lines in the Ground Plane converge, which is, to draw a Line from the Foot, parallel to the Parallels, and, from the Point where it cuts the Ground Line, carry up a Perpendicular, equal to the height of the Eye, &c. This is perfedly as Ubaldus does, as I have fliewn in feveral Inftances; but the tenth fays better; “ If an Angle be made at the Eye, equal to the Angle under the Sides of any Polygon ; the Lines contain¬ ing that Angle will Rnke {or cul) the Table in the Points, to which the Perfpec- fives of all Lines, parallel to the faid Sides, will converge,” &c. This is well meant; but I don’t find that he applies it to pradice. The eleventh Propofition is the molt elTential one, viz. “ Any portion of a direSl Line, contiguous to the Table, is to its whole Perfpeftive, as the fum of its length, and the Eyes, Dif- tance from the Table, is to the length of the whole correfpondent Radial.” But why of dired Lines only ? are not the finite Parts of all converging Lines deter¬ mined perfpedively on the fame Principle? The twelfth, if a Line be parallel to the Ground Line, its Perfpedive lhall be parallel to it allb; and the 13th that the Perfpedives of all Lines perpendicular to the Ground Plane will, if produced on the Table, be perpendicular to the Ground Line. But, why the Provifo, if pro¬ duced? what difference does that make in their Pofition ? or, what need was there for two Propofitions ? feeing that, in both, it refpcds Lines, fimply confidered, parallel to the Pidure, only; their Pofition, in refped of the Horizon, is a necef- fary Confequence. Six unneceflary Corollaries follow this Propofition; becaufe they are either the fame as in fome preceding Cafe, or they are wholly impertinent. The three remaining Propofitions contain nothing either ufeful or extraordinary, fave the 15th which is very exceptionable, as it is made general, but holds true in a particular Cafe, only ; viz. when the inclined Line is parallel to the Pidure, as the Tranfverfe is underftood to be. ^ Vf e now proceed to the Pradice, of which, I cannot but give an loftance of his firff elfort, with the Diagram anne.xed ; Fig. 28. is a true Copy of it, which is the moft prepofterous one I ever faw ; for which no e.xcufe can be alledged, for want of room, as is fometimes the cafe. The Problem is, to find the Seat of a Point in the Perfpedive Table. By a Point of Sight and Dlftance. The Eye is at A, the Point of Sight B, the Diftance C, the given Point F ; E G is the Ground Line, and C II the Horizontal. FD is drawn, perpendicular, and DE made equal to DF; then, the Radial, DB, cuts the Line of Dijlance, C E, in /, w'hich IS the Seat of F, as required. By Seat is meant the'Reprefentation. Now, although this Procefs is ftridly true, yet have I never leen a more abfurd Figure to illuftrate it. Firft, the Diftance, A B, is exadly half the height of the Eye, I. e. of the Space between the Horizontal and Ground Line ; and the obli¬ quity of the fituation of the point F is fuch, that B H is more than four times the Sea. IX. A PARALLEL, 92 H. Ditton. the Diftance; the confequence of which is, that the Optic Angle, being twice BAH is more than 150 degrees, which is, at leaft, three times what it ought to be; befides, the Diftance being laid down, on the other Side, ate, would deter¬ mine f more accurately. After this Figure follow two, taken from Guidus Ubaldus, Prop. 6. B. 2. the firft: method of drawing a Triangle, in Perfpeaive ; the theoretic Figure is inverted, but differs in nothing elfe; fare the horizontal Line being drawn, in both; other- wife, the praaical Diagram is a perfea Copy, in every refpea, though badly de¬ viled in the Original; but he makes more application to it. In the following Dia¬ grams, for plane Figures, are the moft dlftorted delineations imaginable; in one of which (the 21ft:) the Diftance is little more than a third part of the height of the Eye; by which means, the Perfpeaive of a direa Line (F W) is almoft double the Original. Now, as he gives no Rules for determining thofe matters, or points out the bad Confequences in making ufe of too Ihort a Diftance, how is It poflible for any Perfon to acquire a right notion of them, from fuch Works? without great, natural Abilities, ’tls not poflible. The firft Solid is a pentangular Prlfm, a moft diftorted Figure; which, by mif- take in fhading, exhibits a different Objea, turning its oppolite Faces towards us. What he has done in Solids is taken from Pozzo, particularly in the delineation of a Pedeftal (Fig. 27.) a petit, trifling Figure. We are told how to delineate Pyra¬ mids, regular and irregular Solids, Cones and Cllinders, perfpeftively, without a Figure to refer to, or fo much as an Example, how to deferibe a Circle, in Per- fpeftive; yet we are told, how to find the Axes of the Ellipfis which reprefents it. Such is the praftical part of this Work, even the delineation of an Icofaedron is deferibed without a Figure to refer to, a method I have never feen ellewhere; It is, with me, a matter of doubt, if he could have drawn the Figure he preferibes Rules for; but he prudently advifes, to place it fo as to be the leaft trouble. Here is a lame attempt at Anamorphofes, which he makes fubfervient to the pro- jeiSion of Shadows, by the projedlion of a Reiftangle (as it is called) on the Ground Plane; which is all that is done on either Subjeft. Refleftion on Mirrours is fome- what better handled, yet greatly deficient and imperfedt. Horizontal Perfpeflive, as he calls it, is of a piece with the reft; if we will take his Word for it, ’tis mucheafier, in praflice j but I find nothing done to juftify the Afi'ertion. On in¬ clined Pidtures Mr. Ditton criticizes on B. Lamy, yet without proving him to be erroneous; nor does he handle the Subjeft much better, rather more mathemati¬ cally ; for, in his laft Problem, to draw the Repiefentations of Lines perpendicular to the Horizon, on an inclined Pifture (which, he fays, is a difficulty) he con¬ cludes, after two Pages, talking of Points and Lines of incidence. Apices, Co- fecants, and Co-tangents &c. i. e. after a trigonometrical Demonftratlon, of no¬ thing (for he never refers to a Figure but once, to a Line Bo) with, “ After this, I believe there cannot be any difficulty remaining, to the Pradlice on inclined Pic¬ tures.” Three Problems follow, on Inverfe Perfpeftive; with an Appendix,, con¬ taining nothing material. On the fubjeft of inclined Pidlures, particularly, may be perceived the narrow- nefs of fuch contrafted Principles, as in this Work, compared with Brook Taylor’s; which are quite general, and regard not the pofitlon of the Pidlure to the Horizon. The Center of the Pidture is where a Perpendicular, from the Eye, cuts it; but here, he calls the Point, in which Lines in the Ground Plane, perpendicular to the Interfedlion, or Ground Line, converge, the Point of Sight, as in upright Pic¬ tures. ScHOL. P. 135. fays, “ All the differenceis, that the Line C B is, there, per¬ pendicular to the Table, and here oblique; which neceflarily arifes from the dif¬ ferent pofition of the Table, in this Cafe; but, in both, it is parallel to the Hori¬ zon, and where it ftrikes the Table determines the Point of Sight.” Such are the Notions here inculcated; which, with the Errors in referring to the Figures, want of Letters, fometimes Lines, and the irregular difpolition of the Figures, in the Plates (which occafion much trouble and lofs of time) and being badly devifed, render it, altogether, a poor performance. 4 IN^ Sea;IX. REMARKS ON BROOK TAYLOR; LL. D. and R.S.S. IN 1715, the World was favoured with the firft Produftion of this able Ma-Dr. Brook thematiciaii, in this branch of Science; to which, all future Publications on theTAv'LOK. Subjea (lave Ware’s Sirigatti, and Fergufon’s) are indebted; in reality, rerpecl- 1715. iiig the Principles and Theory, they all may be deemed Comments, of which; Dr. Taylor’s is the original I'exti This Work is a meer Pamphlet, in oflavo, of 42 Pages, entituled, “ Linear Peripeftive, or a new method of reprefenting, juftly, all manner of ObjeGs, as they appear to the Eye, in all Situations.” Heie it is neceflary, in the iirll place, to remark on a capital Error, in the Title Page; of which he is fenlible in his fecond Efl'ay. It appears, from this Title Page, that the delign of Perfpeflive, is to reprefent Objedls as they appear to the Eye ; a Circumftance which has mifled many, in their notions of Perlpedive; fo that, when they are informed it is not fo, they impute it to fome fallacy or imperfeftion in Perfpeflive; which I have vindicated from fuch Afperfions, and made clear, to Demonftration, in the 6th Sefl. B. I. of mv Treatife. 1 look on it, in this place, as an overfight, not as an Error as Judg¬ ment; for it does not feem probable, that a Perfon of his Knowledge in Optics could be fo far raiftaken. » In his Preface, or Addrefs to the Reader, he fays, “ In this Treatife I have en¬ deavoured to render the Art of Perfpeftive more general, and more ea'y than has yet been done. In order to this, I find it necelTary to lay afide the common Terms of. Art, which have hitherto been ufed, fuch as Horizontal Line, Points of DiL tahce, &c. and to ufe new ones of my own; fuch as feem to be more fignificant of the Things they exprefs, and more agreeable to the general Notions I have formed to myfelf of the Subjefl.” In this he has Ihewn great Judgment, for thofe Terms have really cramped the Ideas of Artills, in general, fo that, fome can never acquiie a clear notion of the Subjeft, on general Principles, as they ard laid down by this Author. Although I have faid that I cannot attribute the Error in the Title to an Error in Judgment, yet it is clear that he had not properly confidered, that the Repre- fentation of an Objeft, in Perfpeflive, is not the true Appearance of it, as is ma- nifeft from the firft Paragraph; in Seif. I ; where he fays, that, “ Perfpeflive is the Art of drawing, an a Plane, the Appearances of any Figures; by the Rules of Geometry.” This is manlfeftly a Definition of Perfpeflive, but a very erroneous one ; of which he muft have been fenlible, had it appeared in its proper light; for he certainly knew, that a Globe appears round, however lituated ; but if (as it cannot be doubted) he had any knowledge in Conic SeiSions, he muft alfo know, that the perfpeftive Repreicntation of a Globe is always one or other of them ; and; that its moft general Reprefentation is an Ellipfis, yet always appears round. Now, if a Globe, lituated obliquely, in refpeft of the Piifture and the Eye, be repre- fented as it appears, that is, round, and alfo of the fame apparent magnitude, in refpefl: of another, in the Center of the Pifture; then, the Eye being in the true Point of View, it is manifeft, that the one feen oblique would neither appear round, nor of the magnitude intended. For, the Doiftor fays, in the next Para¬ graph, that, “ to produce the proper EfFeift; the Light ought to come from the PiSure to the Spedlators Eye, with the fame Colour, ftrength of Light and Sha¬ dow, and in the fame Direliion, as it would do from the correfponding Points of the real Objeift, as if it were placed where it is imagined, for rather where it ap¬ pears) to be which could not be the Cafe, being reprefented as it appears ; be- caule, one of its Diameters being feen direift, muft fubtend a larger Angle than that which is at right angles with it, being feen oblique; therefore, it cannot ap¬ pear round, as the Objeift does, feeing its Diameters appear unequal. It is eafy to prove that it would alfo appear lefs than the Objeift, at the diftance it is feen; but, as a Diagram is requifite, 1 muft refer the Reader to Fig. 37. Plate 7, of the Trea¬ tife; SeS. 6. Art. 3. B. II. Page 93. In this Traft he gives but ten Definitions; from fome of them he deduces Co¬ rollaries, with great propriety, which are valuable Leflbns to the Delineator. The Point of Sight is omitted; the Center of the Piifture correfponds with what was A a formerly ■J- bea. IX. A PARALLEL, Dr.Brook formerly io oallca. ilis llrft 7 'lieor.em is, that “ the Reprefentation of a Line is 'fay lor. part of a Line pafling tlirougli the interfering and Vanifhing Point of the Original I.inc.” He deduces from it, firft, this Corollary ; that Lines which are parallel amongft themfelves, but not to tlie Piaure, have the fame Vanifhing Point; but not without the afhftance of his Definition of a Vanifliing Point. But, that the tvvo lollovviiig are dcducible from :thofe Premifes, I cannot acquiefee in ; the firft ot which is, that “ if the original Lines are parallel to the Piaure, and to each other, their Reprefentations will be parallel to each other and to the Originals;” but, if this be granted, the next will eafily follow ; viz. “ that the Reprefeiita- tions of plane Figures, parallel to the Pidure, are exadly of the fame fhape as their Originals it is rather an unfcientific expreflion, for a Mathematician. He lias no more than foui Theorems, and one of them is of very little conlequence. viz. that the Reprefentation of a Line is parallel to a Line pafling through its Direaing Point and the Eye; becaufe the applying it, in pradice, is neither con¬ venient nor expeditious; nor, in many cafes, pradicable, for feveral reafons. I fhall pafs nightly over the problematical part of this Eflay (having given the whole Subftance of it in the Work) which, in twelve Problems, contains almoft the whole Elements ,of Pradice, refpeding right lined Figures, and plane Solids. The Diagrams might have been better adapted, and ’tis pity he had not bellowed more care in rcvifing the Prefs; for, although lo fmall a Trad, there are many Life References; and the whole might be better digelled. In Example 3, Fig. 21, we are referred to Prop. 15, for the Operation, yet ’tis very differently performed; and, though founded on the fame geometrical Princi¬ ples, I am of opinion, that the affinity between them is but feldom feen. But what makes it Hill worfe, is the negligent manner in which it is done; for, inflead of the Angle being bifeded, as we are told, it is divided in the ratio of 2 to 5, as near as may be. The next is, in relped of its geometrical Principles, a very ele¬ gant Problem; but, the Diagram is lo ill conftruded, as to render it prepoflerous. jt is, to draw the Reprelentation of a Circle, through three Points given, per- fpedively, in the Circumference. In order to bring it within compafs of the’piate, the Diftance of the Pidure is taken about two fifths of the height of the Eye; fo that, if the Circle was compleated, being very large, in proportion to the Diftance, and lying .almoft wholly on one fide of the Center, it is drag’d out fo very oblique, as to make it appear extremely diftorted. However, the Principles are the fame; and, although he only fhews how to get another Point, (and that, notin the moft eligible manner) it is fufficient, to one converfant with the Properties of Circles. (See Prob. 11. Sed. 4. B. 3-) Example 6, Fig. 24, would (had the Figure been well proportioned) have been, at that time, a fine one. It is a Flight of four Steps ; but the Steps being, in height, not a fourth part of their width, and, being inclined, the Lines come fo veiy dole together, that the Diagonal, by which they fhould be determined, is not diltinguiffiable, the Angle being fo Imall. The Pidure is inclined, as is ufual, ill order to render his Principles general, fo, that the Center falls on the fecond Step ; for it is the fame whether the Pidure or the Steps incline; but, as the Cen¬ ter of the Pidure is confiderably below the Vaniffiing Line of the horizontal Face of the Steps, which he calls the Vaniffiing Line of the Plane of the Horizon, it certainly implies that the Pidure is inclined. This is the firft, and I think the only time he ever ufes that Term. The next Example is of a regular Tetrae- don, the procefs of which, from a Side given, he delcribes very concilely; but the Diagram is very ill conftruded. It contains three Tetraedons; one Ihews three Faces, another two, and the third ((hewing but one Face) is fo diftorted, that the whole is an unpleafmg Figure. The Center is given, but very injudicioufly ; and (as well ill the laft Example as this) we are told, that the Diftance is equ.al to the Line L, which is not to be found. After this Example, he fays, the Reader may exercife himfelf, in drawing the Reprefentations of the five regular Solids, and proceeds to (hew how their Plans and Profiles may be drawn, geometrically, without attempting to deferibe them 7 perlpec- Sea. IX. OF THE ENGLISH A U T H O R S. perfpeaively; therefore, they had been as well omitted, wholly, as they had no- t iiig to do m a Book on Perfpeaive ; and, although Highmore (after Mr. Hamil¬ ton) has tieated them, at large. I cannot think much of their utility ; or that InTr’he T ft P of PerLpedive more' facile. The eighth and the latl Example, is indeed a curious one, and truly worthy of its Author- but like the Platonic Bothes, it is of little ufe, which Lde mrovSo^ and omi It in the Treatile. However, as I have, fiiice then, coiifidered it mord ma- t^urely, I thought it worthy of a place m this Appendix; it is, to find the Repre- fentat.on of a Sphere, ha^ng one Radius perfpedively given, and its Vaihfhing Point; which, with a pra&cal Example deduced from it, I have given in the pre? ceding Seaioii. (Sec Figure 9 and 10, Plate 9.) ^ tne pre The Principles, given, for projefting Shadows (Sed. HI.) contained in three Problems and one Example, are too limited, and very obfcure; which, I am of hf'rh‘°P to much account. The laft Problem, though clear in the Premife,, is illuftrated (or intended) by a Diagram which, I muft^own I cannot comprehend, being the moft uncouth and perplexing Scheme I everfaw- inueed, his Diagrams, for Shadows, &c. are all trivial. As this Problem is fre- quen ly, necellary, in projeaing Shadows, and alfo, in finding the reflede™ Images of Objeds, on plane Mirrours, I (hall give it, as follows. ^ T/jc CefiUr and Diftance of the PlBure being given, and the Vanifiing Lines of two P&«er,_ With the Rfrefcntation of their common InterfeSlion ; alfo, ihe^Reprefentation L d,i, ZiffLf " 1 » Ji.a * R.fr./,IL .f i„ doJie in each other, this is already done, 111 Ftg. 16. 1 1.9. where the Seat of the inclined Dine FG, is determined on a horizontal and on a vertical Plane; I fliall therefore give an Example which s more fn Ei^ ’vo A R ^ ^ “‘ter. as well !s to the Horizon! In f ig. 29. AB is a given Line, whofe indefinite Seat is DF, on a Plane whofe Vanifhing Lme IS GH; the Center of the Pidure is S, Diftance SO; it is re¬ quired to find the Seat of AB on another Plane, whofe Vanifhing Line is GI- the common Interfedion of the two Planes is FG. ® e is ui, FiiH K and L, the V.mifhing Points of Lines perpendicular to each Plane, whofe Vanifting Lines are GH and GI: draw KL,\vhich being produced! cutT the yanilhing Lines at H and I, the Vanifhing Points of Lines per^icuLr m FG in each Plane. The Seat of a Line on any Plane, being obrainerby Perpen: diculars to the Plane, therefore draw AK and B K, curing DF at D and^E- confequently, AL and BL reprefent perpendiculars to the other Plane; then, be- DH H "" Lines perpendicular to fS draw ^ .L’L being drawn is the Seat of AB on the other PlaL. it cuJthe'pLr iTFi h“d ^AP’ “n L, the Point where s the Plane it FI be drawn, AB produced cuts it at M, which is where it ''Tf !he“vififL ’''^^ 'be fame Point. ■ I! ^“‘“*bing Line GI had palled through K, the two Planes would be at nght aisles; but, as It ftlls without, the Angle is obtufe towards the Pidure. At No. .. GI falls within K and therefore the Angle is acute towards the Eye, and he given Line, AB, inclines the contrary wa}', or reclines from the Pidure- and 'be Point to which its Seat, In thele Diagram^ FG, the common Interfedion of the two Planes falls be¬ tween the two Vaniftiing Lines, which is the moft rational, but Dr Tavlor irives tt without- and the pofition given, of the Seat of the Line, is’fuch as renders it S! four* sldir^n Sfl becaufe I think it is irreconcilable. I lie tourtU bed.on, on Refledions, is very concife, comprized in three Paves and "f. So irfUiT " "'■’if''' ‘i ''«■ 39. oon..i“l.o¥»i„”, yet art Lr fho.t of what is neceffary. to make it clearly underftood. The fifth, and 95 Dr. Brook T.aylor, Fig. 29. 96 Sea. IX. A PARA L L E L, Dr.Brook and laft Seaion, on Inverfe Perlpeaive^. is not much more copious, but is fuller on Taylor, the SubieT, and contains all that is efli-ntial in it. This Imall TraT lias nothing ill the Places to embellifh and fee it off; here is no ornament, to pleafe the Eye^ nothing but limple geometrical Diagrams, which are by no means ftriking, in eighteen oiSlavo Plates; but they contain more general Principles, and (to thole who have taken the trouble to inveftigate them) inculcate more real knowledge of- Perl’peffive than all that had, before, been publilhed on the Subjeef. The loth Plate, and Fig. 27. in the ninth, are of no ufe in the Work, as they contain the geometrical conftruftion, only, of the three laft regular Solids. 1 N the Year 1719 he publifhed another Trafl, not a fecond Edition of the former^ but a diftind and leparate Work, in 70 odavo Pages, with a copious Preface (the former having little more than one Page) ; 1 could wllh to tranferibe the greateft part of it, ’tis lb very pertinent. He begins with “ Conlidering how few and how limple the Principles are, on which the whole art of Perfpedive depends.—I have often wondered that it is ftill in fo low a degree of Perfedion.” And, fo long after he has publilhed thole firaple Principles, and lo many, Ibme voluminous, Com¬ ments on it have been fince publifhed, were he now living, he would find more caufe for Wonder; that he is, at this time, fo little underftood, by thofe, to whom it is more eflentially neceffary. “ Some Books, on the Subjed, he fays, are very- voluminous, but they are made fo by a tedious explanation of common things, or by a great number of Examples, and a great variety of curious Cuts; which indeed make fome of them valuable; but they convey no Inftrudion, or Improvement in the Art.” Here he has an Eye on Pozzo, and fpeaks juftlv of it; for 1 know no other, exifting then, to which it can be applied, lave the fecond and third Parcs, of the Jefuit’s, refpeding curious Cats, the ocher are fine. “ In this Book I have done my utmoft to render the Principles of the Art as general, and as univerfal as may be;” and he has fucceeded in it, for it is not poflible they can be made more general. The objedions which, he finds, have been made to his firft Ellay induced him to publifh the fecond, in which he has made the Schemes more ornamental; which prove, evidently, the great advantage his Principles have, over the common Rules, by abridging the Procefs, and divelling it of a vaft confufion of Lines ; yet, that is ftill, and ever will be, a grand Objedion, which deters many from the Study of it; being too indolent to bellow much pains, and not having a fund of Geometry, fufficient for the inveftigation of his Principles; for want of which, they cannot perceive their excellence, nor feel a true relifh for them. •“ Perfpedive (he fays) is more particularly neceffary to the Art of Painting; a Figure not truly drawn does not reprefent what is intended; fo that a Pidure, which is faulty in that particu¬ lar, is more blameable than a Compofition in writing that is deficient in Grammar; yet how many fine Pidures, highly valuable in other refpeds, are entirely faulty in this. Indeed it is fo very general, that I do not remember ever having leen a Pic¬ ture entirely without it; and what is more to be lamented, the greateft Mailers have been the moft guilty of it, whofe Examples make it Ids regarded, but the more to be lamented, and requires more Care to prevent it in future.” The grand Caufe, he attributes to the wrong Method taken in their Inftrudion; for which, he would recommend it to the Mailers, to begin their Inllrudions with the technical Parts (that is, the geometrical) before they are let loofe to follow the didates of their uncultivated Imaginations; in which he is certainly right; for, having no judgment of their own, nor Rules to corred their rude Sketches, which are the refult of a fpontaneous and luxuriant Fancy, they are hurried into the greateft Abl'urditiesj owing to their not having a right conception of the difference between the appear¬ ance of the real Objed and its Reprefentation on a plane Surface. Nothing (fays he) ought to be more familiar to a Painter than Perfpedive; for it is the only thing that can corred the Judgment, and aflift the Invention. The inventive Part is common with Poetry, volatile and undigefted; of which, the Pic¬ ture is but a Copy, of the Defign formed in the Imagination. The executive Part is wholly confined, and ihould be tied itridly to the Rules of Art, which cannot. Sed.IX. OF THE ENGLISH AUTHORS. on any account, be dilpenfed with; by which, theArtift ought to govern himfeJf, and regulate his Defigns, and not to take any liberties whatfoever; tor what is per- teQly agreeable and juft in the original Objeft, can never appear defeAive in a Pic¬ ture,” on which thofe ObjeAs are cxaflly copied. He fliould.have added, when the lituatioa of the-Objeft, the diftance and pofition of the PiAure are judicioully cho- ■fen; of which, many of his own Examples are glaring Inftances to the contrary. An ObjeA, being well proportioned in all its parts, can never appear diftcited, nor .offend the Eye in any Point of view; but being delineated on a Plane, without due regard to its fituation, to the Eye and to the.PiAure (tliough truly defcribed, by the infallible Rules of PerfpeAlve) may ixeverthelefs appear extremely diftorted and prepofterous, when viewed direft; as in Fig. 8. .Plate 8. which (though an Ana- morphofis) is a regular PerfpeSive of a well proportioned Vafe; and, being fecii in-the true Point of View, exhibits a true appearance of the original ObJeA. In the firft Definition of this fecond Part, he has correAed the Error of the former, and,fays, that PerfpeAive is the Art of defcrlbing i\\t Reprefentations ai ObjeAs (in the other it is Appearance^) on a plane Surface. We have, here, nineteen Definitions, not difpofed in the moft regular order; chiefly the fame, in fubftance, as the other, with fome additional ones, particularly the Point of Sight, the only eflential one. He does not deduce Corollaries from them, as before, but enlarges, and new models his Theory, which is preceded by four Axioms and a Lemma. The firft is this, that a Line drawn from the Center of the PiAure to the .Center of a Vaiiifhing Line is perpendicular to the Vaniihing Line. This, I have made the 7th of the ad, the 8th of the ift Impreffion ; hav¬ ing, previous to it, given a full Theory of Vaniihing Lines, their AfFeAlons, and Pofitions in refpeA of other Lines, and, in fome Cafes, of each other ; the lecond is not eflential; the third is the 12th of mine; the fourth is the ninth of the 2d; the tenth of the ift Impreffion ; for, I look on tire parallel pofition or Lines to be the fimpleft; ’tis certainly the eafieft in praAice, to a young Student, and for that reafon ought to be firft difcufled; the fifth, that the Reprefentation of a Line is parallel to its DireAor, as it is not of much confequence, in praAice, I have made the laft. The fixth, that the Vaniihing Line, &c. is parallcd to the IiiterfeAing Line, being the firft property of Vaniihing Lines, nceceffary to be inculcated, 1 have made it the 2d of the 2d, the 3d of the ill Impreffion. The 7th and 8th are in the.ioth of the 2d, the 9th of the ift Impreffion ; for, being almoft feif evident, and either being underftood the other is deducible, it was not necelfary to make two Theorems of what might be comprized in one. He has reduced, here, the moft eflential one, in PraAice (the .fourth of the full Part; the 13th of mine) which determines the Ratio of the leveral parts of Lines, divided perlpeAirely, which are not parallel to the PiAure, to a Corollary, troiu the fixth. Nor has he, any where, a moft neceflary one (the nth of mine) tor determining Vaniihing Points; which demonftrates, that the Radial of a Line, producing its Vaniihing Point, makes the fame Angle with the Vaniihing Line, as the Original Line makes with the InterleAion. Here are fevcral Corollaries de¬ duced, which I have made dlftinA Theorems; for they do not appear, to me, deducible from thofe Premifes; as that above, fimply, from the Parallelilm of the Vaniihing Line and.InterfeAioii, &c. The problematical part of this ElTay is illuftrated with fomewhat more ftrlklng Figures; the firft Elements differ very little, but he has extended the Principles more, to inclined PiAures, and Planes in general, in the 14th and three following Problems.; but the Application of it, in the iSth is mecriv delcriptive; for, in the following Example, iii projeAing the Dodecaedroa, I think he Iwerves from his own Principles; the Excellence of which conlills, chiefly, in determining the pet- IpeAive lleprefentations of ObjeAs, by means of the Vaniihing Lines and Points, of their leveral Faces and Sides, and not, as here, by a perfpeAive Plan and Ele¬ vation; which, though not repugnant to his Principles, have a near Affinity to the Method ui'ed by Pozzo, and other old Authors. In this ElTay, he has given two .Methods for defsribmg a Circle perfpeAively ; but neither of them is praAicable, J 5 .b when 97 Dr. Brook Taylor. 98 Sea. IX. A PARALLEL, Dr.Brook when the DIftance is confiderable; and there are much readier, or more praaical 1 aylur. Methods. He has alio given fome Examples for projeaing Shadows, and for Refjcaions on Water, and Mirrours, of which there are none in the former; but he is not very explicit in either. This Traft is not divided into Seflions as the former; but here, at Page 54, he makes a fecond Part, on Inverfe Perlpeftive, comprized in fix Problems|^ and but five Pages; the whole of which is in the fitch Sedflon of his firft Effay. He con¬ cludes this Work with an .Appendix, deferibing a Method, for projedfing or curved, or irregular Surfaces, by means of a Torch, which is to little purpofe. After which, is propoled a Theory for mixing Colours, to be pradlifed by Painters, on the Prin¬ ciple of the prifmatic Colours, by Sir Ifaac Newton ; whicli, I am perluaded, was never yet reduced to Pradlice, and moll probably never will. He has entitled this 2d Part, New Principles of Linear Perfpedfive, or the Art of Deligning on a Plane, the Reprefentations of Objefts, &c. thofe Words, as they appear to the Eye, h<‘w<^oas\\XtA\ but, had he conlidered it as an Error, he Ihould have cautioned his Readers againft it. It was the fate of this Treatife, alfo, to be overlooked, and negledfed by tbofe, for vvhofe ufe it was chiefly intended; fo that, finding it was but little read, and the Principles, on account of its brevity, and the mathematical drels it appeared in, not being applied to pradlice, the Dodlor (if we may credit Prof. Cowley) Intended to publifli another; and, in a more familiar Eflay, to (hew its pre-eminence above all others, and adapted better to the capaci- tip ot young Artifts; which his Death preventing, that Age was thereby deprived of the advantage of fo perfedl a Work, as might be expedled from his great abilities; which, however, has been abundantly compenfated fince, and perhap.s, better than he could have done, p’or it frequently happens, that another Peribn, leeing the Deficiencies of an Author, may difplay the Principles he has fet forth, to greater advantage than the Author himfelf was capacitated to do. Remarks THE laft ElPay of Dr. Taylor’s was publifhed in 1719, and nineteen Years after, on Mr. i't ( 73 ^’ appeared a colollean Work, by J. Hamilton, Efq. F.R.S. between which Hamil- Periods, I don’t know of any other Publication on Perlpedlive. This Work is, TON, very properly, entitled, A Complete Body of Stereography; it is dedicated to Sir 1738. Joleph Jeklll, Knt. M.ifler of the Rolls; to whom he gratefully acknowledges great obligation, for puting it in his power to collefl the fcattered Fragments of a Work, which was begun, and had been carried on during the Recefles of Bufinefs; and, but for him, had perhaps never been in a fituation to vifit the World. He dates his Dedication from the Six Clerks Office; from which I conjcflure, that he praiftifed the Law, and that his Patron had put him into that Office, in Chancery. This Work is indeed a mofl: flupendous Produdlion ; but unfortunately for its Author, I fear, that his Reward was by no means proportioned to the Labour attending the execution of it; I am in doubt it he was refunded the Expence attending the Publication, much lels paid for his Time in writing, digefting it into the order it appears in, and reviling it, from the Prefis, which has been done with great care and attention ; inlomuch tliat, 1 never met with a Life Reference in it, altliough they are lo numerous. It is, to me, aftoniffiing how he ever got through the Work; tor, althougli I may lie thought an Enthufiaft in the Subject, 1 would nor, for any confideration, be obliged to perul'e the whole, with the attention re- quilite to a thorough liiveftigarion ot it; for, being entirely .and rigidly mathema¬ tical, there can be but little entertainment accrue from it. However, I candidly acknowledge, that I received information from it, in the Parts Iconlulted, and full fatisfdblion ; but, in all the 150 Plates, which it contains, there is not one ftriking or interefting Objefl; fothat, to go through the drudgery of it, without feeing what Ihould relult from it, in the executive parr, muft render it extremely irklbme. In his Preface, he feems fiurprized at the low ebb in which Perfpe^live then was, and although lo many Treatiles on it were rhen extant, that fo little inftruaion was to be obtained from them. He fpeaks of Brook Taylor’s, with relpea ; that fmall Trad containing more real knowledge in it, than all the voluminous Works he had coiifulted. 3 Se ^ P 7 '‘^'"g,"’h‘ch were ufelefs and undigefted, fo he though It would fecure him from little ill natured Criticifms; and he confeflbs hTs utooft EreA?'’'''7 r abundantly exceed Ins utmoft Expeflations (this he might truly fay, or any body’s elfe) for he had been fo fortunate as to have the Work fo approved, and recommended, by Gentlernen of great Genius and Knowledge, that he now began to think it fecure from public Cenfure, under thew kind and powerful Proteflion. This may be called MoJe/iy' but, being faidof fuch a Produdtion. rather favours ai Prefumption, in my opinion 1 he poia^rful Protea.on he had, might indeed be a means of recommending it "o that k hiT irt'efcToH''^^®'' ’i ^ r 'V''® ^ ^ffurl him that It has not efcaped private Cenfure, nor fome public; nor is the great good Confer Of this Produftion, although^a chafn of (fe Patr;rrr ft' f The public attack on ( < a- /) IS a proof that this is not my own private Opinion, whieby D d by 105 Jofiiua Kirby, ip6 Jofliua Kirbj. Ware’5 Sii'igatti. Sea. IX. A PARALLEL, by forae, may be imagiiieJ to arife from Spleen; than which nothing is farther from niy Heart, nor did 1 know the Author. On the contrary, it would give me pleafurc, to find that his Merit (fur which he was rew.arded) bore any proportion to the Reward; far furely, nothing can give greater Satisfaflion to a liberal Mind, than to fee yeal. Meiit patronized aird rewarded by thofe in Power. ..The Appendix contains fbme farther Obfetvations on Shadows by the Sun; -al- . ready twice handled in the foregoing Work. It leems as if he had made Ibmc new pilcoveries in that part; for, in it, he dilplays more of real Principle, in projefting tluin, than before; though he lays down no general Rule, and confines his Ex- iamples almoft wholly to perpendicular ObjeGs, or Lin.es; nor ever conliders their pofition to the Plane on which the Sliado,w is projeQed; though moft elTential. Next he fpeaks of the down Hill, or direft Pelcent, as having always appeared .of great Difficulty to Painters, and will, he fays, ever remain impraflicable, fince .in the nature of the Thing it is impoffible to be done. .Of this Matter I have al- .ready fpoken largely, in SeG. 6. Book II. Art. 8. Page 97. and have given another Specimen or Example, as a proof to the contrary, in this Appendix (SeG. 3.) in 'which I have made appear, that the fame Space taken on the PiGure (hall appear either to afeeador delcend; though not (as he fays finely., or) fimplv as fuch, but from the concurrence of Lines and ObjeGs fituated on, or adjacent to the Plane. A {light touch on Birds Eye Views, which is moll paltry; with the defeription of an Xnllruraent for taking e.xtenfive Views, of his own Invention, he fays, confifting of,a horizontal and an upright Scale; which I have deferibed Page 26, and the defeription of a Camera Obfeura, for the Pocket, concludes the Appendix. This Work is in quarto, containing 172 Page?, arrd-5.1 Plates, in the whole; jvilh a. Frontifpiecc, deligned and drawn by Mr. Hogarth, ’Tis a humorous,Piece, fhewiug the ablurdities a Perfon may be liable to, who attempts to draw without having forae, knowledge in PerfpeG'ive. As the ProduGion of that great Genius, }t, is entertaining; and, though abounding with the grollefl abl'urdities, poffible, niay pafs and pleafe; otherwife, 1 think it is a palpable infult, offered to common Senfe, -and tacitly calling the Artifts a parcel of egregious Blockheads. There is not a finiffied Piece in the Book, but the Malbns Yard and the Landfeapes; fo that, I queftion if the whole of the Plates were 40 Pounds expence. It was firft printed for himlclf, at Ipfwich, dedicated to Mr. Hog.arth, and publiffied ip the Year 1754. IN the famcYTar, and foon after Mr.Kirby publilhed bis firft ImprelTioii (1111754) Ifaac Ware, Efq. publifhed a Tranftation of Lorenzo Sirigatti (originally in Italian) which had been i.dvertized feme time before (about the time that Kirby’s made its Appearance) feting forth, that a Work, on PerfpeGive, .would fliortly be publifhed, on. the moft fimple Principles poffible, the eafieft to be conceived and applied to praGice. This was done (as I am informed) with intent to prejudice the fale of Kirby’s ; between whom, and Mr. W are, fubfifted a lettled Animofity. A .Pal- fage in the Preface, which is very fhort, feems to indicate the fame; for, he pre¬ tends that he is not Influenced by the hopes of Gain, arifing from the Sale of his T’ubllcation, having no expeGation of it; and I cannot attribute it, wholly, to pub¬ lic, fpiritednefs, adilpofition to benefit others at his foie expeuce, whatever pretences niiiy be made on that fcore, without fome Vanity, or Spleen, be gratified in it; yet, if we will give Mr. Ware credit for it, that was the chief if not the Ible motive fpr his publithing it, in which ,1 cannot acquielce, implicitly. - This Work Is in folio, comprized in forty-three Pages, called Chapters, t’nough many .of the Pages are not half full; a Plate faces every Page, the defeription of One being printed on the back of another; to fome Chapters there are two Plates ; die Figures arc unnecefl’arily large, and but .little work in them, fo that, it bad been better in a quarto Volume. There is nothing either ftrikiiig or interefting in if, being all plaiie’ Figures, and fimple ObjeGs.; a Violin, or other Viol, and a Gult- tar are the principal. As I have, in the firft. SeGion, given a full account of the Method here made life of (.is in Vignola) it is needlefs to dwell longer on this Work, \ 4 bich was, altogether, luidefcrving to be revived, at that time; as the Arts, 1 am ^^rfbaded, would iiot be much-improved,, or .benefited in it. NOT Sea. IX. OF TFIE ENGLISH AUTHORS. NOT long after this Work, by Mr. Ware, appeared, Mr. Kirby drew up a Par.rl. lei between the Methods of practice, according to Sirigatti, and Brook Taylor, whofe fuperior Method he had, fo lately, publilhed an explanation of; between wliich, it rauft be obvious to every one, there is no comparifon ; the one being perforrhed on the-moft perfeft geometrical Principles, the other is a meer mecha- nical Procefs, dependant on no Principle, but built wholly on the fuppofition that Villon is conveyed in a right lined Direftion, which is taken alfumptively, and not, by a Poftu'late, requefted to be gtanted. The true Date of this extraordinaty Performance I cannot afcertaln, as it is very rare to be met with, the Sale of it being fuppreffed. ,I remember having feen it, and -remember alfo, that I thought the Author of it difplayed more warmth than was necefliiry for the Cau-fe, and a greater lhare of Acrimony on its Author than 1 conceived him warranted in,- being ignorant of the Difference lubliffing between them; infomuch that, his Zeal, in the Gaufe he had efpoufed, hurried him into feveral Errors, and fome unbecoming, rather fevere Refledlions on his Adverfary, which retorted on himfelf, and clearly Ihewed him not to be that modeft Author, and inoffenlive Man, he was reputed to be. As I cannot now fay more of it, trom memory, I (hall-only quote a. few PalTages from the Monthly Review, for January 1758, to which I refer the Reader for a full account of if; it begins thus: “ The Author of thefe Remarks is informed, that Mr. Kirby hath the charaaer of a modeft and good natured Man ; if he dtferves this-charaaer, will it not be difficult to account for his manner of treating Mr. Ware, in this performance?— The alTuming air and fufficiency with which this Compater diaates, appear very unbecoming; and would be offenftve though his principles and his practice were without an error; but if his errors are apparent, and if he is miftaken, even where he exults in his own fuperior Icience, how ffiould fuch a Man be treated ?-The following citations from his own Book, in his own words, will (hew hovv he is difpofed to treat others in fuch cafes.” Here, Mr. Kirby cites a paffitge-from Sitigatti (Mr. Ware’s) refpeTlng the per- fpeflive Reprefentation of a Circle ; which, being an oval figure, called an Ellipfis, he thinks may be much ealier performed, by taking the greateft Diameter from the Sciftion-line, and the lefler on the vertical Seflion. After which Citation, he fays; “ That -a regular Ellipfis is the_ perfpeaive Re¬ prefentation of a Circle, is an abfurdity, I believe, not to be met with in any other Book on this Subjea-; for every one muft know (who knows any thing of Per¬ fpeaive) that the fore-part of a figure which reprelents a Circle is more round than the back part of it, becaufe the former is nearer to the eye' than the latter; and therefore, the figure cannot be deferibed by anv two -Dkimeters -whatever.’^ I well remember, though it is many Years (ince I faw this Performance, that this Para¬ graph was fmeared -all over with Ink, through which it Was legible ; which in¬ duces me to -fuppote that he, having difeovered his error, too late, had ferved all the remainder of the Copies fo; poor compenfation to his prefumptiye Arrogance, The Author of thefe Remarks, now, interrogates him, refpefllng the perfpec- tive projetftion of a Circle ; whether it is -net, neccflarily, that Seffion of the Cone of Rays, by the Pidlure, which produces an Ellipfis? &c. and adds. If this befo, then, according to his own Note, he knows nothing of Pcrfpective ; becaute no Pcrlbn can know what is -not, in the nature of the thing, to be known; con(e- quently, by his own argument, he ndlnng of PerJpeSiive. Now, what can be faid in vindication of Mr. Kirby, or, after Inch a proof of bis Ignorance of fo elfential a-part of the Science he has' heretofore taken upon 'him to treat -on, what opinion muft we-form of his Modeify ? h,is-it not the appear¬ ance of a Malk for Arrogance and Selt-conceit ? What poor, futile argument, (hat the hither part, being nearer the Eye, appears rounder than the oppohte; hefurely never confidered that the one is convex, towards the Eye, the other concave, which is the caufc of their appearing equally and fimilarly curved. All that caii.be al- . lodged in excufe for hint, in this, and, as I conjecture, what has led him into the Eirror is, that the reprefentation of any Diameter of a Ciicle isMpot the traufverfe 107 io8 Sea. IX. Kirby’s Parallel. A parallel, Ax^s of the Ellipfis which reprefents it; becaufe, the hither Semicircle, neareft the Piaure, has Its rejrrefentation, on the Piaure, larger than the other; but it does not follow, that the whole together is not a perfed Ellipfis. C.in fucha Perfoii be fit to write on a Subjed, and lay down Rules for others, vvhohas confidered it fo very foperhcially himfelf? To ward off the imputation of 1 lagiarifm, he acknowledges that he has taken great liberties with Mr. Hamilton • but iurely, he never examined the fecond Seaion, of the third Book, or he did not clearly comprehend what is there advanced on this Head ; where, although H It i^an abfurditv not to be met with elfewhere, he might have foufid the ablurdity (tf it be one) fully and clearly demonftrated. After leveral other true Remarks, on various Paffages, and quotations of very ungcnteel Rcfieaions by Mr. Kirby, on his Adverfary, in fpeaking of Shadows, he fays, ‘ it is irapoffible to find the Shadows, but on the Principles of Dr Tay- or; ,n «-h,ch he is greatly miftaken; for they may be found, or determine^ though W ith more labour, and have been, by various Authors. In refpedt of his own bhadows, die Author of thefe Remarks obferveg, juflly, that although they are truely projeded, relpeding the figure, or outline, yet, in every other refpedf efehLd Lai of Nature! He remarks on a manifeft error, in the reprefentation of his (Mr. Kirby’s') wind¬ ing Stairs ; and that the error in the Tetrahedon, by Sirigatti, is not owing to the perfpeawe piojeaion, but to the geometrical conftruaion ; on which Mr, Kirby o I erfpeflive s upon true principles, he would never have given himfelf the trouble ot publifhing the tranflation of a work which does not contain one true principle ; but is thoroughly divefted of all mathematical Da/a, and hath not even Tb"f^^i truely drawn, or which difcovers the leaft tafte or elegance.” Thefe laft words may, with juftice, be applied to his omi Work. - I the truth of Sirigatti’s Principles, the Author of the Remarks juftly observes, that, if by Principles he means Theory, there is no pretence to f Ts ’ if f that the praaice is falfe, he is miftaken, for though tedious. It is not falfe but, as I have heretofore obferved, more to be depended on, in f nevv Method, by Brook Taylor, which, in feveral places, he calls Method. And, for the atter part of the Sentence, “ thoroughly divefted o all mathematical data, he acknowledges his ignorance of the fenfe of the word Data, m that place, and juftly apprehends, that Mr. Kirby does not underftand the meaning of the Word ; and indeed, I am of opinion, that he made ufe of it for no better reafon than, imagining there was feme deep, and latent meaning couch^ed under it, he affumed, thereby, an air of mathematical Coiifequence. ^ 1 ftiall pafs oyer the Paragraph m which he remarks on Mr. Kirby’s preftiming to applaud Sir Ifaac Nevyton, in preference to all others; infinuatiiig thereby, that he has read, comprehend^s, and has compared hirp with others, elfe, how is he warranted to beftow fuch pra.fc on him? and take notice of the next ; in which he obferves, that, “ all perfpeaive reprefentations which are not produced by a f Alliance of the eye, will be falfe and erroneous.” And again, fpeaking of ‘’■A Lt know, I pre- wfw -fr *bat there was an«,^/o/a/fHff^^of choofing a proper diftance.” Now, If by proper Diftance (adds our Author) he means one nue and certain fond ’hff Demonftration, as he feems to do (and ought to naean nothing lefs, by what he afferts) there is no fuch thing in na- will he f ‘if* f^Aigned, but that, either nearer or farther off will be equally true; and that it is not owing to Diftance, which renders the Per- Ipeitive falle or erroneous. It is indeed certain, that one Diftance may be preferable to another, but it is entirely difcretioiial, and depends on the judgment of the Artift only; the truth ai i. is f.,erntly 5 of Sea. IX. OF THE ENGLISH AUTHORS. of the Projeaion does not, in the leaft, depend on the Diftance taken, though on Jofhua a prudent choice depends, in a great degree, the excellence of it, in the harmony Kirby, and agreeable difpofition of its feveral Parts; which I have exemplified, in various Inftances, and been very particular in. Whoever was the author of thefe Striaures (the above is but an Abftraa) which have, now, been twenty-four Years before the Public, he was well qualified for the Undertaking, and has difplayed great Judgment, mixed with Candour; but he has overlooked a Circumftance, which Ihews that (being intended as a Parallel) Mr. Kirby dealt very unfairly in it. For I well remember, that he crowded more Lines into the Diagrams of his Adverfary, and abridged his own of what were effential in them ; in order to make the other appear intricate and perplexed, com¬ pared with his; which is a piece of diflioneft Art, too frequently prafticed on fuch occafions. He concludes with, “ Indeed, the appearance of Modefty difco- verable in his firft performance, may have warded off the Cenfure which might have been paffed upon fome miftakes in that Work.—And pity it is, that in this latter Publication he difcovers fo much Arrogance and Self-conceit. It may not, therefore, be improper to remind him, that even Merit acquires wero charms, when attended by that graceful Nymph called Modefty. That Ignorance herfelf does not ftiock us, when ftie chances to be feen with that amiable Companion. But, when Ihe is obtruded on the Public by her ufual Affociates, Arrogance and Ob¬ loquy, a more difguftful appearance is hardly to be met with.” Mr. Kirby, Author of the foregoing Parallel, and the preceding Work on Kirby’s which I have remarked, feeras at this time to enjoy, unrivalled, the whole Field to Per- himfelf, without a Competitor. Being fuccefsful in the fale of what remained of the spective firft Impreflion after ferving the Sublcribers, a fecond was printed in the Year fol- of lowing, 1755 ; what number were taken olF I know not, probably five hundred, Archi- whkh were ten Years on fale; for a third Edition was publiftied in 1765 ; whichTECTURE, I prefume is not yet fold off. Mr. Kirby was one of thofe F.avourites of Dame 1761. Fortune, who are more indebted'for her Favours to Circumftances, and a lucky chain of Events, than to real Merit. Although the Work publiftied by Mr. Ha¬ milton fifteen Years before his, was infinitely fuperior, yet he was fcarce known; that Work not being at all calculated tor the ftudy of thofe who profefled them- felves Artifts, nor do I fuppofe that he was any Artift himlelf, which Mr. Kirby had fome pretenfions to ; and being introduced to the Body of Artifts, by the cele¬ brated Mr, Hogarth, he was received by them, as a Perfon qualified to clear up the deep Myftery of Perfpeflive, which was but little known amongft them ; and, in confequence of his reading three Leftures to the Society, then lately founded, in St. Martin’s Lane, they publiftied the following Advertifement. Academy of Painting and Sculpture, in St. Martin’s Lane : Jan. 24, 1754. Mr. Kirby, author of a work, intituled. Dr. Brook Taylor’s Method of Per- fpeclive made eafy, &c. has read three ledures (being the fubftance of his intended work) to the gentlemen of this Society, which appeared to them fo clear, fimple, and extenfive, that, in order to do juftice to fo excellent a Performance, they have unanimoufly given this their public approbation, and declared the ingenious author an honorary Member of their Body. By Order, F. M. Newton, Secretary. Being confidered as the firft who attempted to familiarize the new Principles of Perfpedlive, by Dr. Brook Taylor, and nothing better than the Jefuit’s being then extant, that is, known to them, it is no wonder that moft of them became Sub- feribers, and interefted themfelves in the undertaking, (which was not very enor¬ mous ; for I don’t fuppofe the whole expence was above jC-ioo') ; flattering them- fclves, that they would now become Proficients, in what they thought eflential to the Arts; and he was, luckily, fo much an Artift himfelf, as to be utterly averfe to mathematical reafoning on the Subjeift, and being mafter of fo much Finefle, as not to pretend to more knowledge than they, was a means of ingratiating himfelf into E e favour I lO Sea. IX. A PARALLEL, JoIIiua favour amongft them. As the World, in general, are influenced in fuch matters, KirLw. too much on credit, Inch a public Manitefto, of their Approbation, was greatly in his favour, and doubtlels was of Service to the Publication. But a more for¬ tunate Event was, that his Majefty (then Prince of Wales) being a lover of the Arcs, and fond of architeflural Drawing, was defirous of knowing fomething ot Perfpeiflive. Mr. Kirby was propofed, to teach him the Principles of the Art ; by which fortunate Circumftance, a foundation was laid for his future Fame. Being thus introduced cn the great Stage of the World, under the fanQion of the Societyof Artifls of Great Britain; obliged to Mr. Hogarth for bringing him out of Obfcurity, and holding him forth to public View, as the firfl; Mailer of his Profeliion ; in which he made no inconfiderable Figure. Elated with his great fuccefs, he undoubtedly thought himfelf qualified for lomething more aipital than his firfl Produdlion, which had already gone through two Editions. In fuch a Station and coulpicuous Point of View as Mr. Kirby now Ihone in, there was great realbn to expeft fomething extraordinary ; no com¬ mon Performance could now be difpenled with. The VVorld was not long igno- iiorant that luch a Work was preparing, as would outdo every thing of the kind ; when, lo! in 1761 appeared a Colofl'us indeed, of gigantic Stature, truly worthy of its great Author; adorned with Sculptures, by the moft eminent Artifls of the time, and dedicated, with great Pomp, (engraved on Copper) to the KING. In the Preface, he gives us to underftand, that he has treated the Subjefl: in a manner entirely new (which is certainly true) and, in the Title Page, he fays, by two Rules, only, of univerfal Application. “ So great and cxpenfive an under¬ taking (he tells us) he fhould by no means have attempted, had not a munificent Hand held forth its afliftance, and enabled him to do, what, otherwife would have been impradlicable. Under iuch favourable and happy Circumftances (he fays) even the moll indolent would be roufed into Adtion, and the moft unproraifing genius might be iulpired ; which, added to the lolicitations of his F'riends, and the reception his former Work had met with, he had certainly every poflible itrduce- - I menc for exerting his utraoft abilities, in the Service of the Public; and which, he avers, liad more weight with him, than lucrative confiderations.” Nevdr Author had a fairer opportunity for difplaying his Talents to the World ; and therefore, as he lays he has every inducement for exerting his .utraoft Abi¬ lities, We'may be allured, that this Work was his utmoft effort; for, although he has promifed (conditionally) that this Volume Ihould be tbllowed by another, I never yet heard that it had made its appearance, nor even attempted. It was Ids misfortune, uotwithftanding all thefe favourable and flattering Cir¬ cumftances in his favour, to produce a pompous Nothing; not worthy of notice by thofe who are underftauding in the Science, or Art, only (for Science it con¬ tains none, of his own). Had he, indeed, done all that might have been expefted, or lie promiled, there had been nothing left for me to, do.; lo far 1 am obliged to him. On a Survey ol this Work, in which, from the pompous manner of its being uihcred into the World, one would e.xpedl to find fomething very excellent, or at leaft ulefu! to the Arts; and fo indeed, we do, tor it contains Engravings of great merit; but it is to be lamented that the Defigns were not delerving fuch execution. In fa£l, the whole feems calculated more for Pomp and Show than real Ufe; for it is amongfl: the lall, of thofe which treat on Perfpeaive, that I would recommend to the Public. In relpedt of itSiTitlc (the Perfpeftive of Atchitedlure) I am forry the Author has not explained its meaning. Architcdlure being, here,' in the Genitive Cafe, it implies, that Perfpedtive is lomething derived from, or appertaining to Ar- chitediire; 1 never conceived that Architedure, in any wife included or compre¬ hended the Science or Art of Perlpedive. Architedlure, itfelf, cannot be called a Science, bat an Art, variable at dilcretion. Architetlure is the Art of Building; even the Orders of the Grecians are not, in themlelyes, Architedure, but decora¬ tions and embelliftiments of it, only; then, what affinity has Perfpedive to Archi- iciffure.? none at all, but that it is applicable to Architecture, perhaps better than to many other Subjects. The SedV. IX. OF THE ENGLISH AUTHORS, Ilf The Work now before me, although fo promifing in Appearance, is but little Jofhua known in the World, where it is fuppof'cd to be raoft neceffary; for which reafbn, Kirby, the Remarks w'hich I am about to make will anfwer but little purpofe; and there¬ fore, fliall be as brief as poffible, and defer a more minute Inveftigation to a more favourable opportunity, when more at leifure for it. But if the lame munificent Hand was held forth to defray the Expence (Society, at large, not being fufficiently interefted in it) there is matter for a large Volume, in order to explain, to correfl, and to retrieve Perfpedive from the Ignominy with which it is here treated ; and which, was the danger as great to the Community as to the Arts, apparently, I Ihould purfue it with fatisfadion; but, in many refpeds, it is fo. very infignificant, as to be below notice, and unworthy ot Criticilm, had it not been ulhered into the World in fo magnificent a Drelk and Equipage. Here is a curious Frontifpiece, defigned by Mr. Hogarth; but not in the fame ludicrous ftile as the former: It were to be wiflied that he had explained its mean¬ ing; for, being fymbolical, the meaning of it is not fo obvious as the other. To me it conveys the Idea, which Milton, fo poetically, defcribes; of the Angel, Uriel, gliding down, to Paradife, on a Sun-Beam; but the young Gentleman lias dropped off before he had arrived at his Journey’s End, with Palladio’s Book of Architedure on his Knees. A Ray of Light from the Sun, riling, over a dillant Mountain, is direfled to a Scroll on the Ground, on which are two or three fcraps of Perfpedive; over which, fupported by a large Block of Stone, is the upper part of a Scepter, broke off; the Shaft, very obliquely and-abfurdly inclined, 'fomewhat reftmbling the Roman Fafcis, and girt, above, with the Prince of Wales’s Coronet, as an Aflra- gal; through which the Falces rife, and fwell into a Crown, adorned with em¬ broidered Stars; this is the principal Objedf, but moft vilely drawn. The Ray pafles through a round Temple, at a conliderable diftance. which is alfo fallly re- prefented; the Curves being, for the diftance, too found, and confequently, the diminution of the Columns is too great. It appears to pafs over a piece of Water; on this Side, the Ground is fertile and luxuriant with Vegetation, abounding with Trees and Shrubs ; on the other Side, it is rocky and barren. What is indicated by this feems to be, that, where the Arts are encouraged, by the Rays of Royal Favour, they will thrive and flourifh; but where they are neglefted, and do not find encouragement, they will droop and languilh. The firft P.irt, containing 82 large, imperial Pages (the whole of which may, with much more propriety, be comprlfed in half the number,oflavo) is the deferip- tion and ufe of an Architeftonic Sector, by Mr. Adams, of which there are two Plates, one of each Face; a Limb of a Circle (fomewhat more than a third part) near af in width, the outer Curve 7 Inches Radius; with a Seftor 12 Inches loiig, and two wide; through which, near the middle, the Arch palTes. There are 33 Plates, fhewing the Application of this Inftrument, in proportioning the Orders and their feveral Parts, Impofts, Doors, Entablatures for Doors, Conloles, Balluf- ters, &c. for which, Mr. Adams is more obliged, than the Arts for h'ls acquifitipns ■to, Perfpedlive, the whole of which is comprlfed in 24 Pages. 1 fhall therefore pafs over this Part as fo much wafte Paper (for I am of opinion, that the Inftrunjent was never m:ide fo much ufe of fince) being entirely foreign to the Subje^f pf Perlpeftive, of which he propofes to treat; and confequently, fuperfluous in it. The fecond Part, with the fame Title Page as before, omiting the Title of each feparate Part, is thus entitled : “ The Perfpeffive of. Architeflure, a \Vork entirely new; deduced from the Principles of Dr. Brook Taylor, and performed by two Rules oiily of univerfal Application. Begun by Command of his prefent Majefty, when Prince of Wales. By Jofhua Kirby, Dcfigner in Perfpeftive to his Majefty. Volume the Second.” By which, it feems to be intended as two Volumes, yet the firft is wholly on .^rchiteflure, as performed by the Seftor. Here is no Preface to this Part, but that which is to the firft begins tbps: “ Whoever attempts to go out of the common road of feience, or to tread in any new and unbeaten path, mnft experft Inch a fcrutiii}' from the public, as is'confillcnt with the nature of his 11 ^ Sea. IX. A PAIIALL EL, Joftua fubjsa: and however trivial their opinion may have been thought by felf-fufScient Kirby, writers, yet I have always efteemed it the very bell, if not the only criterion, by which a modeft author would defire to be tried.” In this we have an obl’ique Complement to his own Modefty. “ All the figures, which are produced as gene¬ ral rules in this work, I have ventured to call my own.” Although 1 fliall not dilpute this Point with him, on the whole, yet is there nothing new or particular in them, being ufed not only by all the modern Writers, but alfo by the Antients He then adds; “ Now if any one (hould fay, that tny rules (ftriaiy fpeaking) may all be obtained from the ftudy of Dr. Taylor, I would anfwer, that the fame kind of remark will hold good againft every mathematician, that has wrote fince the time of Euclid. And I would at leafl: defire him to conlider, whether the digefting theorems into a regular order, deducing proper-corollaries from them, and illuf- trating them by new fchemes and examples, has not as juft a claim to the title of original, as any thing that can be produced in an age like this, when almoft every fubjea feems to be quite exhaufted.” I fhould imagine that this Pafliige alludes to his former Work, for here is no Science, as alluded to above, no Theorems or Corollaries deduced, in this Work, being wholly praaical; and although he refers to the other, fometimes, by Note, yet, in general, it feems as if he never had, or entirely forgot that he had, publillied any thing before, on the Subjedl, it is fo far Ihort of what might be expedled, feven Years after; fo like the Produdlion of a Per- fon wholly ignorant of the fcientific Part; for, what has any pretenfions to Science in It, he IS indebted to Mr. Cowley for it, by way of Remarks; in which there is nothing, but a tew Analogies of Proportion, fome erroneous. I prefume he means by the words, in an Age like this, fo barren of Men of Science, of Genius, and Let¬ ters ; for, lurely, he had no caufe to complain of the times, as not properly reward¬ ing, or giving due encouragement to Merit, where it flione fo confpicuous. In what he calls an Introduftion, we have thefe Words. “ It fhall be our bufinefs to ftrike into a new path, and endeavour to eftablifti Jucb principles for this part of Perfpefllve as fhall have a rational theory, and fully anfwer the end propofed by them. In order to do which, we will begin in a regular manner, and go on ftcp byftep, till w have fully illuftrated whatever lue lhall advance.” The title of this fecond Part, or Volume, is, A new Method of drawing the five Orders, ele¬ gant Strudtures, &c. in Perfpedlive, That the Method is new, may with trnth be faid ; but, fucb a Method as, I am of opinion, none but himfelf ever pradliccd, or ever will, if they are acquainted with Perfpeaive, on true Principles ; yet, al¬ lowing his Method to be new, he Purely does not mean to infinuate, that there is any thing new in the Principles of it, which he talks of eftablilhing on a rational Theory; he rather means without Theory, or Principle, like Sirigatti, whom he cenfures for his deficiency therein; but how much more is he cenfurable, for mak¬ ing fuch a poor ufe of fuch perfeft and infallible Principles? one might be led' to imagine, from this pompous Paffage, that he had juft refuted, and proved all for¬ mer Principles to be erroneous, and was about to eftablifh new ones, oh a faiional Theory. Poor Gentleman; I am afraid that, being intoxicated with the Confe- quence he now imagined to be vefted in him, the intenfe ftudy, and labour Of this aftonifhing Produflion, had Ihook, and fomewhat impaired his upper Wofks; what a ftyle is here to diiftate in ; fuch as (though it might have become) is not to be equalled, by Brook Taylor, himfelf; who, as he truly fays, finding Ele¬ ments and Principles of Perlpeflive, fo narrow and contradled’ he was obliged to throw afide the old, and invent new Terms of Art, in order to enforce, and ef¬ tablifh his new Principles. But what has Mr. Kirby done ? why he has, by his (Ignorance I cannot call it, but) Vanity, and Self-conceit, endeavoured to lap the Foundation of thofe excellent Principles, by aiming to level them to the Standard of his own Capacity; in treating fo valuable, and ufeful (it may not be Prefump- tion to add) fo noble a Science ia fuch a trifling, fo puerile, and contemptible a manner, as he has done in this, his laft Performance. But, what muft we think of Mr. Kirby’s Underftanding, who could attempt to draw fuch a Parallel, and expofe it to the Public’s Eye; that the fame Argu- 4 ment Sea. IX. \ O F T I! E E N G LISH AUTH ORS. ,, nient may be alledged againft every Mathematician fince Euclid, refpeaiiig the ori- Tolluia ginality of their Works, as to his Rules, which may {^Jlrickly [peaking be all ob- Kirby, rained from the fludy of Dr, Taylor ? I am aftonifhed at the unparalleled Effrontery of fuch Language ? Does he not know that the Mathematics were in their very Infancy, in the Time of Euclid. In Aftronomy they had fome knowledge; but how contemptible the Ptolomaic Syftem, compared with the Copernican, fo infi¬ nitely fuperior ; every Appearance in the Heavens fo rationally and clearly accoun- cd for, that it may alraofl be called original, compared with the grofs abfurdities of the other. But, was Algebra, Logarithms, Fluflions, or even the Conic Sec¬ tions. Trigonometry, and many other Sciences, lb much as thought on in thofe Days? Hay, allowing Euclid to have fome knowledge in Optics; yet the many Blanches, into W'hicli it has fince fhot out, as Dioptrics, Catoptrics, and, above all the refi, Perjpehiive, was wholly unknown. And would he draw any Com- parifon between the originality of his Rules as deduced from Dr. Taylor, and of thole Sciences, fince the time of Euclid ? what there is of original in them, 1 lhall next enquire. In the Introduftion he fays, that “ the mofi: general forms of architeflure may be comprehended under the Triangle, the Square, and the Circle; and. All thofe lines that are boundaries to the feveral parts of Architeaure, are either ftraight or circular. And again ; “ if the body of an edifice be a cube or parallelepipedon, %ts angles are right ones; if a prifm, its angles are acute; and if a poligon, then Its angles are obtufe.” His Definitions, or rather the genefis of thefe Solids (Def. 24) in his firft Work (for he defines nothing here) are on a piece with thefe. In the firft place, we are led to conceive, that a Cube is not a Parallelopiped, and that the Angles of a Parallelopi|ied are necelTarily Right; andly, we are to underftand that the Angles of a Prilm are acute, as if necefliirily fo; 3rdly, that the Angles of a Poligon are obtufe ; not always fo, unlefs regular. He does not feem to have any Idea that a Cube is a Parallelopiped, and a Square a Parallelogram; that all Paral- lelopipeds are Prifms, and that, whether they are right or acute angled; for he fays (Def. 24) that “ If a Line move uniformly about two angular Figures, &c. the Line by its motion flrall deferibe, if it has three Sides, a Prifm ; if four, a Cube or Parallelogram” (meaning a Parallelopiped); whereas, if the four fided Figure be a Trapezium, a Prilm will be generated, but not a Parallelopiped. This is almoft the general Idea, that the Bafes of a Prifm are Triangles, only; but even in that cafe, theie rnay be one right, or obtufe Angle. A Prifm is generated as he de- fenbes; for it is a Solid having, or contained between, two parallel, equal and fimilar, right lined Figures, and as many more Planes as one of thofe Figures has Sides, which are all Parallelograms. In this Definition of a Prifm (which is full, and perfeft) it muft be obvious that every fpecies of Parallelopipeds is included, and confequently, a Cube; for, if the two generating Figures are Parallelograms, of any fpecies, the Solid, generated, is a Parallelopiped; conlequently, if they are Squares, and the generating Line be equal to a Side, and moves perpendicular, a Cube is generated, without any contradidlion to the Definition given, of a Prifm. But I am led afide, or diverted from the Subjea, by this, not ulelefs, DIgreffion. “ An order of architeaure (as to its mouldings only) may be confidered as a number of Iquare and circular horizontal planes, of different diameters, laid in fuch a manner upon one another, as to give the peculiar lhape or outline of each ; and therefore to put the leveral mouldings into perfpeaive, nothing more feems necef- fary (as he fays) than two general or univerfal rules; viz. one for drawing the reprefentation of a fquare, and the other that of a circle; and thefe we have deduced from the principles of Dr. Brook Taylor.” An Order of Architeflure confifts of a Column, or Pilafter, with its Bafe and Capital (with or without a Pedeftal) and an Entablature, confifting of an Archi¬ trave, Frieze, and Cornice; the Mouldings of which, he fays, may be confidered, as above. By fquare Planes, laid horizontally one upon another, he muft mean, only, an Entablature around a fiiigle Column, or Pilafter; the circular Planes are to be applied in forming circular Mouldings, for they muft either be all Squares 114 Sea. IX. A PAR A L L E L, Jofiiua or all Circle?. All regular Mouldings are compounded of plane and cylindrical Kirby. Surfaces; in circular Mouldings, the Surfaces are, in feme parts, a kind of para¬ bolic Spheroid. And fo, his two univerlal Rules are, fimply, to put a Square and a Circle into Pel'fpeclive; what a wonderful difeovery is here; and thefe, with great fagacity and profound penetration, -we have deduced from the Principles of Dr. Taylor. What had he to deduce, I wonder? w.as not the Square, put into Perfpeaive, in the very fame manner, by the Jefuits, yea by Vignola, and others before him, long before Dr. Taylor exifted, or his Principles thought on ? and tor the Circle there was little to deduce. Now for the application of his general Rules. The firft Section begins with obfervations on the works of Nature ; that the forms of fome Objefts pleafe every Eye, whilft others create difguft; that he lhall not take upon him to determine from what caufe this arlfes, which had employed the Pens of fome learned and ingenious Men, but that none had fucceeded in the attempt equal to his very worthy and ingenious friend, Mr. Hogarth, in his Ana- lifis of Beauty, and that it would be prefumption in him to attempt it, after him; however, in drawing the perfpedlive reprefentations of Objeffs, the utmoft care flrould be taken to avoid dilagreeable and unnatural Forms; yet, excepting Plates 36 and 37, 50, 55, 63, 70, and 73, there are nothing but difagreeable and unnatural forms in the whole Book; not that thefe are altogether agreeable, yet they do not dilguft, although lome of them offend the Eye. The Dflinitions which Mr. Kirby has heretofore given of Perfpedlive is, to re- prefent ObjeAs as they appear to the Eye; which opinion, though falle, he is, at all times, ftrenuous to lupport. Is it not, then, ftrange, that almoft every Obje£l| in this Work, is delineated in fuch a manner, as is repugnant to thofe tenets? for furely, when two Faces of a right-angled Solid, of any kind, are feen, and almoft equally oppofed to the Eye, there can be no reafon given, why the horizontal Lines, fhould be reprefented by parallel Lines, in one Face, more than the other; for either may, yet be true Perfpeftive; but, although he has given all the Orders, and moft of the other Objefts in this oblique and abfurd pofition, he could not imagine that the Objefl. themfelves, appear fo, to the Eye; for they do not, but appear to decline, on each fide, according to the obliquity of the Faces to fight. See this matter clearly difeufled, in the 9th Seft. of the Treatife, Book HI. P. 198. PI. 23. “ In order to do which, we muft fix upon a proper diftance and height for the Eye, for if the diftance be too fmall, the apparent lengths will be too long; and the contrary when the diftance is too great.” What can he mean by the apparent lengths? of what? for it relates to nothing preceding this Sentence; by apparent, he means reprefentative lengths; and, I fijppofe, he means of Lines receding diredlly from the Piflure, on the Ground; but what fignifies the appearance of thofe Lines when a Solid is reprefented, whofe upright Faces hide them. “ It would be very difficult, if not irapoffible, to affigii one determinate diftance to be univerfally made ufe of; or fuch a one as ftiould anfwer on all occafions; bccaufe the different circumftances relating to piSiures, will frequently render a rule of this kind abfolutely impracticable. This is a truth known to every artift, that has had much praflice in the fcience of perfpedlive; and fuch I would afk, whether experience is not the moft certain, or at lead, the moft ready and convenient guide in this cafe?” What thefe circumftances are, I muft own 1 am not clear in; the abfurdity of the Expreffion, and of the remainder of the Sentence, are fo very- glaring, as renders a Comment on it unnecefiary. We are told to divide the height of the Pidlure into three equal parts, and through the loweft dlvifion to draw the Horizontal Line; which being divided into t\yp equal parts, the point of bifedlion is to be called the Center of the PicSlure; which fliould always if poflible (he fays) be in the middle of the horizontal line, meaning the Pidlure (refpedling the length) but, that a deviation is fometimes unavoidable; and which he has avoided, almoft generally, in this Work. Then, the utmoft width of the Pidlure, being taken, is let off, from the Center, on both fides, in the horizontal Line, which are called the Points of diftance; and then he fays; “ Now this is all that is previoully necelfary for an explanation of the fol¬ lowing Sea. IX. OF THE ENGLISH AUTHORS. lowing fchemes, which I call unlverfal rules for drawing the true perfpeaive ro- prelentation of any buildings,” &c. and this is all the preparation he makes, and all the Definitions that are given, in the Book; after which, follow four, more, general Rules, in order to the application of the former two. The firft is, to draw the reprelcntation of a Line parallel to the horizontal Line, and to divide it into any number of equal or unequal parts. The fecond is, to do the fame when the original Line vanifhes into the center of the picture; the third, when it vanifhes into the points of diltance; after which he fays, “ It is prefumed, that thefe three rules only will be fufficient for the reducing almoft every regular piece of architefture into perfpedtive, and in a greater variety of fituations than has hitherto been attempted.” Was ever anything equal to this Prefumption; or, fhall I call it. Ignorance? for if he but imagined what is here aflerted, he was ignorant indeed; feeing that, the three Rules, as he calls them, had been pradlifed -above two hundred Years. “ The firft rule is adapted to the fides of fuch build¬ ings as diredtly front, or are even with the Eye; the fecond to thofe that run direiftly from the Eye; and the third to fuch as are viewed angle-ways, fo that both fides have an equal degree of obliquity.” * After thefe three extaordinary Rules, he fays; “ But to make this work as univerfal as' poflible, I will add a fourth rule, which may occafionally be wanted, and which being infinite in its application (I am fpeaking of fquare buildings only) will anfwer for every degree of obliquity that can be propoled; however this needs not at prefent to be attended to, being of no uie in this volume. Having given ab for the bottom of one fide of any fquare building, to find the vanifhing points of both fides, and alfo the points for cuting off,” &c. The IntroduiSion ends with thefe words; “ however, this, in order to make the work yet more complete, fliall be followed by another volume, if we are fo for¬ tunate as to meet with the public approbation.” As this fourth Rule is made no ufe of, in this Work, as above, it leems as if he referved the application of it for the propofed Volume; fo that, owing to the Public’s ill-timed parfimony, or want of difeernment, in not feeing the great merit of this Performance, a Treafure, of unknown value, is loft to Pofteiity, alas! for ever; a lofs, which Time cannot repair. In fpeaking of the great inconveniency arifing from diftant Vanifhing Points, he fays; “this inconvenience may indeed be fomewhat removed, by analogical proportionbut even here the remedy will be almoft as bad as the difeafe; the fhorteft method feems to be that of making a fmall model, truly drawn upon paper, and then to transfer the feveral parts of this model to the piffure, by the common method of reticulation or net-work.” This muft needs be a very correft method (to wave the lofs of time, in drawing the Model) firft, to be done in miniature, and from that, to draw it at large. A long Ruler may be procured, at a fmall expence, and all this imaginary difficulty obviated; which, of all other, is the beft Expedient. He now applies his two general Rules to Squares, parallel and inclined to the Piifture (according to the three firft, of the laft four) and to Circles; then to Cubes and Cylinders, and alfo to a Globe. He fays; “ Mouldings may be conceived to be made up of many fquare and circular horizontal planes, like thin pafteboards of different widths, cut out, and laid upon one another, fo as to give the peculiar form or fhape of each moulding,” &c. and fo, by the prolix method of finding the Here, he pays hlmfelf a Complement, at his Reader’s expence, by a Note; the fubftance of It Is, Unlefs the reader perfectly underflaiids thefe general Rules, he may find difficulty in comprehending their various applications, in the following Examples. But, had he made his Rules more general, and expreffed himfeU in proper Terms, the difficulty of comprehending it had been removed. The firft com¬ prehends all Lines which are parallel to the Pifture, and is applicable to every Line in the Faces of Objefts which are parallel to it; which is more expreffive of what is meant, than thofe ftdes which arc even with the Eye, The fecond is applicable to all Lines perpendicular to the Pidlure, wliether they arc in the Sides of Buildings which run direSlly from the Eye^ or in any Plane that is perpendicular to the Pifture; and the third, to all Lines which aie inclined to the Piflure in an Angle of 45 degrees, let them Ire in what Plane foever, knowing where to place the Points of Diftance. t It is not eafily determinable, what he means by analogical Proportion; for, without Analogy there are not Proportionals. Analogy and Proportion, arc almoft fynonimoiis. ”5 Jofhua Kirby. \ '41 n6. Sea. I\'. A PARALLEL, Jolliua rcjirdentations of a number of Squares of different Diameters, as many Points are Kirby, obtained in the Curve, in order to deicribe it; and this is all that is effefted by it. The fame is applied to the Ovolo of a Tufcan Capital, and alfo to a Globe; for defcribing which, in the 8th Plate, he has nine Circles, drawn horizontally, and then delcribes a Curve over their extremes; which certainly, being truly drawn (but that is fcarce poffible) would give the apparent contour of a Sphere; bur, the procefs is not only very liable to error, but is alfo mofl: operofe, compared with the method I have e.xhibited, in Fig. ii. Plate 9. in which, as many Sedions m.ay be taken (at diferetion) as are neceflary, and deferibed with Compafles, and which, may be depended on; the other, being all Ellipfes, very excentrlc, and deferibed by hand, cannot. This he gives, for the perfpeftive reprefentation of a Globe, which is an Ellipfis, and performed on his own, rational Principles; or rather, it is the Principle itfelf, on which he proceeds, for round Mouldings; yet, in his former Work, Page 72. “ fuch reprefentations, not being in the Eye’s Axis (i. e. in the Center of the Pidure, he fays) lhade them how you will they can never appear like Globes to any common Speflator; becaule it is contradiflory to the Idea in general formed of rotundity ;” and I affirm that they cannot appear like Globes it not fo reprefented; for, being round, they would appear elliptical, though ever fq truly ffiaded; but let them appear like Globes, or Spheroids, the Idea of rotundity is ftill the fame. He now proceeds, in Book II. to the Delineation of the Tufcan Order, one feen direft, another in the moft common, though abfurd, pofition, ufually called an oblique front View; which means, that one face is parallel to the Piaure, the other, which is feen obliquely, is necelfarily perpendicular to it. His method of proceeding is by fuppoiing a fedion down the middle, i. e. through the Axis of the Column, parallel to the Piaure ; in which, the extremes of his imaginary hori¬ zontal Seaions, or Planes, which conftitute the Mouldings, are marked with Afte- rilks; a moft ridiculous and unnecellary preparation, in many cafes, impraaical le. Alter the fame manner, he proceeds through the five Orders, giving an Outline and a finifhed Plate of each; all in the fame abfurd pofition, without the leafl; variety, a Pedeftal with the Bafe, and an Entablature, with the Capital of the Co¬ lumn, in each Plate; the Eye being elevated confiderably above the Pedeftal, gives it an aukward appearance; all are feen on the fame fide, and all are equ.illy leen; fo that, the delineation of one Order, with the decorations of the other, had been fufficrenr. But, for what purpofe he has given the Outline, to everv one, is not evident; feeing that, he does nothing towards the Procefs but fet up the heights of the Mouldings, on the central Line; and, in one or two, he marks the extreme projeflures of fome of the Mouldings. Howev'er, to do him juftice, in the 25th Plate, his method for determining the Abacus, and the Volute of the modern Ionic Capital (for this pofition) is judicious and well devifed ; nor do I remember to have feen it lo done, in any other antecedent Work; for the procefs of which, he has no lefs than eight Figures (three or four had been fufficient) with a finifhed one. The Corinthian Capital is not well drawn, refpedling the Volutes and Cauliculas; but the Heads of the Leaves are vile; for, although fix of the upper tier are leen, and the Eye lb much below them, yet, the two laft turn their fronts towards us, inftead of being feen underneath, and the ftalks are as if in profile. In projedting Mouldings, he never attempts to find the Diagonal, or mitre Angle; but, from the height and center of each Square, on the Axis, which is a trifling and round about method, and very liable to error, the whole is determined; and which, being de¬ duced from a much better method, viz. making a geometrical profile of the Mould¬ ings, with diagonal Lines (as in the Jefuit’s) he calls a Method entirely new ; for w;hlch he is fo vain, as to arrogate to himfelf the lole merit; I am of opinion, that none has ever thought it worth attempting to rob him of it. But, how he would have applied this new method of his to Mouldings, when they are inclined to the Piflure, I am at a lofs to devife; as the third Ru'e, for Lines which vanith in the Points of Diftance, is never once applied to Mouldings, in this Work; therefore, is of no more ufe in it than the fourth. What a mis- 7 fortune Sea. IX. OFT HEENGLISHAUT HORS. n fortune it is. to the prefent Age, that he had not the Public’s approbation of this, Jolhu.'i th.tt he might have favoured the World with what would have rendered the Kirby. Work complete and perfea ; what blindnefs to fuch exalted Merit, what a lofs to the Public, never to be repaired. _ The third Book he calls, Gcncr.al Rules for determining the perlpeflive of Sha¬ dows, which 1 have attentively examined; and, except in refpefl of Arches and Niches, in w'hich the Shadows are truly projeaed, and one on Mouldings, find nothing but common-place SubjeTs; the Shadows being projeaed either on the Ground, or on Planes parallel and perpendicular to the Piaure, the Objects being parallel or perpendicular to them alio; with four, iimple Subjeds, on cylindrical Surfaces. In the third Obfervation on the fiift Example, viz. when the Light is vertical on the Piaure; or, as he exprelfes it, “ When the Shadow vanilhes into the center of the piaure, as in this figure;” he fays, “ then the light comes from direaiy-before the piaure ; and then the fides or parts of objeas, wdiich tend to the center C will be enlightened; but the front fides will be the llghteft.” The meanlntr of this abfurd and ftrangely expreffed Sentence is, that when the Sun (for, by Ltght, he means that Luminary) or rather the Piaure is fo fituated that a vertical Plane pafling through the center of the Sun, is perpendicular to the Piaure, that Planes perpendicular to the Piaure and to the Horizon will be illu- mined,’but that the front Faces, being parrdlel to the Piaure, will be mofi illu¬ mined! Now, the Light being fuppofed in the fituation, refpeaing the Piaure, as above, and being, to fenfe, at an infinite diftance, it is confequently, at the fame time, in’ every Plane parallel to the fuppofed Plane; therefore they are not at all illumined; but are as entirely deprived of Light, as if it was on the other fide; perhaps more fo, as they receive lefs from Refleaion; vvliilft the front Faces are as fully illumined as poflible, in the given altitude of the Luminary; therefore there is lio comparlfon can be made between them. In Plate 40, Fig. 2, is a curious Example of the Luminary being in certain Planes, which are parallel to the Piaure, yet a ftrong Shadow is caft on them, from adjoining Objeas. Although his Shadows are, in general, truly projeaed, yet are they as abfurd m fome other refpeas as poflible; as for inftaiice. It is almoft univerfally known, that the Shadow is darker than the Objea which caufes it, when adjoining to it; and although he praaifes this on vertical Planes, yet on the Ground it is always lighter than the Objea; but in Plate 44, the Objea which caufes the Shadow is, in refpea of the Shadow, in full Light, the coiitratt is fo ftroug; and the gradation of Shade is ridiculoufly abfurd, in general, on his Objeas. In his Shadows of the Pedeftals, caft on the Ground, the Shadow begins with a ftrong edge of Shade, which, before it reaches the width of the Pedeftal, is Light, m reipea of the Plinth’ which is alfo gradated. In refpea of Columns, he contradias the former afl'eition; for he fays. Ex. 19. P. 34- Obf. 2. “ this point of contaa will always be the darkeft part of the Shadow,” meaning the Line of contaa with a Plane pafltncr through the Luminary. In another place, he fays, that it will gradate from that p°oint, both ways; on one fide into the Light, on the other into the Refleaion. In Plate 38 is a Nich, which he fays is properly lhaded; yet, in the Head, where the Shadow begins, the contraft is as ftrong as elfewhere, one fide being fully illu¬ mined, the other in full Shade, which, iii Nature, is fcarce diftinguiftiable; at the edge it is not, owing to the concavity of the Head. On the fhaded fide, the teint is uniform ; from the part of the Head, which is nearly horizontal, to the bottom, the whole appearing as a Plane; the Light being the fame 011 the oppofite fide. There arc many Ablurdities in tins Chapter, but thefe aie the chief. The fourth, and laft Book begins thus; “ Before I begin with this part of pet- fpealve (of Buildings in general) it will be neceflary to confider the apparent lize .of the trunks of columns that are placed parallel to the plane of the picture.-- What I am going to advance upon this fingular part of perlpcftive, is not with any intention to revive a former controverfy about it, but only to oftcr forae farther reafons why columns, that are thus fituated, Ihould be all drawn of the fame fize ; ind to give an univerlal rule for this pui polc.—My continuing of the fame opinion ii8 Jodi ua Kirby. Sea. IX. I’ A R A L L E L, Plate X. Pig- 3 °- the evidence of lov ovvo^fenA-s’ Tcin'-^^d “ or fisigularity, but becaufe neut artUb. h.aveall united trc’o,'ini" of emi- and impartlaiitv; and thou-vl, be inV Lr ^ candour able c,iles. he mav, howevcl lend his nfliftfrdetermine in home difput- the qucHion. whicl, heft agrees with liis own'opmiom”'' “Pof ritat tntVrhaTbeen'rmucrcmrro^^ "’hJoh. at rc-maikahle one of his Isno."a.rcc Tl e „ ' T " Obllinacy, it is a Artids, in this/,«•/ of Perfneaivc amount 1 “penence of the moft eminent nor the evideme of Senfe can detcr’m'n ' ' ” neither Experience, Columns that is in deb t'e’, ^ 3 ™ ’i;” “V “PP-^nt fize of th^ •the rcafons which he prorofo here to - ^ Diameters on tlie Piaure; and therefore have no wcipiit Tl’c Cclieme ' founded in leafon, and I'-ig. and a.) for obt^iihn-r r' ht n n ’7 (PJ. 4. being all ofthefimelize, or nearly fo is abfurd • what^ " l'*'’ “V'''*' they may be made equal without it ’ But he' ’ a ^ Schemer how then does lie reconcile that to'his reafolls^fl" Wear; not, tlien, of the dimenfions which Perfoc-aive ^ «'hy "■' Page 103. yet his Sdieme, here aivei/^s"fn^v ^ observed in give it a place in tliis Work. (See^Fig.’ao PI X'\ '""‘a R Two Columns, and E the place of the^Flp aV-' Plans of illuftrates the lame, is XXIrawn n ^it Vilual Rays, EA, EB &c bein? dn ^ the centers of the Columns; the which theXlumiisaXXecWlXer. the Angles A E B, CED, under fartheft from the Eve, fubtends baft' aT . ‘^“"'pSttently, the Column X, being iuftiy oblerves, that tl e SrreCr to ^'e, which the Arc Acd evinces. He ncal PiRure, the Eve beinv in its Ce X- 1 "'<>tdh to a fphe- Coiumns, only, to'a conciwe Cvlmder; in whieVealXthe of the between the Vifual Ravs EC, ED whicli is the s ’ P.^'''^ intercepted Rimn X, compared wilh AB is X it re r ^ ^PP^rent Diameter of the Co- «ut, the P,atL is a Plane, on A G ol Jhbh'tli'e'C I CD, on that Pifture, appears, to the Eve aT R L T”' '''^Ptefented, and 3 S obvious, being leen under the fimeAnalp ’ hT which then, is.lt’poffibl, that cf «“"> lumn of the magnitude, or Diametet CD on th r’o a ^ dotted Line EXvince; that XX .fo’t the A„df CFD Column fubteiuls; confequentlv it wnnM f a S*^ CE/) being lefs than the ..s ,r&. .ihrAir h'l..f ■ “■ ■'« ««ArL'L*t''sr,S5 s'S' “r “’"i -i■'’= fore the pidure ftiould be referred^to tint nhe'e^ f ° 1 Column CD, and there- cut the rays in cd, and therfXe cd w H X ’ T’ CDit will column ought to be made of upon the pia..3e f"'" embrace this opinion and would Vz^i ’ i ' /* ^ therefore, who will .11 of ,1,0 a^ohoo i ; i S o ;w r,'." ,«■ « » '"-to Ham .1.0.0 „i.o ,1,.., [voC“r;; 'fc,™;'™;; i. .0 rori:!’'"'';'r",“,f' v'’, ■""'j '-"‘f". obvious, that cd appears equal to CD to'the '' ' brae magnitude.? Is it net it muft neccfli.niy appear ?efs, becaufe it A JeXdLi Cd'’ "^“''^d, to CD, Limn be added, as Z ; is it not evident tint thf ’ 1* ■’ ®“PP°P® ^"cither Co¬ nor ev-clent, that the reprelentativeDiameter, EG, mull: neceiParily Sefl:. IX. OF THE ENGLISH AUTHORS. iieceffanly be arger t!>an CD, i,i order that it may appear, to tire Ere at E to be equa . or, lather to give an Idea of equality ; and, although tlie Eye may refer FG to fg or rather to fg, yet fureD, FH, being made equal to f g, cannot be referred to fg, under the opt.c Angle FEH, fo as to be equal to fg, buf only to fin Yet, by hi. Rule, we are to make the Column at X equal to cd, and that at Z, to ■fg; but why not rather to rt/ and fg, which are tlie.r true apparent Diameters” or why al this preparation, if they are to be made equal? for it is not an Approxil mate, as he calls it, but is really equal, which is demonftrable; fo that L has a this while been contrivingandenfoi-cing a Rule, only to make them equal, after a 1 . Yet, he is fo jealous that he lliould not have the credit due to the hn-ention that he informs us (by Note) that, (ince the Scheme was engraved, he has been in- oimed, diat one of the lame nature ivas invented, lomc time ago, bv Mr Wriabt an ingenious mathematician, which he affures us he never la w nor received I,; inftruaions from; fo that, without the imputation of plagiarifm, the Invention may be called his own; 1 give him full credit for it. After all this parade, preparatory to the application of the foregoing to regular Buildings, what has he done? or what (atistaaion is derived from it, to thofe who have not penetratioti enough to fee the falfity and abfurdity of it ? thofe wlio have will treat It with contempt, as it juftly deferves; he concludes his lavacious and moft extraordinary Remarks, thus. - That I might cut off all occafioii for con- troveriy, tliefe two methods are offered for drawing the trunks of columns; and I would not on any account, peremptorily obtrude my own opinion upon others, T ^ difputable cafe : and I here declare alfo, tha? I fliall not tl.ink myfelf obliged to give an anfwer to any remarks which may be made, upon what is here advanced: the opinion of candid and fenfible perfons WI be thankfully attended to ; buttlie ftridures of fnarling and malevolent^ritics will be entiiely difregarded. Here he ftmts the Door full in the face of Con- viaion; thofe who either are of the lame, or choolb to humour him in his ab- fiir-^^wh /"a-’*' "c ‘>'2 on the Pidture, can do lb is furprizing. Yet I am certain, that many, who are but fuperficially acquainted with Perlpcdtive, have imbibed that Idea ; and, iji confequence, make their Lines converge the wrong way, imagining them to tend towards the Eye. Whether this Idea originated from the Paffage, above quoted, is hard to fay; but 1 can fcarce fuppofe that the Work is fo much read as to have given birth to fo cxr traoi dinary an Error, as is warranted by it; the abfurdity of which is fp yery glaring, that it fcarce feems poffible for any Perlqn, who pretends to draw at all, to be guilty of it; or having been fo once, or feen it done by others, that it ffiould not ofFeud his Eye, and make him guard againft it, in future, 7 Let J 24 Sea. IX. A PARALLEL, Plate X. P‘g- 3‘- Let ACE be fuppofcd to reprefent a Box, a right angled Prlfm or Parallelepiped; the Face AE being parallel to the Pidure, the Lines AB, CD, and EF fliould re- prefent Perpendiculars to it, and therefore, fhould vanifh in its Center. But, as the Plane of the Top (AC) is feen, the Eye mull be above it; and fince the Face CE, alfo, is feen, it muft be towards the right Hand, therefore, fomewhere in the direflion of DC, produced; fuppofe at O; but, AB, and E F, do not tend there, but downwards, to P, confequently, the Eye muft be there; in which fitu- ation, the other Face, AG, and the under Face, GE (and not thofe which are here reprefented) would be feen, which muft be obvious. Now, fuppofe the Eye to be oppofite P, at any diftance, the Lines A B, &c. would not pafs through it, although they tend to that part of the Pifture to which it is oppofite; whereas, the Center of the Pifture is at O, and confequently, they fhould tend there, ac¬ cording to the general Idea all have of Pcrfpeiftive. By the Lines in Perfpeftive paffing through the Eye, he cannot mean a Pyra¬ mid of Vifual Rays, the Seftion of which, by the Pifture, is ACE; for, aftho’ the Rays, projefting it, pafs through the Eye, the Lines AB, CD, &c. which are projefted, do not; therefore it cannot be reconciled by that means, nor is there any meaning in the Words which follow ; “ and the Point, &c.” In (hort, it is not in my power to reconcile the Paffage, as it ftands, to common Senfe; yet, there follows this Remark on it; viz. “ This is the very conflruftion of a Vanilh- ing Point, on which almoft the whole Praftice of Perfpeftive depends.” By wrefting the fenfe of this Sentence, various ways, 1 find, that if three Words are added, the Senfe is clear, as thus; For, Parallels to all Lines /sen in Perfpeftive, are fuppofed to pafs thro’ the Eye, &c.—which is an eflential Principle of the Science. How Mr. Highmore could leave the Senfe fo vague, of a Paffage fo very impor¬ tant, is, to me, aftonifhingj in it, he confounds the Idea of an Indefinite Repre- lentaiion with the Radial of the Line, producing its Vaniftiing Point; and fays, that it is the Conftruiftion (or Genefis) of it. Immediately after this capital Error of his own (in a Nota Bene) he explains the Errors in the Jefuit’s Perfpefllve of Shadows, with real judgment. Upon the whole, he feeras to be well acquainted with the Projedfion of Shadows; alfo, Refleiftion on Mirrours; but, the abrupt manner, in which he enters upon each Subjedf, fhews him but indifferently capaci¬ tated to difplay the Rationale of them to others, or he does not think it neceffary. Refpedling the Figure referred to, fuch Delineations may frequently be feen; not only in the W’indows of many Grocers and other Shops, in Town, but (I am forry to fay it) in many better Produdtions, fbmetimes in fine Pidlures. What Excufe could be alledged for the Painter, who, having fo little judgment, fhould make his Figures, in the Fore-ground, lefs than thofe which appeared behind, which were fuppofed to be equal? would he not be laughed at by every Dauber? and does not the fame reafoning hold good, in every other Objedf, or in Right Lines ? which may be confidered as the meafures of Figures ; furely it does. How abfurd then, to make the Lines, A B, C D, and EF, converge downward, feeing that, BC is intended to reprefent a Line equal to A D, yet is longer, though appearing (or intended to appear) farther off; alfo, if DE, and CF, are the heights of Figures, in the Pidlure (equal in height) the hither one, DE is lefs than CF, at a greater diftance; which abfurdity arifes from the wrong convergency of the Lines, AB, &c. But, why it fhould ba imagined that thofe Lines are tending towards the Eye, ra¬ ther than at No. 2. I cannot devife; for it is certain they do not appear fo, when the Eye is in the true Point of View (and fuppofing the Figure, No. 2. in the place of the other) oppofite to the Point O, to which they do tend ; but, in either cafe, they do not tend towards the Eye, which is not in the Plane with them. Notwithftanding, it is manifeft, that this Author was converfant with Euclid, and, as appears from the Work, competent in Perfpedtive; yet he abounds with Errors, which are dangerous, as in the Paffage above quoted; and others which are likely to miflead; fuch as in Page 54, Line 19, where, fpeaking of the Inclina¬ tion of a Line to a Plane, he fays (having before obferved, that a Line which is perpendicular to a Plane makes the fame Angle every way with it (90 deg.) and 4 would. Sea. IX. OF THE ENGLISH AUTHORS. would, if the Plane revolved round on it.) “ But if a Plane were to be turned Tofenh round a Line, making an Angle of 30, &c. the Angle would vary continually, fo Highmore as to make every other Angle between 30, and its Complement, i ro.” I fltould ^ be glad to alk the Author, how the Plane is to be turned round.? Suppofe a Plane either vertical or horizontal (Pofition is immaterial) and a Line inclined to it in vo deg. or any other Angle; then, the Line remaining fixed, whilft the Phtile revolves round being all the while in the fame Pofition, how can the Angle vary made \vith the Line? But, I know he means, that, if a Line be drawn in the Plane, from the Point where the inclined Line cuts it, making the Angle of Inclination, that the Angle will vary continually, with that Line, as above; in which he is Hill erroneous; for they can never make an Angle greater than a right one the Line being produced, in the Plane. Many other expreffions, equally vague or unmean¬ ing are to be met vvith; fuch as (in the N. B. following.) » In this Scheme. B, C, L, IS the Vanilliing Line ot a Plane perpendicular to E.” It is needlefs to comment on this; for E, being a Point, has the fame pofition to every Plane and can vary m nothing but Diftance, let the Plane h.ive what Pofition it may. ’ Although I have feledled thefe Paflages, only, as being very exceptionable, yet are there many other, equally fo; to expatiate fully, on all, would make a Volume; let what I have done l^affice, to fliew that I am candid in my Remarks, aiid do not wifli to put any forced conllruaion on the Author’s Words. But, as it is evident that he mmt be well verled in Geometry, I am furprized at a Reference to Euclid! in Rtge 82. big. 65. where the whole is dependant on Proportion, with which Doanne he leems to be acquainted; yet he refers us, for proof, to the 27 28 -0 and 40, of the III of Euclid, which has nothing at all to do w-ith it, being wholly dependant on fimilar, not on equal Triangles. This paffage relates to a grand conteft, which engaged the Attention of the SpeciAative, in this Science, about that time, and which the Author was engaged in refpeamg the apparent, or reprefentative Diameters of Columns; alfo, the Reprefental tions of parallel Lines, feen direa,&c. and he means to prove, here, that they mull be r^refented by parallel Lines, let the Eye be fituated ever fo near, or oblique the Pidure being parallel to the Wall, which is given for Example. The con’ fruition of the Figure, is well meant, and the firft proof, given, is fufficient the latter, is quite fuperfluous, nor does it render the thing clearer; the former is bv fimilar Triangle, only, the latter forms both fimilar and equal Triangles yet the Proof has no relation to the Propofitions referred to, or it is a far fetched ’Proof. I fhall doiiclude thbfe Remarks with the Author’s own Words, who heinp- himlelf a Painter, in fome Reputation, knew the Requilites thereto. After a quotanoii from the Jeiuit’s Preface, In thefe Words; “ That Perfpeftlve Is the very boul ot Painting, and which, alone, can make the Painter a Mafter which he thinks is feting it too high amon'gd: the Requilites, &c. he adds, “ It is certain however that PerfpeAive is an elTential, and that, whatever is erroneous in thi! refpeft, does not truly reprefenf the thing intended; that it is abfolutely neceffary to the perfeaion of Painting; and that fome fubjeds, particularly Architeaure, cannot be reprefented without it.-That great Errors in it are monllrous, and Iho.kmg, a nd that a total Ignorance of it is unpardonable in a Painter, or Defigner ” 1 o the Work is added a Supplement, containing eleven Pages, and five Plates in order to explain, better fome of his former Diagrams, on Shadows and Refleaions ; whi^ (unlefs the Book was printed off, before he thought of fuch Elucidations'! IS a Itrange, and though common, I think a ridiculous way of communicating it. Tis a quarto Volume, containing (with the Suppleirient) 129 Pages, and 48 Plates many of which am not lulf filled T^bere arc no fin.flied Pieces, yet fome tha! fhew Defign, and Tafte; but, in the Diagram Plates, here is the greateft walle of Copper I ever faw, exceH in Kirby’s laft Work. There is an Introduaory Chapter, of eight Pages and two Plates, on Geometry; a Ihort Preface but no Dedication. He fays it was written many Years fince, but now firft publiftied; printed for Millar and Nourfe, in . 763. Price, one Guinea. I believe it has not gone through a lecond Edition, tioi: will, I am of opinion, haftily, I i ON 126 Sea. IX. REMARKS ON Mr. FOURNIER. Daniel ON. a curfory View of a Treatife on the Theory and Praaice of Perfpeaive, Four- by Daniel Fournier, fome time ago, I thought it appeared well adapted for a NiER. praaical Treatife, and have often given it the preference to others, on that Icore; 1764. for, the Plates have fomething ftriking in them, which catch the Eye, the Figures are tarty, and appear rather mafterly, which are apt to prejudice a rtiper- ficial examiner in its favour, more than the performance really merits; which thews, that no judgment can be formed of fuch Works, at light; feeing that, mak¬ ing a few Sketches, or tVen a line Drawing, and treating the SubjeR properly, are but feldom within the province of the fame Perfon, which is here verified: for, although the Work is not deftltute of Merit, yet, on a clofer and more critical- Infpedtion, it falls far Ihort of what I expedted to find it. His Preface begins thus. “ As Dr. Brook Taylor’s Perfpeclive is undoubtedly the moft excellent'perform- ance, of its kind, hitherto made public ; I chofe rather to attempt an explanation of his principles, than to offer any thing of my own, with regard to the theory of this moft ufeful art.” Indeed, if a literal copy of the Doftor’s Theory, and ele¬ ments of Pradlice, may be called an explanation of it, he has certainly done it > but, where he has ventured to deviate from him, he is fcarce intelligible, in fome places not fo, feldom that he renders the Text clearer. He has even copied the Dodlor fo very clofely, as to copy his literary Errors, which indicates his Ignorance of what he attempts to elucidate; for furely, if he had examined it, with due .at¬ tention, necefiary on the occafion, he would have difcovered the Errors. In Theorem II. of the fecond Part (for it is that he has copied) it is thus ex- prelled. “ The perfpedtive reprefentation, or projedlion, of any objedl, is the fame as the ichnographic projedllon of it, on the plane of the pldture, the point of fight being the vertex of the optic cone.” Now, that this is an overfight, or error of the Prefs, in Brook Taylor, is evident, from a remark after the 6th Definition; where he fays, “ it will be evident, from Theo. 2. that it is no other than its Schenogra~ phk Projeflion.” But furely, the fame excufe cannot be alledged, for him who copies it; I faw the Error, in both, on the firft reading; nor can I be perfuaded that any Perfon, who was acquainted with the Terms, could pafs it over unnoticed. In order to copy him with lefs trouble, and more fafety, though fome of his Dia¬ grams are varied a little, they are lettered the fame ; fo that, where the Dodlor has made a mlftake in his Reference, Fournier is the fame ; as in Prob. 6. Otherwila by the Direblors. In the firft Line is DF for FE; and, in the fourth (3d in Four¬ nier) is AF for FE, the very fame in both. This Error, in Dr. Taylor, I had correfted, feveral Years ago; and, on examining this Work, now, I did the fame, before I compared them ; furely then, he who was publilhlng the fame Work, over again (in part) fhould have corredled ihofe Errors, though he had run into others, which is almoft unavoidable. As the whole of the Theory, in this Work, is almoft a literal Copy of Brook Taylor, on which I have already given my Sentiments, it would be fuperfluous to dwell longer on it here; the Definitions, the Axioms, Theorems, and Corollaries, deduced from them, are the fame, in Order as well as in Number; in fome of them, having given other Figures, his Demonftrations vary, in form, though the fame in fubftance; fome of the Dodlor’s Remarks are omitted, and fometimes he makes Remarks from his own Figures. In the 5th Theorem, the Doflor refers, for proof, to Prop. 16. II Euc. which, Fournier, in copying, has made, Euclid If. 16. a mlftake which, as a Copy, is inexcufable; yet I do not impute it wholly to Ignorance, but rather to an indolent inattention, or rather to a volatile difpofition, by nature; it is apparent throughout the whole Work, which abounds with Errors. The other, in which the Original is miftaken, muft proceed from his too great confidence in the Doftor’s Infallibility. The 7th Theorem is in thefe words; “ AH lines in any original plane have their vanifliing points in the vaniftiing line of that plane,’* which he demonftrates thus; “ For as all the original lines are in the fame plane, the lines which determine their vaniftiing points” (feeing they are all in the Parallel of the original Plane) “ will interfedl the pidlure in the vaniftiing line of the original plane;” which, omiting the Parenthefis (the fubftance of which the Dodlor Sedl:. IX. OF THE ENGLISH AUTHORS. 127 Doiftor has) is arbitrary. The 8th Theorem, in the latter part, where he has Daniel thought proper to depart from his Text, is unintelligible, viz. “ Interfeaions of Fournierr all lines in the fame original plane; and alfo, the line which determines the inter- feCtion of that original plane with the piflure, are in that plane.” The Doftor fays only, (after the Semicolon) “ are in the Interfeftion of that Plane.” Both add “This needs tro Demonflrationindeed I don’t comprehend the Premifes in Fournier; fo that a Demonftration would be to little purpofe. However, both the 7th and 8th as in the Original, being clear in the Premiles, are felf-evident. I have included both in one Theorem, the 10th of the and. the nth of the ifl: Imprellion, of my Treatife. The problematical part of this Work is, by much the greater part, a literal Copy of Brook Taylor ; and where it is fo, it may (Errors excepted) be depended on, which cannot, where he leaves his Guide, and ventures out of the direft Path. Problem the I ft. he does not perform, but refers only to a theoretic Fi- gure, for a Solution. In the 2 nd he wanders, ftrangely, from the Premifes he gives, from Brook Taylor; miftaking, or making ufe of the Seat of a Point af- fumcd, inftead of the Angle given, which the Line makes with its Seat, fo that, he performs it by a procefs which is foreign; dnd he miftakes a finite part for the indefinite Reprefentation ; the laft ftep in the procefs is previoufly necefl'ary to what is done before. The 7th Problem, to find the Projerftion of a regular Pentagon, given in the original Plane, he has copied exaftly, with all the Defecfts. One Side being parallel to the Interferftion, there are, Confequently, four vaniftiing Points; the Interfefting Points of the other four Sides are determined, yet no more than three indefinite Reprefentations are drawn; inftead of drawing the fourth (which is as neceflary as the reft) we are told to draw KO, to do what the other would have done better, KO being entirely ufelefs; and yet, neither of them has drawn KO, but the Point it would produce, is affumed; we are told at the fame time, to draw 0 ,N ; and, laftly to draw OP. Now OP and ON are Vlfual Rays curing two of the indefinite Reprefentations, in order to obtain the parallel Side, one of which is fuperfluous; yet, neither one nor the other finifhes it, by telling the Reader to draw the parallel Side. I (hould not have been fo particular in this Problem, but for the fingularity of the Copy being fo exail, in every refpedl, when it would evidently be better to have deviated from the original; but, his View feems to fave himfelf all the trouble he could. To point out every Error in the Work is far from my intention ; I rather expeffed, and wiftied to find in it, matter worthy of praife, but own I am moft miferably difappointed. But what, to me, is moft extraordinary; in many refpeAs, it appears that he is tolerably converfant in Geometry, particularly in the Doftrine of Proportion, yet, in feveral places, he is egregioully erroneous; in the 15th Problem, after copying his Author, literally, both in the Procefs and De¬ monftration (in which he corredfs a wrong Reference) he thinks proper to do it otherwifi-, in which he tells us to take a meafure (FP) equal to the Quotient ari- fing from the fum of the two Squares, of the Perpendicular and the greater Seg¬ ment of the Hypothenufe, of a right angled Triangle, divided by the Hypothe- nufe ; which F P is the oppolite, i. e. the lefler Leg of the Triangle. Let F P B be a right angled Triangle, PC the Perpendicular; then, according to his words. Fig. it will be, that FP=PC fquare -)-CB fquare, divided by FB, the Hypothenufe. Now, PBfq. =PC fq.-|-CBfq. wherefore, FP=PBfq. FB; and confequently, that the three Sides of a right angled Triangle are Proportionals; a difcovery never, I believe, found out before. There is another Inftance of (I rauft call it) his Ignorance, of the abftrufe, or moft fublime part of Perfpedlive, relative to inclined Planes, which requires more geometrical knowledge than many are pofleffed of. But this, for which he is truly reprehenfible, and deferving a fevere Cenfure, is an attempt to prove Mr. Kirby in an Error, in his 71ft: Figure; Plate 13. B. I. but, unluckily, ’tis himfelf that is in the wrong. In Example 32, after illuftrating the preceding Example, by a very ingenious and well-adaj)ted Diagram, he proceeds thus. “ But as a certain modern 3 Author Sea. IX. 12 ? Daiiid Founiier, F‘g' 33 - Sea. IX. A parallel, Authcrr has laid down a general rale (in his treatil'e of Pradical PerfoBaived to find the vamlhing line of an inclined plane and oblique to the pidure, by an angle given which angL of inclination is kl on the horizontal line, without having reglrd to the interledion that inclined plane makes with the pidure, which is falfe; for the vanilhing line of any inclined plane miift be parallel to the iiiterfedioii of that plane with the pidure * (by Theo. 6,) ; therefore, to prevent the reader’s thinking I aiif par- tui, I have given the following example taken from his Pradice.” Here he goes through the procefsj quoted from Kirby’s Book, and then adds, “ But as I laid before, the vanilhing line of that inclined plane cannot be found without having the interfedion of that plane with the pidure; nor can the angle BAG be the angle of nicliiiation. wanted, as the plane is fdppofed to incline to the pidure But on examining the Fig. i. Pl.ate 25. this will appear erroneous.” As It IS mamfeft, that either one or the other of thofe Gentlemen mull be wrong- and I have not heard that it ever was noticed, bv Mr. Kirby, I fliall, by a true copy of the Diagram, lay it before the Public, for their determination who may not have leen either of their Books, referred to and quoted, as above. See Fig. v-i Plate 10 in which, the given Angle of inclination with the Horizon (according to \ 1 r. Kirby) IS B A C ; H L 19 the Horizontal Line, and C the Center of the Pidure; C E is the DiRince. As for the Objed tozx, ’tis not of the leaft ufe; the Bufinefs is, to determine the Vamlhing i^ine VL, of a Plane inclined to the Horizon, as above, L being the Vanilhing Point (given or found) of Lines in the Plane which are parallel to the Horizon. E being the Eye, LL is dravyn; and EH perpendicular to LE, cuting the Ho- nzoiital Line at H. Then, HI being equal to HE, and the Angle HI V equal to BAG, cuting a Line drawn from H, perpendicular to the Horizon, at V; VL being drawn is the Vanilhing Line required. But, Mr. Fournier fays it is falfe i’ for the Vanilhing Line muft be parallel to the Interfedion of the Plane, with the Pidure, which jt certainly muft; but he has not proved that it is not lb, how then can he aflert it is falfe, on that fcore? On the contrary, I aflert, that it would be pamllel to the Interfedion of irBy Original Plane, given, in that pofition to the A idture, which I will make appear, to demonflratioii. « Line, found, of a Plane inclined to the Horizon, in the Angle HIV, equal to BAG. The Angle of Inclination of two Planes is that winch IS formed between two Lines (one in each Plane) drawn from the fame Point, perpeiHicular to their common Sedion f, which is therefore perpendicular to a plane paffing through thofe two Lines (Eu. 4. i,.) in which Plane, the Angle IS truly meafured. L is the Vanifliing Point of their common Sedion, and LE is Its Radta , or Parallel producing it (Def. 14.) and, LEH is a right Angle; where- fore, H y IS the Vanilhing Line of a Plane, to which, the common Sedion is per- pendicular, and EH is its Diftance. Bur, HI is made equal to H E, and H I V to die given Angle, of thednclination of the original Plane to the Horizon; where¬ fore, It LEH be turned up, on H L, perpendicular, and HIV, on H V, until I coinades with E, it may then be feen, that EH is the Radial, that is parallel to the Origina , of tx, and E V of t y and o z, confonant to his own Diagrams (2 and 31 Plate 7.) from B. Taylor f and confequently, that V is their Vanilhing Point j.. But, Lisa Vanilhing Point of certain Lines in the Plane; therefore VL is the Vanilhing Line required (Theo. 7. P. 16.) which would be parallel to the Interledion of the onginal Plane (Eu. 16. ii.); being the Iiiterfcdions of paral¬ lel Planes, with the Pidure. ^ o r Now, this being the cafe, as it muft be obvious, to every uiipreiudlced, or to every geometrical Reader, what excufe can be alledged for this virulent attack on Mr. Kirby, who was then living ; and, although his Work i.s puerile and ungeo- metricd, in a very great degree, yet this Problem is performed ftridly geometrical. Iherelore, I thought it incumbent on me, to fet the matter in a clear light • and, as far as 1 am able, to vindicate Truth from Calumny. It is fo in general; why then fo particular ? ’"■g. j ■ — ■ • - ■ 5 tv:, .0 "vi in', ' ■'rr—.', t See the iutroduaion, B. Hi Art. 4, I fig. 72. in Kirby s Buck, has moveable bchecics, for illuftratiori of the Procefs. ’ Seft. IX. OF THE ENGLISH AUTHORS. 129 Mr. Fournier has afferted that the Vanifliing Line cannot be found without the Interieflioii; becaufe one muft be parallel to the other. Therefore, in the Procefs, by him, amongft other things, neceffarily given, he gives an Iiiterfeaion, as GH; but he has a_!lo given tlie Interfeaion of a horizontal Plane, which, according to his Propolicion, is in no wife neceffary, it being a common Cafe * ; the Ope¬ ration IS therefore performed witliout it, which, on Mr, Rirby*s Premifes cannot, as it is evident, on iiilpeaion. I am really of opinion, that, having given tlie inclination of the Plane to the Piaiire, inftead of the Horizon, he knew not how to obtain either the Iiiterfeaion or the Vanifliing Line. After this follow fome E.xamples on in'clined Objeas, but all in the limpleft pofition; that is, when the Vanhhiiig Lines are parallel to the Florizon, in Wedges, Prifms, and Cubes, telling on a Side, or Edge, parallel to the Piaure. .A Flight of Stairs in this pofition, is the principal Objed; but his defcription of the Procefs IS trifling, and, though tedious, feldom clear; leaving it to the Reader’s Capacity to go through with it. He gives Examples of Chairs, whofe Seats are Squares, and the whole b tame is a Cube; the Backs llreiglit and upright, and two Squares above the Seat. He determines every thing, in reljiea of meafure, by the Vaiiilhing I’oint of the Diagonal of a Square; nor does he, in the elements Pradlice, ever Ihew how to bay down the dillance of the Eye from the Vanilhing Points, of Lines inclined to the liiterledlion or Ground Line, by which, to cut olV any deteimincd portion of the indefinite Reprefeiitation. His Figures are all diiedl, in polition ; an Ifolccles Triangle regularly pofited ; a Square, parallel, and another direfl on the Angle; a Pentagon, direift, and a Square with a Circle lufcribed are the whole. His plane Solids are two Cubes, one direiR in front, the other on the Angle ; a Pyramid on a I'quare Bafe, the fame ; a Chair; as above, and a Table which is a right-angled Parallelopiped, p.arallel to the Pidlurc, Then follows a moll clumfcy Wheel, which he calls a Water-Wheel; but, diverted of a parcel of Blacks, which are placed edge-ways on the Rim, would pals better for a Dray or W aggon broad Wheel, though fomewhat dumber. I have heard fome fpeak of tliis Example, as an extraordinary one, and indeed fo it is, for it e.xceeds ordinary. ^ Next tollow lome Examples of internal Subjects, with the me¬ thod of determining Doors, opened in certain Angles; tliefe mull be feen, in order to conceive a proper Idea of them, for they exceed all delcription. Then follow Mouldings, in an ill-formed Pedertal, with a Cavetto for the Bale, and a Cvma reverfa for the Cornice; with a ckimfey ffufean Entablature (turned upbde down) coiififting of an Ovolo with a head, for the upper Moulding, and a l.irge Cyma reverfa for what is called the Bed Mould; both are parallel to the Piaure. Of thefe, the Defcription and method of proceeding are luch as cannot be im.agined ; yet they are preferable to what Kirby had done, in that way, in his firft Work. The Fufean Bafe and Capital, for a Column, are next handled, and after the fame manner as Kirby, by vertical Seaions, palling through the Axis of the Co¬ lumn ; which, where they apply them, are not of the leaft ufe; all the difficulty conlifts in delcribing the Contour of the Torus, or Ovolo, at the extremes; the reft lying between parallel Circles, the prominency is exprelfed only by Light and Sliade. They are alio (like Mr. Kirby’s) obliquely parallel to the Piflure; but the Cuives are much better delineated; owing, in the Torus, to the method applied, by parallel Circles, as well as to Ins greater lacilitv in drawing from an Objccl. *1 hefe, with the Wheel, are the whole of round Objects; fave two Cylinders, one upright, the other perpendicular to the Picture. 1 have heard his method of de- fcribing^a Glide applauded, hut muft own I find nothing in it either new or lin¬ gular; tis from a parallel Diameter, given, and confequently in the limpleft pofi¬ tion, effeaed by means of the Dillance of the Piaure Lid on the Horizontal Line, the Vanilhing Points of Diagonals of a Square, and the dillance of thofe Points; one of which is lufficient, though he makes life of both. This is the firft iiiftance in which he lays down the Dillance of any Vanilhing Point, but the Center of the * Any intcifeaion being given, anj the Vanilhing Point of any one Line (as L) in the original Plane, the Vanilhing Line is tletcnninKl by the Iccond Theorem, Coroll. j. being parallel by Theorem. K k Piaure; Danielj Fournier. ' 3 = Sea. IX. A PARALLEL, p.-.nid Piaure; and .again, in the 20th Example, for determining the Pannels of a Door Eournier. which is open; but has no where laid it down as a general Rule, before Example 54. Plate 37. (where it is vilely handled) for proportioning Lines in every pofition to the Piflure, but parallel, and m whatever Plane. The 29th Example is in thefe words; “ To find the middle or center of any arch or building,” airy Arch, or Building; fure, never fuch a Problem was given before, in Perfpedlive. Here is given a great lumbering Arch, on two high Piers direft in front, which, at fight, one would imagine was in order to the Delineation; but, ’tis only to find the Center of the Arch, to hang a Lanthorn from. In the next Example and Plate, we have a curious horizontal Pifture ; not on a Cieliiig but on a Floor, feen flying, by fuppofing (as he fays) the Eye fo placed in the Air as to look down into the Building: the method to effedl it is indeed the fame but the Defcription is trifling, and left oft' abruptly. The lafl: Plate, in this part’ ought to have been amongft the firft; the Example, or Problem, is to divide a giTCii line into any number of equal parts, for the Steps of a Ladder. Having done with the delineative part of the Work, he proceeds to Shadows; in which, he feems to lay down the Principles as one who knows it, himfelf but not in the cleareft and moft intelligent manner for thofe who knew nothing of it_ before. I lhall pafs over a few Examples, in two Plates, as they contain nothing particular, and only take notice of the Shadow in the Head of a Nich, which IS erroneous; by which, the Curve is made more convex than it is poflible to be, in any pofition of the Luminary. This is a circumftance which has occa- fioned fome debate, in refpedl: of the Curve, which is rather paradoxical; and which, many, who never inveftgated, or properly confidered the caule, have exaggerated in a moft extravagant manner; as is the difpofition of moft Men, to heighten what leems improbable, by rendering it imfiofiible. The Error, which occafions too great a convexity of the Curve, is obvious; but, as it fuits with the notion many have formed of it, may pafs unnoticed. Inftead of vertical Seftions, parallel amongft themfelves (as in Fig. 39. Plate 45. of my Treatife) he makes them all pafs through the Vertex, of the head of the Nich; although, at the bottom, they are fuppofed to be conftrufled on parallel Lines, an ablurdity of the grofleft kind; confequently, the Curve comes nearer to the Vertex than it could poflibly do, from the Situation, given, of the Luminary. His method of determining the Shadow of a Globe is correfl; but the defcription is greatly defedlive; a general fault in this Work. The next Example (the 50th, Plate 36.) being taken from Brook Taylor, it is ufelefs to expatiate on; but, the Tetraedron, which he calls a regular one, and in the Original appears to be (b is a vile reprefentation. The reft of the Shadows, and Reflexions on the furface of Water, are common-place SubjeXs, not worthy of notice. Refledion 011 a Mirrour is alfo copied from Brook Taylor, excepting that the Pidure on the E.ille is liipplied with a C.age, h.mging from the Cieling ; but the Procefs, although he proceeds in the fiime manner, is, in fome parts, unintelligible, in others prolix and unnecelTarily tedious; feveral falle References, eight or nine in half a Page; and a defcription of part of the Procefs, for determining the Vanifhing Point of Lines perpendicular to the Mirrour, for which, not a Line is drawn, nor the principal Letter, which reprefents the Eye, to be found; Omilfions of this kind arefrequeuit in this Work, in fad, the Author was a wonderful Genius. Here follows an Example of a Down-hill, or dired Defcent, which is well deviled ; being a Slope from a level Ground down to a Brook, which runs parallel, in the Pidure, under two Arches (one on each hand), the Ground riling again’ on the other fide, to a level; the boundary Lines, on each fide, affifting the Deception. The Vanifhing Lines of the Defcent and Afcent, are properly deter¬ mined, and the Vanifhing Points of the Diagonals of a Square, in thole Planes, for each Slope is a Square, as is alfo the Brook, between the Arches. A L.,ndl'cape v; ith a Road over a rifing Ground (a good effed) and feveral others, with Out-lines., as for a Drawing Book, come after; with two, large, rough Etch ngs, of no uft- in the Work, making, in all, 51 Plates, and 94 quarto Pages. Printed for him felf) and fold by Nourfe, in the Strand; publiflted in 1764. IN Sea. IX, REMARKS ON PROF; COWLEY. 131 IN the year following, viz. 1765, a theoretic Work on Perfpeaive was pub- ProfelTor lifhed of a very Angular kind, by John Lodge Cowley, Prof, of Math, at the J. Lodge JRoyal Academy, Woolwich ; which, for thofe who cannot fee the intention of Cowley a Diagram, exhibiting Solids, or Planes in various pofitions, i. e. fuch as do not 1765. enter readily into, and clearly comprehend a Delineation on a Plane, may be af- lifted in forming Ideas of the Subjeft, from this Work. Having formerly pub- lilhed an Appendix to Euclid’s Elements of Geometry, in order to iilullrate the Doctrine of Solids, by means of moveable Schemes, lo contrived as to fold up into the form of each Solid, with diagonal or other Seftions, where required ; which Work was much approved, and defervedly, infomuch that, a fecond Edi¬ tion, on an improved and more extenfive Plan, fucceeded the firft. This induced him to conlider Perfpeflive in the fame manner, in order to convey Inftructions to his Pupils (by Leflures) more intelligibly ; by way of Apparatus, in Leftures on fuch Subjefts, it was necelfary, and eafily praflicable, but to contrive them lo, as to be put into a Book, required Genius; and Indeed, there appears great geo¬ metrical Genius in the contrivance, to lay the various Conftruftions down, in piano, fo as to fold in a Book. At the fame time, the trouble attending raifuig them up, and difpofing them properly. Is more than may be imagined, even to one who knows what they all mean; but, for one who is not, in fome degree, ac¬ quainted with it, to put them together by the Defcription is almoft Impradlicable ; and when done, to find out all the References, for Demoliftration, is a trouble few Learners would go through to acquire it. But, thofe who have leifure for it may be both entertained and improved thereby ; more efpecially, if they have gone through his former Work, they may acquire from this, a clear and comprehenfive Idea of Perfpedlive, in Rationale, and that is all the Author intended ; for he f.iys, in the Preface, that he has no pretenfions or aim at extending or enlarging tlie field of Science by it, but to render it eafy and perfpicuous. Before he enters on the Subjedf, by an explanation of the Diagrams, which are of Pafteboard, being cut out fo as to raife up, in order to form the various Con- ftruflions required (ten of which, with one other Plate, containing two Figures only, are all the Plates in the Work) he gives a brief Hiftory of Perfpetllve, begining with Vitruvius; but, without any explanation of their various methods of PratSice. He fpeaks of Peruzzi, of Sienna, as the Author of Sirigattl’s Me¬ thod ; which he fays was followed by Vignola, then by Sirigatti, and by Pozzo (in his fecond Volume) ; but although Vignola, he fays, copied him, to a degree of fervility, yet he does not altogether approve of that Method, but prefers his other, on the Jefuit’s Principles; I mean, which the Jefuit and others have fol¬ lowed. Next he fpeaks of Ubaldus, as one who has treated it more fcientifically, and as the firft whofe Ideas had a tendency towards rendering the Principles uni- verfal; but accufes him of great prolixity, in extending his Theory through fo many Propofitions, the whole of which might be comprifed in a few Pages. Be¬ fore Peruzzi, he mentions Albert Durer, and Petro del Borgo; who, before Du- rer, wrote three Books, highly extolled by Ignatio Dante, which are entirely loft. RefpeiSing the Jefuit, and others, amongft the old Writers 011 Perl'pedlive, the Works of Peruzzi and Ubaldus, he fays, have been the general Store-houle, to which they have all had recource, for the Principles they make ufe of. Amongft the Moderns, he begins with Brook Taylor, who, he tells us, con- defeended to write on the Subjeft, and ftiles him. The celebrated Geometrician. In his fmall Traft, he fays, the Doftor made prodigious advances, towards bring¬ ing the Art to its ultimate degree of Perfeftiou; and laments, that his Death de¬ prived the World ot a Trealure, which might have accrued from a Work in which he intended to enter on the Subjeft more extenfively. The learned and ingenious Mr. Hamilton, (he lays) with tlie affiftance of the Doftor’s Principles, has copi- oully treated the Subjeft of Perfpeftive, iii a ftrift, mathematical way; which is all he fays of him; but of Mr. Rirby, between whofe Works there is no com- parifon to be made, he is lavifti in his praife. “ This ingenious Author fay atten¬ tively examining and applying Dr. Taylor’s new principles of Perfpeftive to praftice, 1 Sea. IX. 132 Sea. IX. A PARALLEL, J. Lodge praaice, \yas gradually led to a difcovery of their generality and facility in opera- Cowley. tion, law how preferable and excellent they were in praaical applications how hmple and exteniwe their conftruaions, what a vaft confufion of unnecefiiirv lines were thereby avoided, and how beneficial they would be if generally known to artil.s concerned in works of defign ; pofltfled with thefe and fuch like confide- rations, he employed himfelt zealoufly to retrieve them from that ftate of dark- nefs in which their author’s brevity of exprtffion and manner of writing had con¬ cealed them, and became the firft amonj; artifh, who appeared in publick, to ex¬ plain their true nature and ufe in adapting them fuirably to the arts of defign ” Here, we have a remarkable infiance ot the partiality of Mankind, which Ihetvs how little IS to be depended on the vemcity of Writers, in general; one mig-ht be led to nwagine (from a Perfon of Mr. Cowley’s reputation) Mr. Kirby, a Man 1 abilities, in his Line. He flioul’d as candidly have ackiiovvledved that Mr. Kirby, with the affifiance of Mr. Hamilton (as, that Mr. Hamilton’ with the affittance of Brook Taylor’s Principles) had rendered thole Principles foniewhat more prafticable, in a lefs compafs, i. e. in a lefs voluminous Work and in a much lefs fcientlfic m.anner, bordering on puerility, which is the real Cafe ; and which (making life of Mr. Cowley’s manner of expreffioii) is not meeilj' our own bold aflertioii, but has the united concurrence of every Perfon of underftaiidiiig, in the Science, as appears from the Writings of various Authors wEo have juftly cenfured his Works. Speaking, finther, of Ids great Abilities! of the encouragement he met with, at firft, how joyfully the Aicifts, in general embraced his Ddign, his perfevcrance and intrepidity, by which he overcame all the various oppofitions to it, he thinks it a juftice due to the memory of fuch in¬ genious Authors, who have contributed to improve and exalt this Art to perfec¬ tion ; and, that it required liis ‘‘ endeavours to refeue them from the undeferved ceiifure lately palled upon them, ot not having made the leaft improvement * • as well as to vindicate ourfehes, by fliewiiig that what we have advanced in favour of oar author is not our own bold aflertion only, but has the united fuffrave of a body of Artifts, well-qualified to judge decifively in this matter, by whofe ord°r ” &c. 'Here follows the Advertifement already inferred, Page 109. ’ I am afraid, that Mr. ProfelTor, in imitation of Ins favourite Author, has paid a Compliment to the Artills, of that time, at the expence of his Veracity; for I am far from thinking they were qualified 10 judge decifively m it, although their Sum ages were to be regarded, as Perfons wdiole Opinion muft be allowed of w-eigju. He tells us, that Fournier thought his fecoiid Edition worthy his mak¬ ing free ufe of; but muft own, I fee but few traces of one in the other. He then fpeaks of his Perlpedive of Architeaure, a large f and elegant Work, containino- two Rules of univerlal application ; I could wi(h to have alked Mr. Cowley, if he really I'uppoied thole two Rules (to put a Square and a Circle into Perfpeaive) are or can be applied univerlally ? I think he durft not, boldly, have alfei ted it. ’ He juft mentions a few more Authors, viz. Hondlus, W'hofe Inftitutions, he fays were formerly held in great efteem. This is a fmali folio Work, in Dutch, of very little value, apparently, without a Date. Alleaume’s, he fays, deferves to be more known than it is, being well adapted to the purpofes of Artifts: this Work I have never met with. De Chales’s, he fays, is remarkably neat. S’Gravefande’s is recommendable for Pradfice. Lamp’s contains Ibine proper notices on the fubjedt ot Painting. M. De la CaillPs (Sal. de Caux) delerves to be noticed with rclpea,- and the Ireatile, referred to in the Note, as below, is diftiiiguilhable for its bre¬ vity and [ articular fingularities. &c. with which he concludes hisHiftory; and which, feeras to be intended meerly as a Puff, to let Mr. Kirby oft'to the be’ft ad- vantage, in hh power, * See Page 311, of Elfments of Mathematics, &c. with a new Treatlfc of Perfpeaive, for th« ufe of the Royal Academy at Woolwich; by Muller, mathematical Profclfor. t Ihis puts me m mind of a large Pidure, exhibited feveral years ago, which had little or notliino- to recommend It to notice, but length and breadth ; in Strictures on the feveral performances, then ex- iiibitetl, all that was faid of it was, an excesding large Canvas. This Sea. IX. ‘33 OF THE ENGLISH AUTHORS. Ibis Work IS m two P.irts, or rather in three; tlie firft, called the Doarine of Planes,_ contains fevea Definitions, refpeaing their Pofitions to one another &c. and lixteen Tlieorems, chiefly from the nth Book of Euclid. The fecond rs, m the latt part, exceptionable; viz. “ three Lines which meet one another are ui one Plane.” The fifth is alfo very exceptionable, and the Affirmation va? ue • but, as It IS in Geometry, rather than Perfpeaive, and would take up too nwicli time to render it clear, I fliall pafs it over. The eighth is an Axiom, and the eleventh alio. The fifteenth is not in Euclid, the fame, in fubftance, with the 1 ith. B, y. of mine, and is very uleful in Perfpedive ; and, the i6tli is the con- verfe of the ninth. This is the whole of the firfl Part. The fecond Part is alfo called the Doarine of Planes," applied to the true Prin¬ ciples of Perfpeaive, digelted into Theorems, with feveral Corollaries deJuced from them ; Ibme of which are rather too far fetched. His Definitions are full and to the purpol'e, in general, fave the third, which fays that “ the plane which contains the objeas given to be deferibed on the Piaure, Is called the Original Plane." This is limited, and conveys a very imperfea Idea of what y meant as every Plane which is reprefented is an Original Plane, as well as, that on which Objeas are feated, and is what he means; but, that a Plane lliould contain Objeas is ablurd, for it can only contain Figures. In the fifth, he contounds the Axis of the Eye with the Dlftance of the Piaure, which indicates .a limited length; whereas, notliiiig morelhould be meant by it, than that, the Axis of the Eye being produced, determines the Center of the Piaure, and, in that cafe, meafures .its diftance; but, to call the .Dilfance (as he frequently doe.-) the Axis of the Eye is very ablurd,,and renders the lenfe at leafl ambiguous and imperfea. As the whole of this Vyoik is theoretic, it is therefore rather copious; but the fubitance of the whole might be compriied in much lels compal's. Here are ig Theorems, feveral of which are not of the leaft ufe in the art of Delineation, which is the thing aimed at; nor indeed of confequence enough for Theorems. The fourth ffiould precede the firft; viz. “ Original pl.anes, parallel to the piaure, have neith-r vaniflimg, interfeaing, nor direding lines.” Being clear in the Definition of a Vaijifliing Line, this rrfiglit pals for an Axiom, therefore I have made it the firlV, in piy Tre^tife; it follovvs then, naturaRy, to determine what are the confequences arilipg from the Interfeaions of Planes;which are not parallel to tlie Pidure, wliich is determined by the fecond (the firft in.this Work) that thofe Lines are allparallel to each other. What.the lecond Theorem is intended to prove (refpeaing the Vertical ELne) .may all be deduced from the definition of it; the third is to little puipofet the.^th and 6th, with their Corollaries, .are pertinent; but the yth'is of no cgnfeqpence, as it,i;dpeas praailing by the Direaing. Plane, which is feldom .dope, ,^d.ffequeiitly impraaicable, or attended with unneccfliirv trouble. Tile Ml {lioujd have been a Corollary to the.jth, and tlie Corollary to ir would have followed there, better than here; ’tis the lotli of mine; as it relpeds Vaniffiing of opinion it comes better 3lter the Theory ot Vaiiilhing Line.*;, and jUq, after, that Theorem (the, iSth.of this) which refpeas Lines parallel to the Piaure., and.w^hich is, herp, partially determined, in tiiele words, ■“ If an original line.be shen iq a plane, parallel to the piaure, it will be in the fame proportion,” &c. VVliy^conlined to a Plane which is parallel to the Piaure? when it is ma- infeftly the,fame being in Plane/wTC'fjtr fituated. The loth is the fourth, and the 1 Ith the third of mine; the Corollary to wliich is impertinent, ineerly a neo-a- tive to the reverfe of the Premifes of the Theorem. The i2th is the fifth of mine, and the 13th unnccefliiry, being the con.vfrfe of it. The 14th, 15th, and i6th,' a;-epf no confequence, as.Theorems, being meeiiy Remarks, which might have been made .after fpme of,the other; the ryth is a Corollary to the 12th, ane- cefl'ary confequence ol it; and tlie igth, though an extraordinary property, and made a gqeat deal of, is to no purpofe whatever, in Drawing. This Theory is illuftrated by the Diagrams, mentioned above, cut out, in Pafle- hoard, fo as to form every Conftruiftion of the. elementary Planes, neceffary for the Inveftigation, with great ingenuity and trouble, too much.for human patience, to L 1 bellow Prof lii-r Cowley. >34 Stcl, IX, A PARALLEL, Profeflbr beftoiv on each Book. In'fucli a Work, it is no wonder there are falfe References Cowley, and that many of them ftand the wrong way in the Plates, when the conftrufliou is formed, fo that ’tis troublefome to find them out, frequentlv, which is,perplex¬ ing to the Reader. After the Theory (in a Conclufion) he gives five Problems; ■three-of which, had the Schemes been more general, and more diftinft, contain the Elements of Praftice, in .all common Cafes. The firft is, to find the Indefinite re- prefent.atioii of a Line inclined to the Ground Line; but (according to cuftom) in an Angle of 4.5 deg the Diagonal of a Square; (See Prob. i;. Sea. 5. B. III. or the 7th. Sea. 4.^. ^ The third is, a Vanilhing Point being given of certain Lines, to find the Vanilhing Point of other Lines making a given Angle with the former i(See Prob. 4. Sea. 3. B. III.); the Example is of a Right Angle, both Sides inclined ^ equally, ill 45 degrees. The fifth is to find the Image of a Point; (See Prob. 14. Sea. 5. B. 111 . Meth. 3rd.); his Lines are equally inclined. Four Examples fol¬ low; one for the Problem., the feeoiid for a Line perpendicular to the Interlbaioii; the third for Lines parallel to it, and the fourth tor Lines pofited obliquely. The ■Scheme, for illuftrating, as well as performing thefe Problems and Examples, is really ingenious; by which is fliewii, to ocular conviaion, that the Theory mid Praaice perfedly agree; for, after the procefs, the Scheme (which is fimple) being raifed, the correlpondeiice with Theory is obvious; by means of filken threads, fixed to the angles of the Figures, and paffmg thiough'the Piaure to the Eye, in¬ dicating Vifual Rays, by which they are fuppoled to be feen. The Figures are, a Square, parallel, another diagonal ways, and a Pentagon, regularlv fituated, cen¬ trally. Had they been kept farther alunder, fome of them farther from the Inter- feaion, the Pentagon obliquely fituated, and inflead of the Square diagonal way.s, an oblong Reftaiigle oblique to the Piaure, a better Diagram could not be deviifed for tlie purpofe, being very fimple, yet lufficieiit m a Work of tills kind. He proceeds with Annotations on the lecond Pair, which, in qii ntity, is equal to, if not more copious than the Part itfelf. Firft, of Projeaion, in general, and the various kinds of Projeaion ; he fpeaks of Military Perfpeaive (as it is ahfurdly called) as a medley of Projeaions the moft incoiififteiit, unnatural and abfurd; which can ani'wer 110 purpofe whatever, but what may be better attained bv true Perfpeaive. This is, almoft verbatim, the opinion I always had of it, and as I have exprcITed in the lecond Seaion, Page 27. Secondly, he fpeaks of the con- ftruaion ot imaginary Planes iiecelTary in Perfpeaive, by means of wliich, the pofitioiis ot Objeas, in relpea of the Horizon and of each other, are determined- being otherwile undeterminable, which is juftly obferved. He lpe.aks, with pro¬ priety, ot,the limited Ideas the old VVriteis had of Peripeaive, being confined wholly to the Horizontal and Ground I..ines, without ever confidering, that Lines of the fame utility may be applied to Planes in all Pofitioiis; but, that it would be abfurd to ule the fame appellations to them. Next, he fpeaks of the different pofi- tions of the Piaure, relpeaing the Horizon, and what Subjeas are proper to be reprefented on each ; then of its Diftance, and the different Effeas it is produftive of, which heilluftrates, largely, by Lemmas, and Corollaries deduced from them; and concludes his Remarks thereon, rather as a Painter than a Mathematician. The height of the Eye is next confidered, in which he gives a moft unaccountable formal Definition of what is c.alled, fimplv, a Scale, which he calls the Proportional Meafure ot the original Line. Df the Dimenfions of the Piaure he fpeaks truly ; that the whole of It ought to be contained within a Circle whofe Radius is its Diftaiice ; aho, of the bad effeas of viewing a Piaure out of the true Point, bis remarks thereon are judicious and pertinent. He concludes (in the 117th Page) thus “ Having far exceeded the bounds firft prefciibed to this little Tract, we here con¬ clude, rcferving the doarine of lhadows, the method of applying pei fpedive to Iceiioguiphical repreRiitations, as now praaifed in painting the feenes of theatres the maimer .of drawing anamorphofes, &c. for a future difquifition ;” rcfpeaing which, uiilcfs he meant, after the fame manner, to give a Conftriiaion of the Scenery in Pafteboard, by way of a Model, i am of opinion, the Community has luftained no great lols. ^ Sea. IX. REMARKS ON Du. PRIESTLY: Y. THIS Traa, entitled a Familiar Introduaion, to the Theory and Praaice Joseph of Peripeaive; by Joseph Priestley; LL.D. F.R.S. is dedicated, with very Phtest little Ceremony, to Sir Jofliua Keynolds. In the Preface he tells us, that iiecel- ley lity firft fet him to ftudy Peripedive, having frequent occafion for it, in order to Lp o delbribe his Eledrical Apparatus, being fituated in a place where he could get no ' ' one to draw for him.; but finding the Books he ftudied fo immethodically digelled, and badly explained, that, in many Cafes, he was able to inveftigate a Rule him- fclf, from confidering the nature of the thing, fooner than he could find it out from the Books. What Books he ftudied from he does not lay ; but I am of opi¬ nion, that With a competent knowledge in Geometry, he might devife a method as foon as he could acquire it. I fpeak from Experience ; for, without knowing •Geometry, wheai I ftudied it firft, from the Jefuit, I was fo little fatisfied with his Rules, that -I devifed means to convince myfelf that th.2y might be depended on, relpefling Lines parallel and perpendicular to the Pifture ; nothing further is to be acquired from it. _He fiiys, that the whole Art confifts in drawing the perfpeftlve Appearances of Lines, in no more than five different varieties of Pofition, and in fixing Points, at given Diftances, in thofe Lines; meaning, to draw firft, the Indefinite Reprcfen- tation, and to cut off Portions, reprefenting certain finite Parts, in the Objedl. He does not tell us, diredlly, what the five pofitions of Lines are; but, from the Work, I find that tliree of them are in the Ground Plane, viz. parallel, perpen¬ dicular, and inclined to the Ground Line; the other two are perpendicular and incli' ed to the Ground Plane; and which are all reducible to three, in relpeft of the Piffure. He feems to lament much, the general deficiency and negleift in cul¬ tivating fo ornamental, fo valuable, and-neceffary an Art, to many; not only to Painters and other profefled Artifts, but Gentlemen, and others who travel in order to take Draughts of the various Objefts they meet with in their Travels. He is furprized, that amongft the number of Ladies and Gentlemen who learn and are very fond of Drawing, fo very few (though they are capable of drawin-^ with elegance) know any thing of Perfpeftive. 1 can tell him the reafon ; be- caufe there are but few of the Mafters, who teach Drawing, know enough of it, to be capable of teaching others. He exprelTes furprize, that a Perlon who can draw human figures, in every variety of attitude and paffion, yet are not able to take a correift drawing of the moft fimple machine, of a chair, or a table which require nothing but ftraight Lines.” This I can aver is a Truth ; for I have leen, in the Works of great Mafters, right lined Objeas introduced (See Fig. 31. P. 124.) in which, equal perpendicular Lines, whicli are fartheft from the Eye, were reprefented longer than the hither ones; and of confcquence., thofe which reprefent horizontal Lines converge the wrong way; that Artifts have imbibed this abfurd Idea is evident in their Performances. « Of all the imitative arts (fays he) that of Perfpeaive is capable of being brought, and indeed has aflually been brought the neareft to perfedion ; becaule it is wholly within the fphere of mathematical fcience. Accordingly xve, lee, that there is no objeft of fight, be it ever fo complex, which, thofe who are Ikill’d in it, are not able to reprefent, juft as it appears to the eye. By this means, the ideas of all the beauties of nature and art are faithfully preferred; and thofe per- fons who have not opportunity of feeing the objeds therafelves, may ftudy, and be delighted with them, in the works of travellers and natural hiftorians.'” And again; “ How many philofophers, and even perlbns who have been no mean pro¬ ficients in other branches, &c. do we hear complaining of their ignorance of this Art, and of the difficulties they have met with in their attempts to learn it; fo that, they are always obliged to employ a profefled artift, to make drawino-s of the apparatus they make ufe of, in their experiments;” or in their Piibhcation.s. Here, I muft tell him that he is miftaken ; for, in order to fave a trifle (as they imagine) in the Drawing, they often employ a paltry Artift, who perhaps knows jefs of Perfpedive than themfcives; by which, their Plates are often fpoiled. A Sketch m.ay dc, being wanted only, to (hew the Delign; hut, when it is to be engraved, ’tis madnefs, not to have the Drawing corred. DoQor I’rieftlcy. Sea. IX. A parallel, It E a misfortune, a real lofs to the Public, that, when Ships are fitted out, and I eiions lent on Dilccveries, at the Government’s expence, no greater care is t.iken in the choice of the Arrift they take (one is not fufficient) there are many r ounv Artifts who can draw, and even paint very prettilv, nay fine, yet little or no credir IS to be given for the truth of their Portraits. How mucli it is to be lamented, that many fine Works, Publications of various kinds, have been wholly fpoiled] for want of proper Artifts to make the Drawings? not that thev were not to be had, but becaufe they imagined they favecl fomething, in employing a Perfon in no Reputation, but often pay more. If thev confidered only their'own intereft, they are Infers by it, as the engraving would be the fame, and the Drawiiw, in com- pai-ifon of It, at leaft the difference between employing a good Draftfinan and an indifferent one is a meer trifle. In this, I believe many are deceived; thev imagine if they get a paltry Sketch of what they want, that the Engraver can mend ir and make a fine Print from it. The Engraver is often a meer Mechanic; and if he can make a faithful Copy of the Drawing, 'tis all he has to do; not one in ten 13 capable of correcting the Drawing be it ever lo erroneous, yet he derives moft credit from the performance. What a noble Work would tile Hiftorv of I.ondon and Its Environs have made, were the Piints on a larger Scale, and'from correft Drawings; and would not the Proprietors find their account in the fale of it? Perfpeaive, he fiys, is now carried to fuch a degree of perfeaion, we can hardly conceive it pcflible to be exceeded (in which he advances a Truth) ; “ all that is wanting feems to be a method of facilitating the attainment of this art; and, in that relpeft, he thinks there is room to improve upon all the Books he has leen on the Subjea; of which, the (fate it is in (amongft Artifts) is a proof tlmt the attainment of it is difficult.” Here I muft enter a Caveat ag.iin, and inform him, that that a not wholly the cafe; for they want to acquire it without Study, and \\ill nor bear to make ufe of Rules, though ever fo limple ; and, in my opinion no Rules are more lo than thofe uled in Pa'Ipeaive. For luftauce; what can be fimplertban Vignola and Sirigatti, as in this Appendix? uled nlfo by Pozzo in his fecond Volume; uhich Rules are ftill ufed, and ever will be in common cafes- but they will not do generally, as it is now, on the Principles of Brook Taylor; in whole fmail Traci is contained the whole Ele.ments, both in Theory and Prac¬ tice ; but they cannot comprehend it. Hro Doftor lays, that his.Treatifc being only a familiar Introdufiion to Per- fpeaive, is by no means intended to fuperfede other more copious Works, but to make them better underftood ; fo that, to fliew how Lines are determined on the Picture, according to the five Pofitions he Ipeaks of, with the projeflion of a Circle IS all he has aimed at; which, he thinks, any Perfon, having a previous know- Jeclge of Geometry, may acquire iii a few jiours; and ip.deed, 1 think fo too; alfo that every Schoolmafter who is, as yet, .wJiolly unacquainted with the rudiments of It, might make hImfUf raafter of them in a foiv Eyeuings. So they nrighr having the .above requjf^es, and w;hiQ(i, pv4ry ;i,cho()lmafteritJ«^.6r to havcj 'but they can Ipend their Evenings more , agreeably, ^t ^ardi. Drafts,. or Back-Gammon with the Excifcmmi or- Clerk of the PariiJ), or Other-Neighbour. -, ’ This Work is dividdl into thirteen Parts; in the fcft of whicli, he tells us what Utenlils aie neceliary fordrawingj and deftiibes their ufes, eveii.of a black lead Pen cl; winch he is fo particular ip, as to tell us, that, “ they are very ufeful in order to drarv lines that are of no feivice, but as a direaion to draw other-lines by them - becaufe, when they have anlwcrcd this purpofe, they may be taken-out with a few- crumbs of loft bread 1 hq next ts preparatory; in which he defeends to Minu- ti.n, lurn .as, “ The firft thing I do rs. to laften a Iheet of paper upon my drawing boaid ov bitsmt wafer or leahng w.ax-, at each, corner, in order to make it lie fla” and iwiiuy 1 his is, in general, the flile or manner of Defciiption ufed -throuah- out this Work; telling how he does it, rather than how the Students are to pro¬ ceed. 1 do not mean to infinuate, that the whole Defciiption is on a piece with the above, for it is not; and I mult-own, that 1 am hurt to.find ftich puerilities, in . ths Sea. IX. OF THE ENGLISH AUTHORS. '37 theWorks of Men of Letrers and of Science. In this preparation of the Drawing Doftor Board, he introduces five Definitions, and no more are given, here; one of whicli Prieftiey. is exceptionable; viz. “ the horizontal line is fo called (fuppofing I (land upright).” Part 111 . in three Sedlions, fliews how he manages Lines in the three Politions to the Ground Plane ; the fourth, in two Sedions, when they are perpendicular and oblique to the Gmund Plane. The fifth Part is applied, whollv. to dividing, meaiunng, and proportioning Lines, in all the former Cafes. The fixth; ui three Pages, is a futnmary account of all the ellential Rules; in which he fays, a Line oblique to the Ground Plane is meaiured by drawing neth horizontal and ground Lines; _ with other grofs Abfurdicies, and trifling Remarks. In three Cafes; ot the fil'd Seaion, of the (eventh Part, he (hews how a Circle is defcribed perfpec- tivcly, either in a given Square or from a given Diameter, which are judicioufly managed; another, very fhort Sedion, is of different Ground Planes (as he calls them) that is, of Planes inclined to the Horizon ; wherein his Vanifhing Lines are truly drawn, but the Figure, which is intended to give an Idea of defcending and afcending, is inadequate and incorredl; the defcending part appears horizontal, the horizontal Plane appears to atcend, and the afcending part, vertical. I (liould have obferved, that he makes three different Methods of Drawing; all the foregoing is by fuppofing the place and polltioii determined and the rheafures know’ll; the eighth Part in four Pages, is by having the original Figure drawn; on the Ground Plane. He gives but one Example, a Triangle. The other Me¬ thod, in the ninth Part, is mechanical ; a tedious method, by taking the Angle of altitude and declination, from a perpendicular to the Piaure, of every Point. The tenth Part is on what he calls orthographical Perfpeaive, properly ortho¬ graphical ProjtiRion, which is not without merit. 1 he eleventh Part is on Shadows, in which is but little, worthy of notice; the Shadows are chiefly of Lines perpendicular to the Ground; lome thrown on inclined Planes, for which he gives no leading Principle. The fourth, and lad Sedion, is on refleded Images on Water, where he is entirely out of his depth; for, he places an Objed on a Hill, clofe to the W.ater, and meafures the Image from its Foot, on the Hill. Another, at a diftauce, on the Ground, the fame; and an in¬ clined one is drawn from its interfedion with the Ground inftead of the Water. The twelfth Part contains general advice and diredions relating to the art of Drawing in Perfpedive, which is to little purpofe; for he fays, “ But where ex¬ treme accuracy is not required (as indeed it very feldom is) there is little occafioft to meafure any thing ; and yet, a perfon who has a jufl idea of the nature of perfpedive will make a drawing infinitely more jufl, and agreeable, than another perfon can who (hall even meafure every thing He has given two Plates from his Hiflory of Eledricity; the laft feems corredly drawn, though he fays he mea- fured nothing, but only fixed the Point of Sight, drew the horizontal Line, de¬ termined the Diftance, and fixed the Vanifhing Points. He tells us how he did it; but, 1 fear, no Perfon will ever do another by the Delcription. “ I could engage (he fays) to communicate to any perfon the knowledge that is requilite to make thefe two drawings in two or three minutes; whereby he might finifli them, at his lei- fure, in little more than an hour, each:” this is wonderful; nor in as many Days, I fear. The 13 th contains nine Definitions, five of which were given before. After this is a fhort Theory, contained in five Propofitions and two Definitions ; drawn up, he fays, by Mr. Jofeph Prieftly of Hallifax, to whom the Reader is indebted ; and from whom, he once expeded a much more complete and elegant Theory of this Art. He alfo prefixed the Notes, and wrote all the Paragraphs, in which the Propofitions are referred to ; and affifled him in reviling and correc¬ ting the whole Work; fo that, it is by Mefll Jof. Prieflley, or Dr. Prieflley, & Co. There is, on the whole, merit in this Work, and Ingenuity ; how far it may anfwer the End he propofes I will not fay ; but furely, thofe Works which are more copious, or valuable, contain the Rudiments alfb, and do not require othel In- trodudions to render them intelligible; if they do, they are, at lead, very imperfed, * The DoAor has advanced ftrange Doffrine here, indeed, which I deny; he might have laid fooner. M m ’ IN Sea. IX. REMARKS ON NOBLE’S PERSPECTIVE. ■38 Edward IN 1771 was publiflied a Treatife, entitled, “ The Elements of Linear Per- Noble, fpeaive, demonftrated by geometrical Principles, &c.” by Edward Noble. ’ 77 '' Had this Author been more mature in his knowledge of the Science he has un¬ dertaken to inveftigate, and as well verfcd in the art of Drawing, as in Language, or in Geometry, the Arts might have been indebted to him for his Labour ; but, he was in too great hafte to become an Author, and difplay his Talents to the World. The Preface to this Work is wrote in a Stile, and with that Spirit which would do credit to one more advanced in years; but his Eloquence or Zeal, beingfome- what ungovernable, has betrayed him into Error. There is that Expreffion, in the firft Paragraph, as induces me to quote it, literally ; becaufe, I think it a tacit Reproach to many Artifts who make a Figure, in the prefent Age. He begins thus. “ Thofe w’ho are content with learning by rote the mechanical rtiles which compofe the praflice of an art, without any folicitation concerning the Heps which reafon purfued in their inveftigation, are more fitted for works of labour than of genius : however their cotemporaries may admire their induflry, pofterity will never hear of their improvements and invention. In a word, they are totally void of that fpirit of enquiry, and liberality of fentimcnt which, by exerting the mind to trace effeas up to their cautes, becomes the parent of difcovery. It is tliis difpofition to which we owe the perfedion of the arts, and the extenfion of fcience; and which, with pleafure, is obferved to charaflerize the moft eminent of thofe whofe purluits lead them to ftand in need of the art of perfpeflive.” He ranks 'Writers on Perfpeaive in two Claffes; the firft are thofe who have treated the Subjefl in a mafterly manner, maihematically ; but, he adds “ they are unintelligible where they are moft wanted, and ufelefs where they fhould be mqft prized.” In the fecond Clafs are thofe who endeavour to demonftrate the Principles without mathematical fpeculation. “ Thefe gentlemen (he fays) may be compared to an architefl who would fupport a building whilft the foundation is removed. His Ikill and contrivance in a curious difpofition and arrangement of props, might be worthy of commendation ; but his abfurdity would be equally ridiculous, was he to afi'ure us his fabric was more durable, beautiful, and conve¬ nient, becaufe it flood upon crutches. I mean not, therefore, to depreciate the ingenuity of this clafs of writers, but cannot fubferibe to their utility. Their mode of demonftration, by an infinity of pafteboard and firing machinery*, bears the fame relation to geometrical reafoning, which geftures and dumb ftiew do to verbal expreffion; and even this comparifon is more honorary than juft.” I am not a little furprized to find, that a Perfon, who feems to be well ac¬ quainted with Euclid, ffiould fo far forget himlelf; and would afk him, on what the 11 th Book of Euclid is built and fupported, on which the Theory of Per- fpeftive isalmoft wholly founded? are not the Doftrine of Planes, refpeaing their Pofitions and Interfeflions, the Interleftions of Right Lines with Planes, &c. the Elements on which the whole Doftrine of Solids is built ? W’hat are the elemen¬ tary Principles of Perfpeaive, according to Brook Taylor ? is it not wholly founded on Vifual Rays fuppoled to be cut by the Plane of the Piaure in a certain Ratio? What are all the Diagrams in the firft four, and in his'pth, loth, and 31ft Plates of his Work (containing the elementary part) intended to reprefent, but Pafte¬ board and Strings? unlefs, from their clumfinefs, in giving thicknefs to them, he imagines them to be Wood. Nliy, he^ really exprefles and fuppofes thern to be Pafteboard, in the 14th Page. The order in which this Author proceeds in his Work is fingular, and, I think whimftcal, the firft Chapter containing nine Theorems, part of the Theory, only; for he thinks it irkfome, to crowd too much fpeculative Knowledge at once on the Mind, therefore, he is continually perplexing the Reader with long Demon- ftrations to his Problems, to the Operations, Examples,- and Remarks; allb, by way of amufing his Readers, he entertains them with Digreffions. Although I would have Science treated as familiarly as the bubjeft will admit of, yet, I think • The Author, by this Sentence, feems to have an Eye totcwlcy’s Theory of Perfpeaive. it Sea. IX. OF THE GLISH AUTHORS. it very un'cientific and IrrcpruF m hre.-ik the thread ofreafoning thus, and give it pieceme,il. If the Subjed be both theoretic and praaical, is it not moft eleeible to keep the Theory diltincl and feparute, to which we may refer on all occafions ? and not have ,t to leek for in various parts of the Work. ' If the Student choofes to atnufe hnnfelt with the pr.iflicai Part, by way of relaxation from abftrule rea foiling he may, and retiiro to it a ain when he is in the humour for it. Bv wav of apologizing for the Method he has adopted, we have the follorviiig paffaae • ‘‘the warmth of :ma-m„t,oi. and luxuriance of fancy, which impels thehind°d the cultivation ot lire tine arts, is little captivated with abftraaed fpeculatioiis It 13 elTentially ditlerent trom that calm and peiifive turn of mind, that with fllent enjoyment, wdl tr.ice, an intricate truth through all its mazes, and exult in the diicovery With a zeil; unknown to all but mathematicians; thefe are formed to explore the meanders of the vein, and are happy to dig the of fcience, whilft the others apply it to the convenience and ornament of life, by branching it into thole arts wnole utility adds to our eafe and fafety; and whofe polilh enlivens our xancy, and engages our admiration.” ^ Alter bellowing the praife due to the produaion of Dr. Taylor he fivs • “ Yet his fate has been to be more admired and celebrated than underftood' fbecaufe'! He fometimes quotes Euclid in his Deraoiiftrations, and thereby alarms tlWe who know not tuat Euclid's Elements are built upon a few principles of common fenfe wuhout which the moft domeftic .and fimple negotiations of life cannot be tran- laaed; and that what they Ihun as fobjeas too fublime and intricate for their comprehcnhon, are only tne moft familiar truths made artificial by regularitv and dug,,lied by .a technical language.” He appears to be well verfed in Geometrv ay has introduced a greater portion into his Work than is ufual, from the ift ye aid, 5th, yh and nth of Euclid, luppofing it elTentially necelTaiy to Per- fpcaive whidi takes up no lefs than 100 Pages; making Remarks on tL utility or each Propolition, the Deraoi)ftr.itioii3 of which are concife and elegant indicat mg a Talent for geometrical Inveftig.atioii, which, if he has purfued, mull ere this be very great. . ’ ’ The Work is divideddnto 14 Chapters, preceded by an Introduclion, containing the common oblervat.0,1 of feeing Objeas through a Window; which, though pertmeiit on the whole, has lome Puerlities. The firft Chapter contains DefiL for reprefciuing Figures in Planes which are not parallel to the Piaure. Although he has given the Definitions of the firft Book of Euclid rcguLirly omiting lu^ as are to little purpofe; yet, here. In deferibing the ele- mea.ary 1 lanes, he deduces but fix Definitions, at firft, viz. the Piclure, the Original Rye, and Objea, the Riteniig Line, the Vanilhing Plane, and Vanilhing Line, befo e he begins with Theorems. The firft is, that all Original Planes which are parallel have the lame Vamlhing Line; and the fecond, that the Vanilhing and Buying Line {Interje^on) are parallel to each other; after which follow fix more Defiyions, vm. the Center, and Diftance of a Vaiiifliing Line; Original Line yd Entering Poim, its Diftance and Vanilhing Point. The third Theorem is in theft words. yi miginaUines which are parallel to each' other have the fame Diftance and Vanilhing point. 1 he 4th 1 heorem runs thus; “ The Diftance of ay orymal Line IS the InterlecToii of its vifual plane, with the vanilhing plane y that original plane, in which the Paid original line is fitmited.” This is no Theyty but a Defimuon; tending to let us know what we are to undetftand by the diftance of an Original Line; but properly of its Vanilhing Point. lam ot opinion, that in the wnole Book there is nothing dependant on this Theorem. The 5th IS meey a Delmition, informing us, that “ the v^ual line oi any origi- nal line IS Re fta,on of the vifual plane and the piahle.’' which he has previ- yfly d.finey a Lme joining the entering and vanilhing Point of any original Line ; the Vtfml Plane is defined after the third Theorem. The 6th Theorem informs us, that “ the peTpea,vc reprefentation of an original Line is a part of Its vifual Line. Tftie 7th is an illullration of fix of the preceding Definitions, by a delcnption of Fig. 4; after which he fays, that, “ The interleflion of an^ two '39 Edward Noble. J40 Sea. IX. A PA RALLEL, Edward two vifual lines Is the perfpeaive reprefentation, of the interfeaion of their ori- Noble. ginal lineswhich is of no confequcnce as a Theorem, but may be deduced as a Corollary from feveral. The 8th is, in fubflance, the fame as Cor. to Theo. 5. of mine; and the 9th is the tenth of mine ; an ellential one in Pradice, though omitted by almoft all the preceding Authors (as obferved heretofore) from which a pertinent Corollary is deduced, with judgment, which concludes the Chapter. Chap. II. contains Pradical Obfervations on the foregoing Theory; in one general Problem, viz. “ To find the perfpedive reprefentatlon of any right-lined figure, fitnated in a plane not parallel to the piflure;” for which there are three Opera¬ tions, of the various fteps, followed by a Demonftration ; the wliole referring to a theoretic Diagram ; after which is a fourth Operation, only to draw the vil'ual lines, i. e. the indejinite Reprefeniations, by which the Figure is determined on the Piifture; followed by two Remarks, with Demonftrations to each, and remarks on them ; for which is another Plate and Figure (alfo theoretic) and which, hav¬ ing no other difference, but the original Plane turned down, and the vanifhing Plane turned up, into the Pidure, ferves equally for both. Then comes the loth Theorem, in thefe Words; “ When the place of the eye and the original figure are laid down on the fame plane, the diliance of any original line is paral¬ lel to' that original line.” Brook T.aylor, in his fecond Part, gives this and the fourth In one Definition; for furely, to draw a Line, from the Eye, parallel to an Original Line, may be done, or imagined; the Point in which Inch a Line cuts the Pidure, he calls the Vanifhing Point of the Original Line ; and the P.i- rallel meafures the diftance of the Vanifliing Point; the Term is arbitrary. That the Reprefentatlon will tend there is proved afterwards (Prop. 3. B. 2.) viz. that the projedion of a ftreight Line, not parallel to the Pidure, pafl'es through its Interfeding and Vanifhing Points. Here, it is a Definition, only, as above. Chapter III. contains various methods of finding the reprefentations of right- lined F'igures not parallel to the Pidure, which might as well have included the general Problem in the foregoing Chapter. It is remarkable that he proceeds to Figures immediately, without firfl; determining Points, and Lines in their various pofitions, by which, all plane Figures are determinable. Here are two Methods with four Examples, in Triangles and Parallelograms, with Demonftrations? after which is- Theorem i ith; by which, the proportion of the finite parts of any Line are perfpedively determined; the fame in fubftance as the 13th, of mine; then follows a third Method, with three Examples. A Lemma, with a Problem, follow after, for determining Lines parallel to the Pidure; and then we have two more. Definitions, with two other Methods; which, fave the Terms defined, and ufed in them, contain nothing new or particular. Chapter IV. begins with a lingular Problem. “ By any original line, which is parallel to the Pidure, to extend a Plane which lhall be parallel to the Pidure;” which I conceive no meaning in, nor ufe for, in the leaft; to conftrud various Planes, geometrically, on a Plane, is impradicable, and the operation abfurd. This fliort Chapter is wholly theoretic. The 12th Theorem Is, “The perfpec- tive reprefentatlon of any original line, which is parallel to the pidure, is paral¬ lel to that original line.” Now, as an original Line, parallel to the Pidure, is ne- ceflarily parallel to the Interfedion of whatever plane it may be in ; its Reprefen- tation, being parallel to the Original, is alfo parallel to the Interfedion (Eu. g. ii.) the foregoing Lemma is confequently deducible from this Theorem, as a Co¬ rollary, and not at all neceflary, previous to it. Four more Theorems, refpedlng Lines parallel to the Pidure, comprehend the whole of this Chapter, all which, fave the 15th, are deducible from the 12th; and, from the fame Diagram, a general ratio of the proportion of the Reprefentatlon to the original Line is determinable; in this, we have only, the ratio which the Image of one Line has to another, being the fame as is between the Originals; but, the ratio of the Image to the Original is no where determined: being equally diftant from the Pidure is what thould be underftood, of the Lines, their meeting in a Point is not effential. This Chapter (being applied to pradice) as it is fimpler in the operations, fhould have preceded the two foregoing. 3 In Sea. IX. OF THE ENGLISH AUTHORS. 14 In the fifth, two Problem? of very little confequence (refipefting Lines parallel Eclw.arcl to the Piaure) of which an nnneceffary p.irade is made, in Solutions, Demonftra- Noble, rions. Remarks, &c. to as little ptirpofe, precede the, ipih Theorem, which fums up the whole eflbnce of the haft Chapter; that the reprefentation of every plane Figure parallel to the Pidure is fimilar to the Original ; which (had he determined the r.atio of the reprefentation to the original, as well as the parallelifm) is alfo dcducible from the 12th. We have, now, two Example.s of plane Buildings, having a Face parallel to the Piaurc, which, to me, i,s moft furprizing; that any Perlon, who leems to underftand the Doarine of Proportion, fliould°attem'pt to lay down Rules by which others are to delineate Objeas, which they do not apply themlclves ; for certainly, never Drawings were fo prepofterous as thefe, here e.x- hibited, as Specimens of the cfFea of parallelifm ; in which tire Doors, one cl another 7 times its width ; common Windows 4-J and c times ; lb that, allowing 3 feet for the width, the Doors are from ifif to 2! feet high ; the Windows from 13! to 15 feet: Doors, full in front, at leaft thrice the proper height, Windows more than twice. ° I have been rather particular on thefe Chapters, in which may be feen the un¬ common method of proceeding by this Author. Neverthelefs, p'rovided that each Chapter, being independant of the foregoing, was prefaced by a I'heorem, or two, on which the reft of it depended; and being well digefted, the Method is not to be defpifed, but may be improved into a good one, for a praaic.il Treatife. What I think him moft reprehenfibie for, is his attempt to new model the Science, by innovations of his own ; fuch as altering the Terms and Definitions. This' is a fault peculiar to young Authors, who are apt to imagine that they have more difcernraent than others of riper Years. For inftance; the Ground Line or In- terleaion of anj: Original Plane, he calls the E/ilerir.g Line-, and the Point, in which any original Line cuts the Piaure, the Eutermg Point. The Radial or Parallel of an original Line producing its Vamfhing Point, he calls the Dijfance oi the Line; a ftrange Term indeed; the Indefinite Reprefentation of a Line he ciilL its Fifual from the old "Writers; what induces him to retain this obfolete Term,'l wn’t devife, as nothing can poflibly exprefs their meaning better than Indefinite Repre- fentations, as given by Brook Taylor, himfelf. . Wording Plane is another Term he is very fond and makes frequent rife of; as this is an entire new Term of his own, I lhall explain it. Having given, or fotind, the Vaiiiftiing Line’ of any Plane; by means of that Vaniftiing Line, to draw the Reprefentation of aiiv geo¬ metrical Figure; that is, to perform the elementary .Problems, iii Perfpe'atve- and as that Figure may be fuppol'ed In fome Plane,'baWeady determined,' he calls It the Worhng Plane, an ufelefs and unmeaning Term. Scale Line, , ox ■working Lme, and dividing Center, are alfo his own ; the'firft is either the real Interfcaion or an imaginary one ; the other is the Eye Point, transferred, ’ from Its true place’ to the Piaure, in a Line parallel to the former. The two next Chapters (both Chap. VI.) arc called Digreffions, the firft is concerning the refraaion of Light, the conftmaion of the Eye and the nature w IJ ’ entirely optical, I lh.all pafs oyer; having given, to the World, my Opinion on' thefe matters, and here is nothing advanced that is either new or fingular, it is liut reafonable that others m.iy, unmolefted, give theirs fuftering the Reader quietly to adopt the Opinion he moft approves. The 2 nd is concerning the diftance of the Eye in refpea of the fize of the Piaure, &c. in which he fpeaks, with judgment, of the Diftance of the Piaure, and of the diffe¬ rence between the reprefentation of an Objed and its appearance ; .and determines truly, the pofition of the Pidure, the Station being previoufly determined, in re- Ipca of the Objea; which are the chief of what is contained in this Chapter. .1, J nearly equal to all the foregoing, containing, “ Univerfal me¬ thods of finding the reprefentations of objeas, in any affigned part of the pic¬ ture, without a geometrical plan.” Here are two more Problems (3 and 4); the firft teaches howto determine the Vaniftiing Points of Lines makIn. IX. ?43 OF THE ENGLISH AUTHORS. Cclumns (as above^ winch are parallel to tlie PiAiire; iti which he, Ucry ludici« oiifly, (lefcants on home pafl'ages in Kirby’s firft Work. I could vviih to trahfcribe lume of his remarks, but mult refer the Reader to the original, begiiiing at Page 146; or to the lalt Paragraph, P.;ge 117, ot this Appendix, on the fame Subjetl. One palTage (Page 160) is lo very trite, that, in juffice to the Author, I lhall cite it. Attei (hewing the abfurdity of his Keniarks, refpetling the reprefentations of Columns, he refers to the Frontlfpiece, which, he fays, is a tacit encomium on the atL (lee hage i o6); atter wiiich, “ I (houM imagine that our author, in what follows, means a iimilar complement to the Science of Geometry^ by bringing toge- thcr, in this place, all the alhuruities which a man may commit who attempts^ta 1 ealon on a mathematical fubjefl, without fome knowledge of its elements.’’ From what has been remarked on the iirll feven Chapters, the Reader may conceive a tolerable Idea of the Slile and Charaaer of this Work, which, on the the whole, is not a bad performance; had the Author been as well veiled in Prac¬ tice as in the Theory-of Perfpeaive, it might have been more ufeful, with but little more expence; but that is a talent tew are vefled with, who have treated on the Subjea, for want of which, they necelfarily failed in the main defign of their Undertaking. As I cannot, now, enter fo fully on the remaining Chapters, the Reader muft not expea I fliall he accountable for what may efcape my notice in them. The 8th is on inclined Planes and Plaures, Ihewing firft how to deter- mnie Wnifhmg Lines, in thofe cafes ; in which, the Author’s knowledge of the mot- abltruie part of the Science, is manifefted, for it is done with judgment, huS by very uncouth piagrams. In thus Chapter (Page 171) the Center of the Pidlure IS aehned; it is fometimes mentioned in the laft, but more frequently called ths cennn- of the Horizontal Line; iji a Note, Page 82, it is defined the Sek ef the Eye (33 It cert,ain,y is) and Jomdwm (he fays) it is called the Center of the Piaure. Fie.a IS a Plate (33) fiiewing a Uefeent, direa (i, e, having the Vauifhiug Line parallel to the Horizon) down two Streets, at right angles with each other; which, being properly confidered, 15 abfurd and moft unnatural; in the next Figure is both pfcent and defeent, in the fame manner, having the inclination perpendicular to thu Piaure, in which is intended fomewhat of the fame Idea as in Plate IV, In the next Plate IS exhibited the infideof a Room on an inclined Piaure, a ftrange Sub¬ jea indeed; in ihort, thefe muft be feen, to form a juft Idea of them. Ill Page 10, of the Preface, we have an Apology for want of elegance in the Plates, whicn (he fays) were not intended to pleafe the Eye, but to aflift the Under, Itandiiig, in thefe words; “ Ornament does not facilitate perfpicuity; fine prints are va.uab.e as pieces of art, but they are ufelefs in books of fcience; If obfeurity IS avoided, be.;,uty m.ay be difpeiiftd with, provided there ij an adequate abatement Ill the price ot the book. But I muft oblerve, that Perfpeaive is an Art as well as a bcieiice whicn is the foundation of all elegance in fine Prints, and therefore, cannot well be difpeiifcd wim in Treatifes on that SubjeG; otherwife, it feems reafonabie to conclude, that nothing elegant can be produced, wholly by its Rules (as IS too much the opinion of many) feeing no Specimens given to the contrary. In the ninth yiapter is difplayed a good deal of Ingenuity, in an original wav; for I have no waere met with the like. In this Chapter, 'the IForkins; Planc'U more particularly applied to u(e, on which (being previoufly prepared) is folvetl 14 Problems; the firft of which is from the 6th. the ten following, from the ift. ‘ Euclid; thefe are done on the reprefentations of Planes m v.yious pofitioiis to the Horizon and to the Piaure. for which, the working Line ferves as an Interfeaion to the working Plane; which is intended to reprefont the Slate or Paper, &c. on which Problems are ufually fplved, geo¬ metrically. I could fay a good deal on this Chapter, but muft ways it for the pielent; foiffice it to fay, that it is ingenious (but might be abridged) and may be luccefsfully applied to PraGicf. b Z * “y i- Chap. X. IS on Shadows, in general; and firft, when projefled by the Sun; which he treats 111 a far more theoretic manner than Mr, Kirby, notwithftanding h.s ridiculous parade of Lemmas, and Planes of Rays. &c, or indeed thap any othei. who has treated on Sliadows in a V^ork of this kind, fave Mr. Hamilton. 7 ’ Thg Edward Noble, 144 Scft. IX. A PAR A I; L E L, Edward The Introduction is not equal to what might be expeifted, from the abilities Noble, which are apparent in this Author, by the obi'ervations he makes, in general. His Theory of Shadows is comprifed in fix Theorems and a Lemma, which is as much a Thec.-cm as the reft; three or four pertinent Corollaries are deduced. The whole fubftance of this Theory, whiclj occupies eight Pages, is comprized in the three Rules, as I have called them; (but the two firft are meerly Definitions, and the third a Theorem, or Corollary deduced from the 6th. B. II.) with the Nota Bene on them; Se£f. 2. B. IV. P. 26;. The Figures given, for illuftration, are petit and trifling, and by no means latisfadlory; the References are rendered doubt¬ ful, in fome cafes, by means of two Letters the fame (two A’s, and a’s reprefent- ingthem); and, when he tells us, that a Line (A,B, Fig. 72.) is oblique to the Pidlure, it is evident, from the Diagram (of which there are two, fo near alike, that one would, with propriety, have ferved every purpofe of both) that it is meant to be perpendicular. In Art. or Seft. CX. he fays; “ If any opaque line be inter- pofed between the Sun and the enlightened Plane, &c. and will caufe a right-lined Shadow,” &c. as he is exprefly particular in the fpecies of Shadow, fliould he not have been fo, in the Line projefting that Shadow? but what diftindlion is made by opaque Line I do not conceive. I fhall pafs over two Examples, in 11 Pages, which are fcarce worthy of Criti- cifm, and take notice of the Shadows by candle light, in the next Chapter; deli¬ vered firft, in four pertinent Problems, with two Cafes, and two Corollaries, to the laft; after which is a Theorem, and an Axiom, which fliould have preceded the whole Theory of Shadows; a repetition of the 2 2d, given before. The Figure (73) for illuftration of the Problems, is not badly deviled; but the 74th is palrrv. The 12th Chapter is on Refleflions, on plane Mirrours, which is entered on rather abruptly, and confidered as a matter of amufemeiit, fcarce fit to be ranked amongft the uleful parts of Science. He gives four Theorems, which may all pafs for Axioms, and two Corollaries. Two Examples, when the Mirrour is perpen¬ dicular, and inclined, to the Horizon; ift, to find the vanifliing points of refledled Lines, in a plane perpendicular to the Mirrour, and then of Lines perpendicular to it, which is. included in the former; two Cafes of the latter (when the Line is or is not parallel to the Picture) with two Problems (not titled) conclude this. The 13th Chapter contains fome, not meerly curious Subjedls, but what may be turned to ufe, by feafaring Perfons, or thofe who would make proper Obferva- tions of particular Places they may toUch at; fuch as t.aking a View of the Place, by Reticulation, from the Maft Head of a Ship, &c. for which purpofe, the frame is reticulated unequally, the Threads expreffing (by their diftances from the Center) the Tangents of the Angles formed by the Points of the Compafs, half Points, &c. by which means, the bearings of the Parts from each other is afeertained in the Drawing. The Part preceding this fhould, I think, come after; which is, from a Drawing in Perfpeiftive, to determine the Bearings, and proportion of the Parts of the Originals to each other ; and laftly, four Problems in Inverfe Perfpedlive. The 14th and laft Chapter, is of the Anamorphofis, and the reprefentation of Objefls on irregular Surfaces, or on various detached Planes, as in a Theatre; on which Subjedls, he has rather given a few hints than preferibed Rules for the ' performing them. Upon the whole, there is difplayed a great deal of Ingenuity, and knowledge of the Subjedls contained in this VVork; but, like fome other, it is, in many places, obfeure, on account of the Diagrams, not being the moft intelli¬ gible; many falfe References, Lines and Letters omitted, going to and again from one Plate to another (fome being mifplaced) is very difagreeable to the Reader; we are often told to make one Line equal to another, which is only to reprefent an equal Meafure; thefe muft render it perplexing to a Learner, who knew nothing of the Subjeft before. This Work (an oflavo Volume) is comprifed in 298 Pages, and 48 Plates, for the Perfpeftive; with upwards of too Pages, and four Plates, for the Geometry. It is dedicated to Sir Joflnia Reynolds; and printed for T. Davies, in Great Rufl'el Street, Covent-Garden. 3 THE Seel. IX. REMARKS ON FERGUSON’S PERSPECTIVE. H5 1765. THE laft Publication liive one (and my own) on the fubjea of Perfpeflive, T4 mfs IS by the celebrated Mr. James Fergulon, F. R. S. a Man (o well known to Fergu- tbe World by his Leflures and V\ ritings. particularly the former, that the bare sort mention ot his Name to the Work is a lufficient recommendation of it. Inftances ot this kind of partiality to the Produdions of an Author may be met with, but none, in which the expedations or the Public could poflibly be more difappoi’nted, or their hopes, of acquiring a clear conception of the Subjed he treats on, frulirated^ than m the Work now before me. As it is almoft the lad piiblifliedon Perlpcdive’ lb I affirm it to be the very laft in merit, that has fallen into mv hands; in which, wc have an inftance of the credulity of Mankind, who form their Opinions of Au¬ thors too much on cicdit. As I never had opportunity, to attend Mr. Fergufon’s Ledlures, 1 cannot give my opinion of them, but, from common report, he was. clear and explicit; no wonder, having repeated the lame Experiments fo often over. Indeed I Icarce knew him, perlbnaily, nor have I had leilure to enter into the merits of any other ot his Produdions; in forac of thole I have looked into, there is an appearance both ot Knowledge and Genius, communicated by Schemes app.ireiitly well devifed and coiiltruded, and calculated for conveying Inftrudiou in a familiar manner; which rtiould be the aim ot every Author, who writes to inflrud thole wiio are ignorant, a qualihcation attributed to this Author. He begins his Preface tnus. “ In my infirm date of health, a lituation that is very apt to affect the mental facultie.s, I thought my late book of Mechanical Exercifes would have been the laft 1 Ihould ever publilh,” ’Tis pity it was not the laft, if It had more merit; but 1 have heard that Work fpokeii of, by a Per- fqn of approved Judgment in Mechanics*, as being erroneous in the firft Prin¬ ciples, It IS a misfortune attending (ome Authors, that they are not fufficienrly acquainted with their own T alents ; and 1 niuft own that I am really hurt, when I meet with any puerile perform.incc, of a Perfon who has acqui.-ed Reputation; for it does no: toilow, that becaufe be has an extenlive general knowledi^eof things, he is fufficiently competent in them all, and qualified to treat 011' th° m ; many Inftances may be brought to prove the contrary ; why then will theyh.izarcl the Reputation they have acquired, by publilhing any ill-digefted Performance? To gratify a Vanity, of being thought Man of gener.il knowledge, feems to me to be the chief motive, and the moft excufable; but, if it be raeerly with a view to their Emolument that they write;, depending on their N,ime, more than on die meiit of the Work, for the fale of it, they are dcferviiig ot the contempt their M^oiks will, in the end, be treated with, and juftiv; when thev, h.iving reaped a prefent advantage from it, are perhaps no more ; forae have fell ihe Mor¬ tification of It, and feeii a Icrutiny take place in all their Works, owipv to their treating oil a Subjedl they were not competent in. It is but realbiiable to expecl, when we find an Author, ot Reputation, has failed, greatly, in iome of his lattec .1 roduftion?, tiiat, vvere we as competent in the other Subjects he;has treated on, they might be founa equally deficient; and confequeiitly, mull Icfl'entlie opinion we had heretofore of the Author; ’tis Impoffible it ffiould be oclierwife.' He,(ays ‘' I have of late amufed myfelf, at intervals, with ftudying Perfpeaive.” , i 'hpve no conception that advanced Years, and andnfirin Rate of health, w'as a,fit time .to begin frslh ftudies, for publication. Indeed he acknowledges (farther-oir) that the Public are Indebted to his Friends, for this Work. Having draiyi'vthe F;guf 4 (which are here exhibited) as I.ellbnsjfor his Pupils, without anyJntqijtipn to,lay .them, before .the Public, he lays; /‘.But, upon ihevving thele|dr,avyiijgs; accidentr ally to lome friend,, tliey exprelTed. their dclire that I Ihould, write a cielcriptlon of the rules,by which they vvere delineated. I complied with their delirej and it is pitirely owing to their partiality to me, that I have confeuced to this pp,tiliifationt.'v' g/t Mr. Rogers, a Ci.ach-makcr of fome di(finaidn,*in Wincheftiir. •ul ■ a t J'”’’ Vof aiiology as'Kirby makes; ftrange, that any'Perro,n fhoiilJ he influenced to pubhfh their Works, niccflr bythc idftlgation of others. If the Autlioi; he not hiin- felf, fufficiently competent in the Subjeas he treats on,,to judge of what is fi to publilh, who is to Idvife, or jud^e tor him? ^ i 7 ^ - ■ ■' . • ‘ O o 146 Sea, IX. A P A R A L L E L, James Fergufon In obferving how requifite it is for Painters, and others, to be acquainted with Perfpeaive, he takes notice of the great deficiency therein, which is fo glaring- in the celebrated Cartoons, by Raphael, with truth and prop-rlety; firft in the proportion of the Figures to the Boats, in the miraculous draught of Filhes; and in the Transfiguration on the Mount, which, in refpea of the Figures (he lays) “ appears of thefize of a little hay-rick.” ’Though he does not confider this Work as a complete fyftem of Perfpeaive, yet he thinks he may venture to lay, that thofe who are raafters of what it contains will find no difficulty in proceed¬ ing to what length they pleafe, without any further affiftance; but I do allure them, then, that, unlefs they have far better Ideas than can be acquired from it, they will never underftand Perfpeaive. In the laft Paragraph, he requefts thole who already underftand Perfpeaive to confider, that (if he fhould appear too ver- bole) he never wrote any thing for thofe who are well Ikilled in the few branches of Science he has treated of, but for thofe who willi to attain a moderate know¬ ledge of them; moderate enough, if they are all like this. This fmall Traa is divided into three Chapters; the firft of which he calls the Theory of Perfpeaive; but fuch a Theory I never met with before. The firft Sealon is a poor Definition of Perfpeaive; after which, he informs us how to trace Objeas on a Plate of Glafs; the fecond (in four Lines) tells us that the nearer an Objea is, to the Eye, the bigger it appears, and the farther it is off, lo much the lefs, both In height and breadth. In the 3rd. he tells us, that all Ob- jeas become vifible by means of rays of Light flowing from the Objea, and paf- fing through the Pupil, form their Images ou the Piaure; and, in the 4th, he re¬ fers us, for proof of it, to take the Eye of a Sheep or Bullock, newly killed, on which to make the Experiment; the 3th explains how the Image is formed. In the 6th we are informed what an Angle is, with a tedious defeription of it ; and the 7th ffiews how it is meafured, by the Divifions of a Circle, called Degrees ; the 8th. Is a Definition of an Equilateral Triangle, and the 9th. ffiews how to conftrua it, on a given Line. The whole of this extraordinary Theory feems to cqnfift in the conltruaion and vvonderous Properties of an Equilateral ’I riangle ; for the 10th. Section tells us, that “ No objea can be wholly and diftinaiy feen under a larger angle than that of 60 degrees.—And as this is generally reckoned to be a good angle of viiion, we ffiall keep generally by it, in the following praaical part of this Work, where the reprefentations of large objeas are delineated. But it will not do well in re- prefenting fmall objeas; for, when a perfon looks at a common drinking-glafs, or a die *, he never brings it fo near to his eye (unlefs he be very near-ftghted) as to view it under fo large an angle as that of 60 degrees; becaufeexperience te.aches him, that he can fee it better under a fmaller angle; that is, when at a greater diftance from his eye.” What has all this to do with the determination, or choice, of a proper Diftance for drawing the perfpeaive Reprefentations of Objeas ? it relates wholly to Optics, not meerly Perfpeaive; giving us fome conception, at what diftance from the Eye diftina Vifion is performed. In the i:th Seaion we have thefe words; “When a Perfon ftands right againft the middle of one end of a long avenue or walk, which is ftraight and equally broad throughout; the fides thereof feem to approach nearer and nearer to each other as they are further and further from his eye, and if the avenue be very long, the fides of it at the fartheft end will feem to meet : and therc^ an object that wonld cover the whole breadth of the avenue, and be of a height equal to that breadth, would appear only to be a mere point.’’ The whole lubftance of this truly ridiculous Seaion maybe clearly exprefled in a few words, thus; However the Eye be fituated between parallel Lines, they will ;(it eonMnaef)) appear to meet in a Point; coiifequently, the whole Space between them vaniffies in that Point; but it is Ixy no means necefl'ary tliat the Eye, or the Pcrlon,_ ffiould be right agalnjl the middle^ or at an End, for it is fo if the Eye be in the diieaion of either Side, or any where between them. It is fomewhat lirange that two fucli lingular Objects fliould olfer them.elves together, fo readily; ■but perhaps they wjre familiar to him. _ Se£l. IX'. OF THE ENGLISH AUTHORS. In the preceding Theory, we meet with neither Theorem, Lemma, Axiom, nor James Definition, in Perfpeflive ; but, in the 12th and laft Seftion, we are favoured with Fergufon; four, viz. the Point of Sight, the Place of the Obferver, the Horizon, and the Point of Diftance; thefe are all the Terms he defines, every one of which is exception¬ able. It is not poffible to explain the abfurdities of thefe Definitions; and of tlie whole Seflion without a Figure; therefore, I have taken the 34th Figure from tile firft Plate, Fig. 4. and the lecond Fig. i. The third Figure is two parallel Lines, piir. as AE and DF, which are divided into Squares; AD is the width df the Avenue ^ ^ and O the Station, which he calls the Place of the Obferver, without telling us to form the Triangle ADO, but that we obtain from the foregoing; S is taken where you pleafe, for here is no Rule to fix it, and is called the Point of Sight, the two Li lies AE and DF are conlequently to tend there ; SP is called the Horizon, but how' it is to be drawn, or for what reafon, he does not informs us ; and a Point taken therein, either to the right hand or to the left, dillant from S equal SO, we are told, is called the Point of Difiance-, which is, in reality, to take a Diftance at ran¬ dom (not at diferetion) for S was taken fo. Now, from this Figure, ’tis obvious, that O is the Station for viewing the Avenue; or it may, with equal propriety, be confidered as the Eye, or Point ot View ; and S, being prope-rly determined, is a Point perpendicularly oppolite thereto, formerly called'the Point of Sight, but norv, the Center of the Pifture. Here is no Iioterfeftion, or Ground Line determined ; but A D ’tis plain, is meant for it; this is I believe the firft Treatife on Perfpeflive in which It is omitted. This being the Cafe, of confequence, the Perpendicular, OG, is the diftance of the Plflure, and GS is the height of the Eye ; but he takes the whole of both for the Diftance, yet he has told us (Seft. 10.) that he (hall generally make ufe of an Angle of 60 degrees, which AOD is; how then can SP, equal OS, be the Diftance for AD, under that Angle? The following plainly evinces, that the height of the Eye is added to the Diftance. “ N. B. In whatever point the obferver’s eye is fuppofed to be placed, either for a diredt or oblique view of the fide of the objeft that is neareft to him, ajlraight line drawn from the point offight to his eye m-jft he perpendicular to the horizon-, which will be the nearer to the eye, or farther from it, as the obferver is fuppofed to ftand upon lower or higher ground.” This is a moft extraordinary Paflage, indeed-; the firft part means little or nothing; that in Italics (it is fo in the original) means, what it does not exprels, that a right Line, from the Eye, perpendicu-lar to the Pidlure, and to the Horizon¬ tal Line -'(not to the Horizon) determines the Center, alias the Point of Sight; 'but, that it will be nearer to the Eye or further from it, as, &c. is what I cannot com¬ prehend, the Pifilure being upright, i. e. vertical, as it is prefumed to be. How¬ ever, according to this and all his Diagrams, ’tis plain, that the height and diftance of the Eye are added together; and conlequently, if its height, G-S, be more or lets, the Diftance he lays down is alfo greater or lefs; nor is it poffible to make more or lefs of it. And yet be luppofes, all the while, that AD (a fide of .t Square or other Objefl) is feen under an Angle of 60 degrees, when, by this Diagram, it is not above 25, by others lefs. When it is viewed oblique (as at 0 ) ’tis more abfurcl; for he ftill draws the Lines AO, and -DO, inftead of CO, which would give AOC for the Optic Angle; but, of that, he does not feem to have the leaft Idea. The pradlical part of this Work, in the fecond'Chapter, is of a piece with the Theory, which, in reality, is too contemptible for Criticifm ; nor ftiould 1 h.ave thought it worthy of notice, but that,-the Author -having acquired Reputation (as above) and, as it is not poffible for thole who are unacquainted with Perfpedlive to form a judgment ot it, I think it nece'ffany to guard them agiinft imbibing fucli 'jmperfeft, luch abfurd and dangerous Notions of k, as can only be obtained from this Work; for, the Impreffions firft made, though by Ideas the moft abfurd and ’inconflftent, are not eafily erafed, and more perfeft Notions implanted in their ftead. On the contrary, if true and comprehenfive Principles .ue-firft inftilled, ’tis impoffible that luch as are limited or falfc can make any Impreffion ; the Mind being guarded, with Opinions which are orthodox, will eafily detedl Error, nor is there any danger of becoming a Convert to falfe and unwarrantable Tenets. 7 This 148 Sea. IX. A PARALLEL, James This fecoiid Chapter confifts of 27 Operations, as he calls them; a Specimen of Fergufon. which, in the firft, will luffice to ftiew what may be e.'ipeactl from it. A Square is given (in ftrange terms) for the Leffbn ; we are told to make AD equal to a Sideof it, and, “ at any convenient diltance, draw the horizon SP parallel to AD. Take O according to Sedl. 9. and make OS perpendicular to SP, S Ih.ill he the true point of fight (§ 12.)” FIcre, the pofition of the Horizontal Line is determined, but its diftance from AD (the Ground Line) is at dilcretlon. He then tells us to deferibe the quadrant O^ P, on, S, with the Dillance OS; and P, “ in all cafes, fliall be the true point of Diftance (§ i 2.)” The procefs being com¬ pleted, by the Diftance SP, there follows this moft extraordinary Remark. “ If the oblerver had flood further than O from the fide AD of the fquare, as fuppofe at o, he would have feen that fide under a lefs angle than 60 degrees; as the angle A 0 D is lefs than the angle AOD: and then, tiie point of diftance mull have been at d in the horizon; becaufe the point of diftance in the horizon muft al-ways be taken as far from the point of fight therein, as the place of the obferver (O, or o) is from the point of fight, as we fliall prove in § 14. and that, if the point of diftance in the horizon be taken either nearer to, or further from, the point of fight, than the diftance of the obferver is fuppofed to be from that point, there will unavoidably be a falfe perfpeflive reprelentation of the objeft.—For, fuppofe the placing of the point of diftance in the horizontal line be left to the dilcretion ot the artift, as is generally done by writers on the fcience of perfpec- tive, and that he had put it at e.” &c. Surely, nothing can equal this; I know of none who has left it fo much at dif- cretion as he does. Has he not told us to draw SP at any convenient diftance? and, does not the diftance he ui'es (added to OG) depend entirely on it? yet, to talk of feeing the line A D under an angle of 60 degrees, which at that diftance is not 26 ; and to tell us, aibitrarily, that, in all cafes, it fliall be, the true Diftance; and that, if it be taken either greater or lefs, there will be a falfe Reprefentation ; afto- iiifhing, all. The whole of this Operation and Remark evinces what I have ob- ferved ; and, th.at the diftance of the PiSure depends on the height of the Hori¬ zon (as in his Nota Bene) a moft extraordinary circumflance indeed; how the railing or lowering the Eye can alter the Diftance, I don’t conceive. Fig. 34. The 14th Section he calls a Demonftration of the above Rule, for finding the true Point of Diftance. “ Let AE and DF be part of two parallel Sides of a ftraight avenue, divided into equal Squares, and let trees he pl.inted at the corners of each Square, A, B, &c.—the two ftdes of the avenue feem to come nearer and nearer to one another, as they ar,e farther and farther from his eye, tending to¬ ward the point of fight S, in the dlreflion of the two ftraight lints AS and DS.” We are now told to draw the Lines B O, E O, &c. from the Trees to the Eye at O, and to draw be, &c. parallel to A D (wbicb is necefjarily fo) and then be (ays; “ Thus wc find, the apparent places of the trees, B, b, &c. mull demonftralivdy be at b, e, &c. as lien from the point O, &c.-Now we (hall fee, by placing the point of diftance in the horizon SP, according to the above rule, wlielher we fliall or (hall not have the apparent places of the trees in the fame point as before.” This being done, and AP, bP, &c. drawn, which (though it is manifell he does not know the reafon, in Geometry) becaufe they cut DS in the fame Points, is, with him, a Demonftration, that SP, equal OS, is the only true Diftance; as if it would not be fo at any dilt.ince, O S being equal to SP and A D to CD; aifo, O S parallel to CD, and SPtoAD; of which, he fays nothing, nor feems to have any notion ot the matter. Hence (lie fays) it is evident, that, fuppofing the Diftance had been taken any where between F andS (as, luppofe at n) the lines w'otild have gone ii'. ovc tlieir true places, &c. and the contrary, if the diftance had, been taken beyond P, &c. And (in § 15) he fays, “ Hence it is manlfeft, that, when large cibjeifts are to lie drawm in perlpeiftive, the point of diftance muft be taken atdeaft a.s far from the point of fight, as the oblerver could ftand from the point of light vyhen he lees the fide of the objeft iie.xt to him under an angle of 60 degiees.” So much for OF THE ENGLISH AUTHORS; his Demonftration ; but what he has demonftrated I know not; the Diagram James fliews, that AP and OC cut DS in the fame Point (on the Premiles above) but Fergulbn he demonftrates nothing, yet thinks he has done fomething mafterly. ° It is almoil unnecefi'ary to fay more on this extraordinary Paflage, and more extraordinary Demonftration, the abfurdityof the whole is fo very glaring. With- ou regarding the Angle AOD, which means no thing, all the Proof given is, that, DS being confidered as the indefinite reprefentation of DF, and OS as the diftanceof the Pifture, or of the Vanifhing Point S, it is immaterial in what po- fition OS and CD (equal SP and AD, refpedlively) are placed, on the Piaure, fo they are parallel to each other, the point c is uecellarily the fame ; cD repre- fentingthe length CD, equal AD. But, to imagine, that SP is proved to be the true Diftance of the Piaure. for feeing any Objea, equal A D, under an angle of 6o degrees, is falfe and moft abfurd; and Ihews that Mr. Fergufon knew not what he was about. Or how the planting of Trees at each corner of the Squares, which he makes a pan of the Premifes, or Conditions to be granted, affbas the Demonftration, or m any wife illuttrates it, 1 muft own 1 do not fee. If the Square A BCD be drawn by the Diftance OG, the Perpendicular of the Equilateral Triangle, which he gives as a general Rule for determining the true Diftance, for large Objeas, and at the height affumed (GS); it would be more prepofterous titan the one which he fays, “ a Child could tell that it would be a monftrous reprefentation of a Square in perfpeaive.” Sa is the Dif¬ tance, according with it, and A a cuts DS at r; then, be being drawn parallel to AD, gives AbcD (inftead of AbcD) for the reprefentation of ABCD; as by his Diftance, determined, and Height aflumed. He now proceeds with his Operations, in full confidence of the infallibility of the Rule he has attempted to demonftrate; for, throughout the whole, there is not the leaft variety or deviation from it, except in the laft Plate; in which is giiten a Chair with a fquare beat, and a moft clumfey Table (a block, being a paral- elopiped, would have done as well) in which the Sides tend to the point of Dif¬ tance, in the Horizon. All the Objedls, in this Work, are Iquare (as he calls thein) that is right angled, but chiefly Squares, and compofed of Squares; except a drinking Glafs (a fmall Rummer or Goblet) which he makes an attempt on, but a vile one, exceeding all defeription, and two rows of Cones, inftead of Co- lumns, fupporting a long extended Plane, feen underneath ; the Cones being re peated eleven times, on each hand, like his Trees, planted at the corners of Squares. Such ridiculous Subjedls (as are often repeated in the Work) attradt the attention of ignorant Perfons, in Perfpeflive. who are ftruck with aftonilhraent, at the appearance of a great length, on the Pidlure ; for what elje there is, worthy of Wiiting Rules for, at the requeft of his Friends, I cannot find. The whole Work alvounds with fuch Puerilities as are fcarce excufeable in a School-Boy ; as for Example ; “To put a fquare Pavement in Perfpedlive, confift- iiig of any given fquare Number of equal black and white fquare Pieces of Mar¬ ble, and viewed by a Perfon ftanding at a Diftance from it, almoft even with one ot^ Its Corners.^ He explains, by a Note, what a fquare Number means, which might be neceflary in Arithmetic ; but neither the explanation nor the Term has any bufinefe in Perfpe&Ve, that 1 know of. That the Pavement confifts of black and white fquare pieces of Marble is childifh ; what difference does their Colour make in the Operation ? or whether it is at all neceflary to be known, of what Materials they are. That his viewed by a Perlon at a JDifance dsosn it is certain!v neceflary, but that might be underflood, as it could not be feen otherwife; but that he Ufandittg, we Ihould not know; and being even with one of its Corners, requires an explanation, the term even has no meaning, here. The fame Figure uiideigocs another Operation (the 8th) as an oblong fquare Pavement, whofe length is.any given number of times its breadth. This is the general method of pioceeding, with fuch Authors, who have no conception of cuting off any deter¬ minate length, in an indefinite reprefentation of a Line. P P Operation REMAR.KS ON CLARKE’S PERSPECTIVE. 150 James Operation 15th. “ To put five fquare Pyramids, in Perfpeflive, {landing up- Leigulon right on a fquare Pavement compoted of the Surfaces of 81 Cubes.” Never, furely, was any thing more ridiculous; the Surface is not cornpofed of Cubes, but of Squares, and the ihkknefs of the Floor is immaterial. The iSth. “To put a fquare Pyramid of equal fized Cubes in Perfpedlive.” Is it poifible for any Perfon to conceive the meaning of this? The fquare Pyramid is four fquare Steps, whole height is equal to their breadth (a thing not very common) with a Cube on the uppermoft; i. e. begining, at the top, with one Cube, the upper Step is formed of nine, three in each Side ; the next five, leven, and, the bottom, nine; the fquare Number, 81, as above. To remark on every part of this moll extraordinary Performance, I have neither leifure nor inclination for, as every Paragraph in it is more or lefs exceptionable; one Operation is, “ to put a Square Hollow in Perfpeftive ;” another, “ To put Stairs with Flats and Openings, {landing on a horizontal Pavement of Squares.” The Figure, poor as it is, is taken from S. Serlio, an obfolete Author, who pro¬ portions every Objedl by Squares, a trifling and childifh Method (See Se£l. i.P. 16.) and thus is every thing done la this Work; which I have dwelt longer on, for the veafons given above. But, to conclude, the 3rd Chapter contains a defcrlption of an Apparatus for drawing Objedls, without Rule, which has fome genius in its Conflrudlion. A Sketch of it, he fays, was given him by the late Dr. Bevis, who he fuppofes was the Inventor, having never feen the like before. It is very Ample, confifling of two Equilateral Arches, as in Fig. 35. with a Label fixed at each corner (A and B; or threads of Silk, or fine Wire (Itrained tight) fixed to pieces of wood or mettal (C, and D,) fo contrived as to fix, by a Notch on the edge orotherwife, to the Arch, and to Aide freely from one extreme to the other (from A or B, to S). The Arch being fixed upright, and having a Sight-hole to look through (as in Fig. 13. Plate II.) the two Labels, or Threads, may be brought to correfpond with any Point or Angle of the Objefl:; then, a Frame being contrived to fold with hinges, at the bottom, or on either hand, having a-Paper fixed on it, for drawing, being turned up, or fideways againfl the Arch, mark the place where the Threads, or Labels, interleft; and fo proceed to take as many Points as are necelTary, and join them by right Lines, or as they appear in the Object; by which means, though tedious in the proccfs, a jull reprelentation of any regular Objedt may be obtained. Henrv THE lafl writer on Perfpefllve, at leafl that I have heard of, in England, is Clarke Mr. Henry Clarkf, teacher of the Mathematics, &c. at Manchefler, who pub- 1776. lilhed a pradlical Work, in oftavo, in the Year 1776, the fame in which the firft Impreflion of my Work was intended to be publilhed, but was prevented by the Fire at the Printers, in the Savoy, on the and of March; about 300 being delivered to Subferibers, the reft were deftroyed, there. This Work is in a Courfe of Leffbns for the ufe of Schools, intended in two Volumes; but one, only, has,yet appeared in public, though treated, in every refpeft as if the whole was publilhed. He lays, it may have the appearance of Vanity to attempt to write on a Subjeft, which feems to have been quite exhaufted; and again “ I do not pretend to offer any thing new in Principle; but the Method I have obferved, I flatter myfelf, will be found to be better adapted to the Capacities of Youth, than what is propoled in any Treatife that has hitherto appeared on the Subjeft.” For which purpofe, he has been at the trouble of colleaing all the different Treatifes he could hear of in all Languages; and from a Comparifon, he fays, it appears that while one part have written purely for Mathematicians, the other have treated it in fo limited a manner, that the Reader could not acquire from them the lead Idea of the Prin¬ ciples of the Art. This has been faid again and ag.ain, by others; and yet, is it not ftrange that Mr. Clarke, although a Mathematician, Ihould not give a Theory to his ozvn W’ork? “ The Principle (he lays) upon which this Method is founded is fo obvious, that it is a matter of furprize it has not been imiverfally received by the Connoilfeurs,” This OF THE ENGLISH AUTHORS, This leading Principle is only the common obfervatioii of feeing Objedfs through Henry a Plane of Glafs, from which, his Method “ (the only rational one,” he lays) is Clarke^ deduced; the whole Bufinefs being to find the interfering Points of the Vifiial Rays. Surely, Mr. Clarke does not propofe, in this, to offer any thing new, for it is, I believe, as old as any Author, we are acquainted with, who has written on Perfpeiftive; and, in my opinion, gave the firft Ideas of the Subjeft. On that Principle, Vignola and Sirigatti, and others before them, performed all their me¬ chanical Operations. “ Indeed (he fays) the Demonftrations given, to this funda¬ mental Propofition, may not be comprehended by every one; but, perhaps, to fuch. It may be thought a fufficient Proof of the truth of the Operation, to find, that, when the Planes are all brought into one, the Thread, or Vifual Ray, ftill •interfedls the Pifture in the fame Point.--When the firft Leflbn is clearly under- ftood, the main Point is accomplithed. For as Lines, Planes, and Solids, of what¬ ever Figure, may be eafily conceived to confift of Points, the Perfpeftive of them may be found by this one general Rule.” It is Indeed very eafy to fix on and de¬ termine certain Points in Objedls, but not to conceive that they confift of Points. “ This alone I have often found fufficient to feveral grown Perfons, to let them into the whole pradlice of Perfpedlive;” indeed there are many who cannot readily comprehend any other; for fuch, the Method is well adapted, and the Demonftra- tion he gives of it is full as fatisfadlory as that given by Mr. Fergufon. The Jefuit’s Perfpeftive,(he fays) has made more pretenders to it, than any other; a mere jumble of Pradlice without Theory, and full of Abfurdities ; whole moft general method, in reprefenting a Building, &c. is to have one Side parallel to the Line of Interfedlion. When the View is partial, there is, he fays, nothing wrong in this Method ; but when a fingle Building conttitutes the whole Pidlure, nothing is more abfurd. “ It is juft as if a Painter Ihould Ihew you a fine Por¬ trait with half the Face covered.” The Comparifon is really pertinent ; for, in this cafe, he fays, that the Houfe, which ftiould be the principal Objedl, is only a part of a more general View. And, unlcfs the Obferver be fituated exaiily in the front of a Houfe, (he means, fo, as not to fee an End) it will always be viewed on the Angle, and muft therefore have two Points of diminution ; which, he further fays, is the only right Method. In thefe judicious remarks, it is apparent that this Author has a juft Idea of Perfpedlive, as it conduces to exhibit the moft agreeable and natural Reprefentations; and, in the application of his Rules, to practice, he is coraprehenfive, but falls far fliort of that clearnefs and precifion which is necelfary thereto. In general, his Definitions are clear and full; but, in the fecond, he confines the Idea of an Original Plane to that on which the Objedl is feated, as others have done; as if every Plane in the Object, which is reprefented, had not an Original as well as the Objedl; the other may be particularized by the geometrical or Ground Plane, I think the loth Definition is exceptionable; that the point in which a Perpendi¬ cular, from an original Point, cuts the Interfedlion is the Seat of that Point. On the InterfeBion it may be fo called ; but, unlefs the geometrical Plane be perpendicular to the Pidture, and the Point in one of them, it is not the Seat on either. The original Point being fituated on an inclined Plane means nothing, more than, that it is not in the Ground Plane; and confequently, a Perpendicular determines its Seat thereon ; by the fame means, it is determined on the Pidlure. I cannot fuppofe, that Mr. Clarke could fo far mifunderftand Dr. B. Taylor’s Definitions of the Diredling Line and Point, the Diredlor of a Line, &c. and am always forry to find unnecellary Innovations; as in Def. ii. in which, he calls the indefinite reprcfenration of a Line the Diredlor of it, or of a Point,fituated therein; alfo, his primary and fecondary Diredtors are infignificant and perplexing to a learner, and mean'nothing; ’tis the Vanifhing Point that diredts the Line, which, being drawn, has nothing to dlredl. The Definitions are illuftrated by three moveable Diagrams, which are not badly deviled, yet capable of being much improved; and in thefe (with four Axioms) confifts his whole Theory, particularly the firft, which is furnilhed with a Thread, indicating a Vifual Ray, to prove that a Point is truly projedled. Th« '5* A PARALLEL, Henry The linear part of this Work confifts of 30 Lcfions, and 24. Figures; mod of Clarke, the Plates (the fize of the Page, 4^ Inches wide) contain two each, fome but one. The firft is of a Point, the and Lines, oblique, (in tl:e ground Plane) and then he proceeds to Figures; as Triangles and Squares; allb Poligons, and Cir¬ cles, with the Plan of a plain Building, direfUv in front, without a fingle Refe¬ rence; in all which, the Reprefentation is determined by Lines drawn to the Eye, from the Original Figure, except when it is produced by the indefinite Reprefen- tations, wholly. He then proceeds to Solids, in Prifms and Pyramids (fome in¬ verted) and alfo to a plane Building (direfl and oblique) iimple indeed; but, in the whole, I don’t perceive that he ever Ihews how to cut oif any portion of an indefinite Line, by bringing down the diftance of the Eye, and applying the meafures, or the ratio of them, on the Interfedlion, or otherwife, though the molt praftical; the other, when the diftance of the Eye is confiderable, or the Objeift large, or remote from the Piflure, is wholly imprafticable, except on a very fmall Scale; befides, it is often very inaccurate, and fometimes cannot be ufed at all. By the other means, let the diftance of the Eye or of the Objedl be ever (o great, any portion of them may be applied and produce the fame effefl:, with accuracy; Purely, itlhould not be rejefled becaufe ’tis common, and ufed by every other Au¬ thor, unlefs Mr. Clarke had found a better expedient. It is remarkable, that, after the Definitions, he proceeds to Praflice, making ufe of Interfedling and Vanilhing Lines and Points, as if they were familiar to the Praflitioner, without any preparation of the Pifture, (hewing how thofe Lines and Points, with their heights and diftances, are determined thereon, or even explaining that they are the Lines, &c. before defined ; why the Eye is placed above the Vanilhing Line, and the original Figure (inverted) below the Inter- (eflion, are never explained or made mention of; how then could he fuppofe that his method of proceeding is better adapted to the capacities of Youth than any other on the Subjedl; ? for I maintain, that, being ever fo clear in the Definitions (which he ftrenuoufly recommends) knowing no more, and not having their ufe and meaning better explained, not one in fifty would conceive what they meant, when applied to ufe, or what the Operation tended to. Next, he proceeds to inclined Planes and Lines, in which, he fays he has been more particular, as it is but little uuderftood; nor does he know any who has rendered it praftical but Kirby. I muft own, that he is more explicit, on that head (except as it relates to the projedfion of the regular Solids, in which he is far outdone by Highmore) than moft others, and am furprized to find that Mr, Clarke (being a Mathematician) (liould benefit lo little from him, but more from Brook Taylor’s ElTay; for, although he proceeds geometrically in the procefs, I am forry that I can fay nothing in praife of it, being intricate and perplexing in a very great degree; even ’sGravefande proportions inclined Lines, in a far more mafterly manner. He makes frequent ule of a Line of Elevation, begining at the eighth Leifon, which is never defined, or its ufe properly explained ; and, (hould he not have given a LelTon for determining Vanilhing Points, before he makes fuch frequent ufe of them in his Operations? He proceeds with a Cube, refting on an Angle; and then to the Dodecahedron, which is projefted on Pozzo’s Principles, viz. by the pei fpedlive Plan and Eleva¬ tion. The Icofaedron follows next, performed by Vanifhing Points but without a Vanifhing Line, fave the horizontal; in which are two Vanilhing Points (Y and n) which we are told to find, of LM and Ill, (rather of LT and HQ) which, being confidered as Sides of the Objedl, are inclined to the Horizon in very different diredlions, but in equal Angles; one vanilhing above, the other, neceflarily, as much below the Horizon. Though this Figure is given in the moft fimple poli- tion, he is by no means clear in the Defcription, nor are half the Vanilhing Points determined, which are necelTary. Laft, he gives a Globe, which is projedted ma¬ thematically, by finding the tranfverfe and conjugate Axes of the Ellipfis which reprefents it; and which are juftly determined, geometrically, and fimple enough. After which, he remarks on the neceftity of feeing a Pidlure from the true Point 5 • . of OF THE ENGLISH AUTHORS. of View i becaufe, the true reprefetitation of a Globe (being an Ellipfis, when feen HenrV obliquely) cannot appear a Circle (as the Globe always does) in any other. He Clarke thinks, “ it would be no bad method, if our Landfcape Painters, and even t.hofe in Portrait too, were to write down on the back of the Canvas, the height of the Center, and the Diftance of the Perfpeftive Plane, fo that the Pifture might be placed (or viewed) to the beft advantage.” Mr. Clarke, I find, has had but little acquaintance with them, or he could not be fo unreafonable as to requeft them to do any thing of the kind j for, how is it poffible that they (hould, vvhen perhaps it never once entered into their Ideas, that there were any luch thinsrs determlnaMe’ for the Piflure they have drawn ? ’ Sciagraphy, or the projeaion of Shadows, is the next Subjedt he treats on which is comprifed in ten Lefibils; and what is, to me, very fingiilar, he begins with Shadows by a Torch or Candle firft, and is the mod copious on it, having but three Leflbns on Shadows by the Sun. Here is no Introduaion nor Definition given, nothing particular, or interefting, in the whole; in the Shadow of a broad Hoop (Leflbn 35.) he has omitted the defcription of that part of the Shadow which is thrown on the interior Surface, and which, is the only part that is difficult; the Center of the Hoop, which is thrice referred to, is not marked, nor the y to be found ; nor a /, in the Shadow of the outer Circle. In the next Leflbn, I prefume he means (in Line 2. Page 77.) perfpeaively parallel, for the Lines ate nbt rePbec- twely fo. In Lefl. 39. Page 81. Line r. and 2. we have Line of Interfeaion, for Vanifh^ mg-Line, and for IV h V, in the Plate; alfo, T is referred to feven times, which, jn the Plate is v; and an r is wanting in the 40th. I mention thefe, becaufe there IS no Errata; and he fays, in the Preface, 1 have been particularly careful to have it ■correa in the printing; becaufe (he adds) a Angle typograpvical Error, isfufficient (forthofe, who fet up for Judges) to pafs Sentence on the whole Performance ■ but I am far from being of that opinion; if it was, / had been condemned, without redemption, or redrefs, having a 00/ilous Errata (as the Monthly Reviewers obferve) yet I intended it to be perfed, in that refped; but, with all my vigilance, I muft own (as Mr. Clarke fays) that, Humanum eft errare. Catoptrics, or refleded Images of Objeds, comes next, in fix Leflbns J which is entered on m the fame abrupt manner. On Water, as a horizontal Mirrour here is nothing but upright Objeds, whofe meafures are all made equal; but there is a fmall miftake in the firfl: Leflbn, which concludes with » the objed and its Ihadow having always a common vanifliing point.” In this Cafe, -only, when the Line’ whofe Image is required, is parallel to the refleding Surface. In the laft Article of the fecond Leflbn, for a Pyramid, his method is erroneous; inftead of determining the Bafe of the Pyramid, continued to the furface of the Water, we are told to make the part of the Image, which is feen, equal to the part of the Objed which It reprelents; but, being inclined to the Horizon, they are not fo. In Fig. 44. nr, the refieded Image of DG, or the reprelentation of not being parallel to the Mirrour, cannot, I prefume, have the fame vanilhiug Point (F) with the top and bottom of the Mirrour. ‘ The 45th Leflbn is a good one, and well defcribed. but the Vanifliing Line of the Mirrour is aflumed; in the 46th we are told to find it, yet, I don’t find any Le^n which (hews how*. 2, 3, and 4, are omitted, though twice referred to, which makes it perplexing; and we are dequently told to find a Vanifliing Point (as Z) which would be confiderably but of the Pidure, without telling us where it would be, or making any apology for it, fo that, it may be imagined to be where the Letter is put. On the whole, he feems to underftand it, himfelf, but is not explicit enough, in defcribing the procefs, to make it clearly underftood by others, who are not already competent in it. • * Leffon 26 IS the only one in which it is determined, but not defcribed. The fame Figure ferves for vr ”1,’ 1 ° Tv’ Z Angle vtV equal to Igiven Angle, and V will be the Vanifliing Point of a given Line; yet we are never told tc draw the Perpemlicular vV, in which It IS determined. After three mote Leflbns, on the fame Figure, we are told to draw VF, which Will be the Vanuhing Line of a ccrtam Plane, Qq And I A PARALLEL. 154 Henry! And now, after what has been advanced, hitherto (by which it feems as if the Glarke? Author was tolerably acquainted with the Subjea) in the 47th Leffon, we are (hewn how to prepare the Pifture, and fix the meafures of the Objeft to be reprefented; and, in the 48th a Dlftance is determined, from which, I (hould have conjeauredj that' he knows very little of the matter. The 47th exceeds all defcription; from the polition of the Pifture to the Objeft, and the fituation of the Eye, he feems to have quite forgot what he alferts in the Preface; that, when the Objeft is viewed on the Angle, it muft have two Points of diminution, and, that no other method is right. He alfo reprehends the Jefuit for having, commonly, one fide of the Objetft parallel to the Pifture; yet, here, he runs into the fame Error, unnecefTarily, and in a far more extravagant manner, than the Jeluit ever does; one would be led to imagine, that, from the fituation of the Pidture, in refpeft of the Objcdt and the Spedator, he meant to (hew the ablurdity of it, by rendering it truly ridiculous; yet, without fo much as attempting to (hew the impropriety of it, and determming the’true pofition of the Piaure, on his o-wn Hypothefis, from a Station determined. Rcfpeaing the Diftance (in the 48th) I am (fill more furprized; at the dilbance S, where he fays, the Angle a S ^ is 60 Degrees, I find it no more than 32; but, at the real diftance, for AB, it is but 22 (the Vaniftiing Line, V A, has nothing to do in it) the Diftance, and Optic Angle, (hould be determined from IN, the Iiiterfeaion. But; to tell us, that, “ from fuch a diftance (viz. 60 deg.) the objeds may be feen to perfedion, the vifual angle being neither too great nor too little,” is truly ridi¬ culous ; befides, it is too great, and occafions diftoi tion in the parts of Objeds at the extremes, on account of the obliquity of the Vifual Rays. The 49th Leflbn is on Theatrical Perfpedive; in which, he pays a Compliment to the Projedors of the Manchefter Theatre, which he fays is admirably well ex¬ ecuted ; but I am in doubt, from the Specimen here given whether his Judgmeiit be competent in it; and, in my opinion, he had (hewn real Judgment in leting it alone; for furely, Mr. Clarke cannot imagine that he has done any thing to any purpqfe, from which the leaft improvement may be made in the Theatre ; or, that aoy Perfon can apply his Lclfon to the leaft uie, 1 muft be (ilent, here, for 1 own, that I can make nothing of it. . . ^ . Horizontal Perfpedive, in two Lelfons, comes next; “ this kind of Perfpedive (he fays) relates chiefly to Cieling-pieces, &c.—And, in order to produce this De¬ ception, nothing more needs be done, than to make the Center of the Cieling the Center of the Pidure.” &c. but why is that necelfary ? 1 am of opinion, that a much better effed may be produced without that coincidence. What little is done, on this Subjed, is much better, and more comprehenfive than the laft. In thefe Figures there is an appearance of the diftance of the Eye being laid down on the Horizontal Line, which is never done elfewhere; but, as the Pidure is horizontal, there can be no diftlndlon of Vanifhing Lines, refpeding the Horizon. The yad and laft Leflbn, is called “ Diredions for taking Perfpedlye Views without any Meafurement.” I muft recommend the Reader to the Work Itlelf, for a Defcription of it, being (as I think) Original, it would not be proper for me to tranferibe it. This Work is comprlfed in 113 Pages, with a copious Preface; dedicated to Charles White, Efq. F. R. S. of Manchefter; befides the three Diagram Plates, here are thirty for the Leflbns, which do not contain one ftriking Objed: the laft, which is given meerly for (hew, is a Bridge (Plate 18 Inches long) cut off at both ends, which makes but a poor figure, and as poorly engraved. It was printed for the Author, and fold by Mr. Murray in Fleet-Street; Price 5 Shillings, (ewed. In the Preface, we have a Plan of the (econd Volume; in which, he fays, “ 1 have (hewn the Application of the foregoing Rules to a variety of Subjeds, viz. to the various parts of Architedure, various modes of Building, Squares, Streets, Avenues, &c. to the projedions of the Sphere, and to fundry notable pur- pofes, in Aftronomy; Aerial Peripedive (tranflated from L. da Vinci) and to cori- clude with fome hints for mixing Colours, On Sir I. Newton’s Theory. Here is much propofed; but 1 fear, that (like Kirby’s) the Execution of it depends'too much on the reception which this firft Volume meets with. C ‘.55 ) •'l io Remsj-ks on. the Reviewers of the Complea.t Ti;eat;I(e on, Peifpedlvei by the Author. ' <’■ ' A lthough the Compleat Treatlfe on Perfoeftive ^as never been pub- lithed, otherwife than by delivering it to the Subfcriher^;' yet bejbg'ifi the hands of fo many, it has been noticed by all the Reviewers ifl rae Lon 2 pbN Review, tor December 1775, which, with the Apppp’do/;'contains a'cppious account of the princinal part; it is concluded in April, 1776; to'whicnaccound is annexed a Plate, taken from the Work, exhibiting fpme of the moif particular and interefting Subjefts and Paflages in the Work,'which are judicioufly "cKdleh^ and evinces their judgment in the Subjeft’. But, as they cannot agree wJth''rte,'tti Hiy phyfical Opinions, I could with they had pointed out in what I have'ttiifcon.i ceived the Philofophers, or the fenfe of their Argunaents, which, 'is tafd^'l Rave fpmetimes rather rudely cenfured; becaufe I might have retrafled my'|itfc^ (bein^ confcious of it) in the next Edition. | . , ' It is, however, fome confolation to me. that I am not ehtircly fihi;lilaPn| my Opinions; for, I find that fome, who have had an Univetfity Eduiairo'ii?'aiid aft deeiped lip incpnfiderable Philofophers, have not been afhamed' to’ dVow" tljeTamfe Opinions, in many refpefls, openly, to the World. Indeed it is my fixed opiniofi, that many more would do the fame, if they durft; but'lb prevalent are the'Oljii- nions of a truly great Man, whofe charafter is univeffaUy eftablil^ed,' rhat others who perhaps are no more convinced by his reafoning than lam, on fomii'Sn'bjefts, dare not venture to contradidl, and own their real Sentiments; left they fhould be deemed deficient in their Capacity to form a Judgment of them. Such, in my opinion', is the motive which induces many Perfons to fubfcfibe to their HypothefeS; bur, whilft I am bleft with reafoning faculties and a power of thinking, I' fhall never b'e alhamed, to own that I cannot acquiefce in Opinions which I do not comprehend, or rather believe the contrary; nor can 1 pleafe myfelf with the Idea of being Very "fagacious, in matters which, I find, my reafoning faculties are not formed to explorft I take this opportunity (which I intended Ipng ago) publicly to return thanks to ,the Gentlemen who were concerned in this Review for the Candour they have fhewn to my Produftions ; heretofore extended to ,my Tf.eatife of Geometry, as well as to the Work on Perfpediiye; “ which (they fay) to do it that juftice it imerits, would exceed the limits prefcribed us.” Remarks on the Critical Reviewers. In the Critical Review for July following (Page 35, to 44) the Tre^tife is honoured with their particular notice and approbation. In the iecond Paragraph of the 37th Page it is faid, that “ The Demoiiftratigns pf the Theorems, are given in a very elaborate manner, and may probably appear very tedious to many,Readers.” With fubmiffion to the Gentlemen of this Department, I cannot.but think they are under a miftake in this matter; the.Examples I have given for Illuftration qre indeed fomewhat copious, becaufe I conceived, that, after Dempuftration (which feldom expeeds ten Lines, oftentimes not above fix or feven, and fometimes not fo many) to fee it illuftrated in a familiar manner would greatly enforce the Demon- ftration, and for that purpofe I have fometimes given two Examples to the fame Theorem, which may feera a part of the Demonftration, or at leaft make it appear elaborate; for I have endeavoured to render the Demonftrations as fimple and con- . fife as poffible, and that by reafoning only, without refering, or as little as I could, to the Elements of Euclid. The 13th Theorem may appear elaborate, on account of the feveral Demonftrations of various parts, which are dependant on it,, thereby rendering the Theorem more general and applicable in practice, which being taken ...altogether, will appear operofe; but, as that Theorem is pf the utrnoft coufequence, ..in p.radlice, it could not be difpenfed with. THE CRITICAL R E V I E W, Their correftlon of the laft Sentence in the next Paragraph is jufl; It was un¬ doubtedly meant that the Opinions have no foundation, which is implied in the imagined Errors having no exiflence; But, their objeflioh to the placing of that Sedtion (the fixth) I alfo think is, without foundation; fince the Sedlion itfelf is not objefled to, I would afk, and could wifh they had fpecified, where it could be placed with more propriety? For, although it is ratherdigreffive, as not being, diredlly, a part of the regular Work; yet, as it is wholly theoretic, it muft neceflitrily pre- cedejftadtice; and, it would have been very improper to have preceded the Theory. This being the Cafe, where could it be placed better than between the two Parts, Theory and Pradice? all the objedlion feems to lie, in numbering it amongft the reft, but rather to have made it a dillindl and feparate Sedlion, as being digreffive, and unconnedled with the foregoing; for, as it could not precede the Theory, it muft neceifarily follow .after; and, it was abfolutely neceflary to guard the'Artlft againft thofe Errors, before he applies himfelf to pradlice, by pointing them out, (hewing how they may be avoided. I cannot agree with thofe Gentlemen, in the firft Seflion of the third Book feeming to be unneceflary, as containing nothing material. It is an introdudlory Preface, to.the Pradlice, which is here treated fo, as to (hew its abfolute dependance on the foregoing Theory, from which, every Rule in it is deduciblej at the fame time,, fo as.to be wholly independant of it; that is, without having perufed the foregoing, every thing necelTary for praftice may be acquired from it. For which reafon, although a general Plan was given in the general Preface, this contains an abridged Plan of this Book, only ; alfo, an Apology for the alteration of fome Terms by Dr. Taylor, which had been general, and for his introducing new ones, (which fome Artlfts have great objedions to) which have a more general and ex- tenfive fignification; together with the rationale and genefis of VanKhing Lines and Points, better fulted to the Capacity of the unfcientific Reader; who, from his deficiency in Geometry, cannot enter into, and clearly comprehend the Theory. That fome of the Definitions are repeated, in the fecond Sedion, which were given before, is eafily accounted for; here are, in the whole, but fourteen, includ¬ ing the Pidure, nine of which, with the Pidure, are neceflary in the Theory ; the other four are not fo, or have different and more general Names. From thefe I have deduced as much of Theory, in Corollaries and Remarks, as I conceive necelTary for the Praditioner, who is unacquainted with Geometry, as Leffons, neceflary to be retained and applied in Pradice. Thofe Gentlemen are pleafed to fay (Page 42.) that, in many places, I reprehend Dr. Taylor, and fometimes without caufe, as in Prob. II. P. 134. they are miftakeix in the Problem, ’tis the iith; and, in the fecond ImprefTion it is the 28th Page. That the Problem is an elegant one I have faid, but, that his conJlruSi'wn of it is fo, I cannot agree to, or his manner of proceeding in the Operation; which, if they had taken the trouble to complete the Circle, as in his Diagram, would be found, as I have faid of it, diftorted and prepofterous, on account of the (hort Diftance, and great dimenfion of the Circle. After which are thefe words; “ Our author (hould here have been very cautious not to err himfelf, where he is blaming another fo much, as we think he has done, in faying, five points in an ellipfis are not fufficienC for afeertaining the true curve of it; for all Geometricians know that they are fufficient.” From what follows (in the Original) it is evident, that by the word afeertained is meant dejerihed, as it is in the fecond Impreflion ; for, how is it poflible that I (hould mean otherwife, than, that it is neceifary to determine more Points, in order to deferibe it ? feeing that, I have (hewn how it may be afeertained by three Points, only; and, having determined two, when thofe words are ufed, I proceed Immediately to find more, in order to complete it. It is alfo faid, in the 5th Paragraph, Page 36. that, in Sedllons 4. and 5. B. i. (which are wholly digreffive, containing matter of meer Opinion, in phyfical Enquiries) I frequently reded on Sir Ifaac Newton and other great Philofophers, with whofe writings I feem not to be fufficlently well acquainted. I have ever held the Name of that great Man in the higheft veneration, amongft Men, but cannot attribute OF THE AUTHOR’S TREATISE. ij; attribute inf.iUlbillty to any Man; and am really concerned for the dignity of a truly great Charafler, when they prefume to attempt an inveftigatlon of what cannot be comprehended. Voltaire, in his Philofophical Diflidnary, Vol. II. P. 63. on the limits of human Underftanding, alks, “ What is Matter? Thy equals have written ten thoufand Volumes on this article; fome qualities of this lubflance they have found, which are as well known to Children as to thee.—See this grain of Corn which I throw into the Ground, and tell me how it rifes again, to flioot forth a Stem with an Ear, Inform me how the fame Ground produces an Apple on this Tree, and a Chefnut on the next to it? I could fill a Folio with fuch Queftions, to which thy Anfwer ought to be, 1 know not. And yet, thou haft taken thy Degrees, and weareft a furred Gown and Cap, and art called DoSlor.” Again (P.77.) “ Matter exifts, this you know; but you know it no farther than by your fenfa- tlons. Alas! what avail all fubtiltles and fophifms, fince reafoning has been in vogue? Geometry has taught us many truths, Metaphyfics very few. We weigh, we mea- fure, we analize, we decompound Matter; but, on offering to go a ftep beyond thefe rude operations, we find ourlelves bewildered, and an abyfs opens betore us.” And again, P. 153. (On the Soul) “ Know, Man! that God has given thee Uuderftand- ing to guide thy behaviour, and not to penetrate into the Effence of the things which he has created.” That the whole of the firft Book, except the two Theorems in the third Seflion, is entirely foreign to a Treatife on Perfpeftive, cannot I think, with juilice, be faid ; feeing that, to have fome Idea of the mechanical caufe of Villon, with an explana¬ tion of fome optical Terms, and other matters in the fecond Seflion, prepares the Student for a clear conception of the Appearances of Objedls; and, to diftiuguilh between the Appearance and Reprefentation, ia perfpeSive, is certainly a neceffary requilite towards a thorough underftanding of the Subjedt; and, although the • greateft part of this Book is digreflive, from the main Defign, yet I cannot con¬ ceive that the Work could have been better by the omiffion of it; for, though fome of my objedtions may be injudicious, others may excite the attention of thofe who are more verfed in tire Subjedts, and occafion a new turn to their inveftlgation of them. That my Reputation ftiould fuffer, by. the appearance of a prefumptiou arifuig from a too fuperlicial knowledge, of the Subjedls adverted on, I have no apprehenlion of; although I am confcious, that the freedom with which I have advanced my Opinions will be thought prefuraing and impertinent by many; but, I think the Prefumption much greater, in attempting to explore, than in owning our deficiency in Ideas tending to comprehend, what is incomprehenlible to our limited Underftandings. It is not to be wondered that the Work Ihould, in another Perfon’s opinion, be fomewhat deficient in orderly Compofition; though it is what I am rather parti¬ cular in, and, on that account, have changed the place of the firft Theorem, in the firft Imprefllon to the eighth, in the fecond, and otherwife varied the ninth, tenth, and eleventh: I could wilh they had pointed out the Deficiency, or mentioned any other Work, on the Subjedl, as a Pattern for my imitation ; for I muft own, that I know not where to make any improvement in the third, on that.fcore. The occafional introduflion of fome things, by way of Illuftration, or Embellifhment, may be apparently foreign, yet have fome diftant affinity to the Subjeft, and not wholly impertinent. But the Charge of difgufting Comparifons, with .other Au¬ thors, is, I think, entirely groundlefs, having'ftudioufly avoided it, as what I have an averfion to; for, except that, improving the Diagrams, and, perfefling the Prob¬ lems of Dr. Brook Taylor, and (hewing their general utility, may he deemed com¬ parative, I know no other Author with whom I have made any Coraparifon. However, making allowance for thefe Remarks, or Refleftions, from profelTed Critics, I think myfelf highly obliged for the Charafter they have given of the Work, as “ a very valuable Performance, containing every thing that is really ufeful, in Perfpeftive;” on which, though large Extradfs, or Quotations, are taken from various parts of the Work, I do not find that they have attempted to criticize, •r, to prove any thing 1 have advanced thereon erroneous. R r It I5S REMARKS ON THE REVIEWERS. It were to be wiflied that the Editor of thofe Crlticifms had been more correfi, in tranfcribing various PaiTages; in fome of which, the fenfe is manifeftly per¬ verted, either by the omiffion, orfometimes by changing an Article, as in Page 38. Paragraph 2. Line 7. where, inftead of, between the Eye and the Objefl, is iu- ferted the Eye of the Objeft. In the laft line of the fecond Par. P. 39. (for the Appearance is to defcend) the Verb-Subftantive (h) is omitted. Remarks oa the Monthly Review. In September following. The Compleat Treatife on Perfpe^tive was noticed by the Monthly Reviewers, but not in fo copious a manner as in the two others, the whole being comprlfed in four Pages; the greateft part of which is employed on- the firft Book, which, they obferve, is not neceflarily connefted with the SubjetSt- matter of the Work. I have, in the Preface, faid the fame, of the two laft Sedlions, but cannot be perfuaded that the whole of it is fo; the third Seftlon, particularly (on Direft Vifion) is effential; nor is the fccond wholly redundant. As what I have obferved, refpe£ting the Title, in the firft Page, of the Preface to this Appendix, was from memory; I find, that I have attributed to the Critical what belongs to the Monthly Reviewers; which they deem a kind of Tax on the Public, when, in order to make a Work complete, more Matter i? introduced than is necelfary for that particular Subjefl; but, to draw a Line, which fhall limit the bounds of what is really and only neceflary, fo as to have the united concurrence of every Critic, is impoffible. That there are fome Sedlions of the firft Book digreffive is allowed; but certainly, whatever is introduflory to the Subjedl, and is not a part of any other diftindl Science (as Geometry, for inftance) I am of opinion ought to be given in the Work. But, as Perfpedlive is a branch of the Science of Optics, whatever is neceflary to elucidate, and enforce the Principles, muft be confidered as a necelfary part of Perfpedtive, as well as of Optics, in general. Thefe Gentlemen are rather fevere on my Scepticifm, refpefting the materiality of Light, the caufe of Colour, &c. but muft own, that I am as tar from being a convert to thofe philofophical Tenets as ever; and, notwithftanding what Mr-. Canton has faid, or can fay, am not yet convinced that Water is corapreflible; which, if it contained forty times more Space than Matter, would not, 1 prefume, admit of a doubt, as it might eafily be proved by Experiment, which would be obvious to every one; although, like Air, it may be expanded to a vety great degree, it has not an equal property of being coudenfed into lefs corapafs, than its natural ftate. For what purpofe, I would alk, are fuch extravagant Doftrines advanced? feeing they cannot bring fufticient proof, in fupport of it. They obferve, that elegance of Style is not expedled, as fuch Subjedl^ will not admit of it. I am not infenfible, that there are a feyv inaccuracies (particularly in the firft Impreffion) in point of Grammar, which is not to be wondered at; an Author being, generally, more intent on tlie Subject, and 1 had no Affiftaut, in the revifal, from the Prefs, as many have; yet, if they had compared it, iji that refpedl, and the Style, in general, with other Works on Perfpeflive, if they fonod no caufe for Praife, 1 am perfuaded that they would, at leaft, have been lilent, op that head. Repetitions are often neceflary, and are done of choice, frequently; but own, that fome had efcaped my notice, before it was too late;. nor do I think it necelfary to make an Erratum of every literary Error. However, 1 cannot but acknowledge, that they condefeend to make ample amends, in what follows, viz. “ We regret this the more, becaufe, as a writer on Peripefiive, he is, in many refpefls, fuperior to any with whom we have yet besn acquainted,” .And again, in the conclufion, it is laid, “ Neverlhelefs, on the whole, this Treatife is comprehenlive, intelligble, and ufeful; it is the moll complete Work, on the Subjedl of Perfpeftive, which has yet been publilhed; the e.-^ecution muft-have been laborious and expenfive, and vve heartily wilh that the Author m.ay meet with fuitable encouragement.” 6 ^/ '^/. 24 V430. \ / E & H • ' F H klS \ \v // \ -- c \ K \ 27 . 96 . , T. J '59 OBSERVATIONS ON VARIOUS AUTHORS. A fmall folio Treatlfe, by W. Halfpenny, was publifhed in 1731, vvhich is wholly praftical; and although 16 years after Dr. Brook Taylor publifhed his firft Trad, there is not the leaft trace of his Principles to be feen in it. This Author I had overlooked, or I fhould have Ipoken of him, in the proper Place, and Date; but, as nothing can be faid in its Praife, there would be no lofs to the Public if it had never been mentioned, or had never exifted. Many more have wrote on Perfpedive, in their Courfes of the Mathematics, in England; alfo Ozanam, a French Author, of reputation, in which I find nothing that is worthy of notice. In Theory he is fomewhat copious, but the whole fub- flaiice of it might be comprifed in lefs than half the number of Pages, and in Pradice he is tedious and puerile; his Operations (on the Jefuit’s Principles) are poor and prolix; fo that, on the whole, (in 72 odavo Pages, and 36 Plates, the fize of the Page) there is nothing to recommend it to the Public. He makes ufe of theTerm, dividing Center,.from whom, moft probably, Mr; Noble borrowed it; but I think ’tis not worth adopting. The mathematical Work, by Muller (mentioned in Page 132.) has about nine Pages, and feven Plates, on Perfpedive. (Vol. I.) The whole Theory, confills of three Theorems only, and thofe not eflential; for they teach nothing more than, that an original Line (not parallel to the Pidure) and its Reprefeutatlon, will meet in the Point of Interfedlon; that the Reprefentation will pals through the Vanilh- ing Point of the Line, and the Line, itfelf, through the Direding Point. He fays, that other Authors have fpun it out into voluminous Works, but have not m.sde the leaft improvement in it; the whole of what they cont;iln (Examples excepted) being comprifed in his firft Problem, viz. How to find the Appearance of a Line, in the Ground Plane. The late ingenious Mr. Martin publifhed a fmall ElTay; with only one Plate, in order to explain the Principles of Perfpedive. He was a voluminous Writer, and therefore, it cannot be exe,peded that he fhould be thoroughly veiled in every Subjed ; of which, this Eflay is a manlfeft proof. The famous Mathematician, Mr. Emerson, in his Works, has alfo touched on Perfpedive, as a branch of Optics. His Theory I cannot fay much of, it is mathe¬ matical ; and, in Pradice ,—1 hope that very few will pradife from it. Here are two Prints given, as finifhed Pieces, fuch as cannot be defcrlbed to do juftice to them ; the Defcriptlon given, and the Prints, .are of a piece, puerile and abfurd beyond all 1 have ever met with; infomuch that, a Boy, of eight or nine Years old, could not have given a more childifh Specimen of his Genius and Abilities, in Defign, Execution, and Defcription. Other Works, by Painters, both antient and modern, contain fome remarks on Perfpedive, which, in lome of them, are pertinent, in others to little purpofe ; as Albert Durer, Lomazzo, Leonardo da Vinci, De Piles, Frefnoy, &c. who fays, that, although Perfpedive cannot be called a perfed Rule, yet it is a great fuccour to Art, but is frequently very fallacious, and often falls into Error; fuch miftaken notions many have of Perfpedive, who ought to be better acquainted with it. Amongft thofe who have written on Painting, in England, Bardwell is the moft copious on Perfpedive, and leems to have a tolerable notion of it; but is fomewhat dogmatical, in relped of the Horizontal Line and Ground Plane, &c. which he imagines to poflefs fome peculiar privilges. Here are upwards of 20 Pages and fix quarto Plates, which fhew tafte in refped of Defign ; but they are all, fave one, in the common parallel pofition; fo that, in refped of the Leflbns inculcated, three or four would have been fufficient, to anfwer every purpofe derived from them. In the lart is a good Lelfon, for a block of Stone obliquely fituated j but, in refped 5 of the Ram’s Horns, he feems inclined to turn the whole into Burlefque, as no Perfon, in his fenfes, would attempt any thing of the kind, by Rule. If the Per- fpcftive in this Work, had been well digefted, in a more regular order, there is what ipany would deem fufficient for a Painter to know; and even as it is, much more than w'hat is generally praflifed may be learned from it, without underftand- kig Perlpeftive, or being able to account for the Rules. Thus, having finilhed the Talk I had impofed on myfelf, as propofed long ago, and planned in the Preface, I hope, that I have acquitted myfelf with that Candour and Impartiality, both with refpeft to the dead, and the living Authors, as I flatter myfelf will meet with the approbation of all who are w'ell acquainted with, and real Judges of the Subjeft, on whofe Decifion I reft my Appeal; Neither, I pre¬ fume, will the living Authors (on mature refleflion) accufe me of making unfair or uncandid Remarks on their Works. A more arduous Talk my Pen was never engaged in; the main defign of the undertaking, particularly in the laft Seaion, being to refcue Perfpeftive from the difcredit of the puerile treatment it has fulFered from incompetent Authors, and to put it on a more refpedlable footing, than it has hitherto been fuppofed to ftand on, in the Temple of Science; for, although its general tendencjr is not fo estenfive, as many other branches of the Mathematics; yet, as it manifeftly tends to the improvement of the Polite Arts, which embellilh Life and Converfation, and make Society more generally agreeable, it is by no means to be difpenfed with, or treated with indifference. Although my intentioii was to be brief, in my Remarks on the Authors, yet, the number of them, and their various obfervations, with my animadverfions thereon, have fwelled the Appendix almoft to another Volume; but, inftead of abridging, I could have extended my Remarks to feveral Paflages, on which there was great room to expatiate, and more fully on others; yet, confidering that the Subjedl is fo little known, and that I have written for the perufal of very few, comparatively, to have dwelt longer on it had been unneccllary, feeing that, neither Advantage (direftly) Pleafure, nor Satisfadlion could be derived from it, to the far greater part of the Community. I %