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Digitized by the Internet Archive 
 
 in 2010 with funding from 
 
 Research Library, The Getty Research Institute 
 
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THE 
 
 YOUNG PAINTER'S 
 
 AULSTICK; 
 
 BEING 
 
 A PRACTICAL TREATISE ON 
 
 PERSPECTIVE; 
 
 CONTAINING 
 
 RULES AND PRINCIPLES 
 
 FOR 
 
 DELINEATION ON PLANES, 
 
 Treated fo as to render the Art of Drawing correflly, eafy of Attainment even to common Capacities; and entertaining 
 at the fame Time, from its Truth and Facility. Founded on the clear mechanical Procefs of 
 
 VIGNOLA AND SIRIGATTI; 
 
 UNITED WITH THE THEORETIC PRINCIPLES OF THE CELEBRATED 
 
 DR. BROOK TAYLOR. 
 
 ADDRESSED 
 
 TO STUDENTS IN DRAWING. 
 
 BY JAMES MALTON, 
 
 ARCHITECT AND DRAFTSMAN. 
 
 That not in fancy's maize he wander'd long. 
 
 But ftoop'd to truth andmoraliz'd his fong. Pope. 
 
 ILontion : 
 
 PRINTED BV V. GRIFFITHS, NO. I, PATERNOSTER ROW; AND PUBLISHED FOR THE AUTHOR, 
 
 SY CARPENTER AND CO. OLD BOND STREET. 
 1800. 
 
TO 
 
 BENJAMIN WEST, ESQ; 
 
 OF THE 
 
 ROYAL BRITISH ACADEMY FOR PAINTING, 
 
 AND TO THE 
 
 ACADEMICIANS anti ASSOCIATES 
 
 OF THAT 
 
 INSTITUTION, 
 
 IS RESPECTFULLY DEDICATED, 
 
 With hope that It may be approved by them and efteemed deferving of being recommended to the Attention 
 
 of the Students under their Care ; 
 
 BY THEIR HUMBLE SERVANT, 
 
 JAMES MALTON. 
 
APOLOGY. 
 
 Desirous to avoid every charge of prefumption, for prefenting a work on Perfpeaivc to 
 the public, while fo many are extant, and during the lifetime of my father Mr. Thomas Malton, fen. 
 who has himfelf fent into the world fo extenfive and fo excellent a treatife on the fame fubjccl ; 
 I deem it but proper to urge a few reafons which afluated me to add another to the number, in 
 vindication of myfelf, (hould any be inclined to cenfure me for having fo done. 
 
 1 had lon<. heard it advanced, and by perfons poffcffing the works of the beft informed wnters on 
 ■this head, n°ot excepting even that by my father, that there yet was wanting a praft.cal treatde, 
 which would exemplify the doarine of delineation, in an eafy, familiar, and engagmg manner j 
 and wherein its rules might be applied to pleafing and painter-l.ke fubjeas I could not but 
 ^dmit the juftnefs of fuch remarks, nor deny that I had obferved the fame, and had very early m 
 life felt a (trong inclination to be myfelf the perfon who fhould fupply that defideratum. 
 
 Vly acquaintance with the fubjea, according to the elegant principles of Brook Taylor, 
 and my havin<^ made frequent, but inefFeaual, endeavours to teach it on thofe principles, and make 
 it engaging at the fame time, reduced me to the neceffity of adopting the method of pradice 
 that Is followed throughout this work, which is a mixture of the fcientific principles of Brook 
 Taylor, with the clear mechanical mode of Vignola and Sirigatti ; making a moft pleafmg, facile, 
 and entertaining, union ; the correanefs and difpatch of which manner of delineation is admitted 
 ■by my father, and {lightly treated on by him in the appendix to his valuable work. 
 
 Independent of the want of an agreeable method of procedure, the figures whereon the generality 
 of authors on Perfpeaive have employed their rules, have, very feebly, conveyed pofitive information, 
 beino-, by much the greater part, ill conceived, and rather difgufting, in lieu of being inviting. The 
 voluminous prolixitv of feme, obfcure brevity of others, trifling littlenefs of many, and partial ap- 
 plication of moft of^them, have neither rendered the fubjeft interefting, nor given general information. 
 Some have been purely mathematical, others wholly mechanical, and few, or none, feem to have 
 made due reference to the painter. I hope that I fliall be found to have proceeded othervvlfe. By nature 
 I was better gifted with the talent requifite for a painter, than for a mathematician ; yet I delighted in 
 the purfuits of both, and was capable at the age of fourteen, to demonftrate any probh-m in the twelfth 
 book of Euclid, of delineating any regular piece of architeaure in perfpeaive, of taking a correa draft 
 from a plafter caft of the human figure, of drawing any of the five orders of architeaure, or of 
 copving a landfcape of Barratt, or of Gainfborough. This, it will be obferved, 1 advance not with 
 a view of boafting of what I was, or am, capable of performing, but to inftance the likdihood there 
 is, that this work will be found lefs tedioufly dry, than thofe of my prcdeceffors on the fame fubjea. 
 
 'The inclination I entertained, I was carncffly encouraged to the performance of, by perfons 
 ^^.ho judged me competent to the talk, fome of whom I had the honor to inftrua in the art. For 
 Kn years paft I have been occafionally engaged preparing the fubjea raattei", from my own knowledge 
 of the art, obfervations from great praaice, and remarks from the obfervations of others, (arifing 
 from imperfea knowledge, or erroneous conceptions concerning it,) and arranging and digefting the 
 whole that it might, as much as I could make it, be worthy to meet the mafter painter's eye, 
 and engage the ferious attention of the ftudent. 
 
 It is not my intention to attempt to prove that the principles of procedure of this work, 
 are the beft that could be given ; there being feveral ways to effea the fame end, each may, 
 probably with g<5od reafon, have its diftina admirers. It will be fufficient for me to aflure 
 my re.iders tliat, from knowledge pf thefe various ways, great praaice, and experience in teach- 
 
 b 
 
ii APOLOGY. 
 
 ing, I have ever found mine moft expeditious, certain, and eafy of attainment. Should any be 
 <Iefirous to fathom the fubje£t to its depth, to gratify a laudable curiofity, they may obtain that 
 fatisfa£tion, by looking into more elaborate works; as my Father's, Highmore's, or Hamilton's, 
 or Brook Taylor's itfelf; but vi'hich labour it was my intention, by this work, to fave thofe 
 whofe defire it is to obtain knowledge of the art on juft principles, with as little trouble as 
 poflible; and with a view to acquire only that fufficiency of it, as to enable them to projedl 
 ordinary objeiSs with truth and facility. 
 
 Throughout this work, 1 lay claim to as little favour as the gentle critic may be difpofed 
 to allow me ; I look upon myfelf as competent to the talk I have undertaken, and am not 
 above telling my readers, it has been a matter of twelve years leifure confideration ; I hope for 
 that indulgence only, which humanity fhould ever allow to human frailties. I undertook it with 
 the flattering hope of pleafmg all, but now publifh it with great fear of not thoroughly fatisfying 
 any. Knowledge of perfpedlive has been fubjccSl of great delight to me, and cannot but be a 
 pleafure ajid advantage to every artift. A grateful defiie to communicate that advantage to others 
 has been throughout, a confiderable motive to my executing this work ; other reafons will no 
 doubt be laid to my account, and which I am by no means inclmed to difallow ; but intereft, 
 i can fafely aflert in this cafe, yields place to more liberal motives. 
 
 Exclamation is but too ready to be made at the great bulk of works on perfpective, as 
 alfo at their expence. It would be advifeable for fuch perfons to refort to Brook Taylor, where 
 they will have no reafon to objedl to either of thofe confiderations. But fully to elucidate and 
 exemplify that author's work, to as to render it clear to common capacities, would extend to a 
 large folio volume or two, with numerous plates. That works on perfpeftive are bulky, arifes 
 from the earned defire their authors have had thoroughly to inveftigate the fubjeft, that it might 
 be fully underftood by thofe for whofe advantage it was defigned ; bulk therefore fhould not be 
 caufe of obje£tion, what is fuperfluous, to the difcerning, may be paffed over. Their expence is 
 certainly ftill lefs a matter of complaint, the moft voluminous and expenfive of them, has fel- 
 dom I believe, exceeded the fum of three pounds. What would three pounds be towards pur- 
 chafing any good pidlure by a great mafter? which is often done by artifts to examine minutely 
 into their principles of colouring, compofition, and the like. And is a knowledge of perfpec- 
 tive of lefs confequence ? A very fenfible writer ^ obferves, " Whatever fome people may think, 
 " a pifture defigned according to the rules of perfpedive, and the principles of anatomy, will 
 " ever be held in higher efteem by good judges, than a picture ill drawn, let it be ever fo 
 *' well coloured. For nature, though {he forms men of various colours and complexions, never 
 " operates in their motions contrary to the mechanical principles of anatomy, nor, in exhibiting 
 *' thefe motions to the eye, againft the geometrical laws of perfpeflive." An artiflr, fenfible 
 of any want of knowledge of perfpedlive fhould purchafe and carefully examine every work on 
 the fubje£i: that is publifhed, until, from fome one, or all, he gleaned every information requifite. 
 
 Almoft every late author on this fubjecl has taken occafion to obferve, that there have been 
 many treatifes written on it, probably prefuming his would preclude the neceffity of any other ; but 
 fo far am I from intimating or imagining the fame of mine, that I hope to fee many fucceed it, 
 and fhall efleem myfelf happy in forming one ftep to a ladder by means of which, fome one, fortunately 
 favoured, ftiall happily reach ptrfeftion, and compofe a work moft engaging to where it is moft 
 applicable, and that Painters, not Mathematicians, fliall evince to the world moft ac- 
 quaintance with perfpedive. 
 
 » Count Algarotti, F. R. S. F.S.A. 
 
PREFACE. 
 
 Jl.T the prefent ^ra to enter on any euloglum on painting, or to endeavour to 
 point out its advantages, either to a learned or commercial fociety, would 
 be, if not impertinent, at lead fuperfluous. Fads that are perfedly eftabliflied, 
 and which are of themfelves indifputable, require net proof. To further the 
 perfedion of the art is all that is now required of its advocates : inflances of 
 its value, and of the great eftimation which it has ever obtained in all poliflied na- 
 tions, from thofe moil able to appreciate its worth, are to be found innumera- 
 ble. No one can refledt on its aid and influence in the fields of fcience, or con- 
 fider how it enlarges the channels of manufacture and commerce, without being 
 perfedlly fenfible of its importance : in an inftant does it impart value to worthlefs 
 materials, and, it may be laid, with god-like power, give to fliapelefs matter, form, 
 life, and beauty ! But the Arts themfelves, though the great fource of wealth 
 to manufaSures, difdain to be reduced to their level ; they may exalt the hum- 
 ble trades of neceffity, but will not float in the fame flream ; vain, very vain, 
 mufl every attempt be to ina7infa£iiire Pictures ! Even the hand that executed 
 the firft production cannot produce an equal copy ; the fire, the fpirit, the energy, is 
 gone. Painting is the fource of the eye's delight, an elegant refiner of life ; and inaf- 
 much as it is brought to perfedlion, is a nation refined, and does fentiment and every 
 virtuous feeling engender that enlarges the mind and expands the human heart. 
 
 More than any other art or fcience, painting labours under difadvantages, as 
 to a certain road to acquirement. The advances of prior explorifts avail but little 
 the emulous enterprizing ftudent, like a vcflcl that proudly traverfes the ocean, 
 the pride of art, and admiration of beholders, painting fleers herflatelycourfe; the 
 artift, whomoft excels, condudts the helm, but leaves fmall traces behind to mark 
 her way, or guide her anxious votary's purfuit. 
 
 The fcience of optics, only, lends a confiderable portion of certain advan- 
 tage to painting, in that branch of it which relates to diredl vifion. . This 
 afiiftance has not been overlooked, but much confidered, and copioufly treated on 
 by numerous writers, under the head perspective. Perfpedive gives infallible 
 
11 
 
 PREFACE. 
 
 rules for delineation ; it is the art of depidling objects on planes, fo as truly to 
 reprefent them as they appear. The very definition anticipates all that can be faid 
 in its recommendation. Linear perfpective, as far as its effect extends, furnilhes 
 a fare and folid foundation to the art of delineation ; but unfortunately, its utility 
 has been infufficiently regarded, and lefs efteemed by thofe to whom its informa- 
 tion was of the utmoft value ; while its merits have been minutely inquired into, 
 and its worth fully eflablifhed by others, to whom it could impart no practical ad- 
 vantage whatever. By the mathematicians it has long been engroffed, they have 
 induftrioully afccrtaincd the infallibility and extent of its powers, and from time to 
 time have ofFered the matured child to its original parents, but indeed fo oblcured 
 by mathematical fymbols, v/itli thefts, hypothefis, and demojijlrction, as fcarcely to 
 be recognizable by them, and the painter-ftudent is literally loft " in the intri- 
 cate mazes of the I'tney labyrinth." Artifts however, fenfible of their right and 
 its advantages, fliould again refume it, diveft: it of its obfcurities, develop its beau- 
 ties, and adapt it to their particular refearches. 
 
 A genius for painting cr for poetry, feems almoft incompatible with profound 
 iklll in mathematical fciences. There are, to be fare, few general rules without 
 exceptions ; not that I know any in the prefent inftance, but there may be both 
 painters and poets deeply converlant with, and who delight in the mathematics; 
 but this I am inclined to imagine, is by no means common. Reafons for this 
 difunion of purfuits, and where one has fome dependance on the other, are not 
 however difficult to be affigned j the exercife of either of the two former fafcinat- 
 ing arts, being produced chiefly by a warm luxuriant imagination, is indignant of 
 reilraint j the fancy, prompt and eager to exprefs its Impulfes, fpurns thofe tram- 
 mels that would curb its impetuofity, or retard its endeavours, rejecting the flow, 
 but fure advances of art. 
 
 The fliortefi:, and only fccure road to knowledge, leads through theory to prac- 
 tice; a negleft of which procedure, with regard to painting, is the caule of the many 
 erroneous productions which with concern we too frequently witnefs: norarefuch 
 errors lefTened when endeavoured to be palliated by the fometimes admiffible, but 
 abufed, term of licenfes. No one can properly be faid to have taken a licenfe but 
 he who knows the boundaries of rule. Poets and Painters have their peculiar 
 liberties mod liberally granted them, and, ufed with difcretion and judgment, they 
 are ever admitted. He who proceeds licentioufly, without inquiry, or guide, mufl 
 not be furprifed to meet the fate of Phjeton. It may be faid I regard not the rigid 
 
 / 
 
 ( 
 
PREFACE. 
 
 lit 
 
 trammels of prefcriptioa ; rule fhall not confine me ; m.y gejiius or my will, fliall 
 have its fway j laws fhall not conflrain me : Then tell the rules tranfgreffed ? Make 
 known the boundaries broken through ? AlTign reafons for fo Going ? Unlefs that 
 can be done, and jull motives be advanced in extenuation, all is anarchy, licen- 
 tioufnefs, and breach of order. Acflive genius may not v^ant the fpur, but fre- 
 quently ftands in need of the curb. 
 
 Sir Jofliua Reynolds, in his lirfl: difcourfe delivered to the Royal Academy, 
 fpeaking of the ftudy and pradice of painting in general, fays, " Every oppor- 
 " tunity fhould be taken to difcountenance that falfe and vulgar opinion, that rules 
 *' are the fetters of genius ; they are fetters only to men of no genius; as that ar- 
 *' mour, which upon the flrong is an ornament and a defence, upon the weak 
 " becomes a load, and cripples the body which it was made to proted:. How 
 « much liberty may be taken to break through thofe rules, and, as the Poet ex- 
 ** preffes it. To/natch a grace beyond the reach of art, may be a fubfequent confide- 
 " ration, when the pupils become mailers themfelves. It is then, when their 
 *' genius has received its utmoft improvement, that rules mny poffibly bedifpenfed 
 " with. But let us not deftroy the fcaftold, until we have raifed the building." 
 
 The modern Painters are lefs regardful of a knowledge of perfpedive than 
 were the ancients. By the ancients it was known and cultivated, and their dif- 
 coveries and opinions of its confequence in painting have been repeatedly handed 
 down to us. By the moderns it is negiedled and almoft loft ; by many, more than 
 neglefted, more than loft, ridiculed, and difingenuoufly reprefented. 'Tis true there 
 are feme painters ingenious in perfpedtive, and who do earneftly recommend the 
 fludy of it ; fome in my knowledge and whom I could here mention, but for ob- 
 vious reafons : the fame motives however do not withhold me refpeclino- the late 
 Sir Jofhua Reynolds, whofe incomparable difcourfes on painting in general are 
 given complete, to an indebted world, by his friend Edward Malone, Efq. and prove 
 that Sir Jofhua's knowledge of perfpedive as well as of painting was confummate. 
 
 Rules and precepts have often been drawn up as guides to the young ftudent in 
 the art of painting. Few have been more confidered, and in many refpects mofl 
 juflly, than thofe written in Latin verfe by Du Fre^noy^ They compofe a work 
 of much labour and learning, and of which there are feveral tranflations into 
 Englifh ; one by the celebrated Dryden, in profe, but in a manner not much to his 
 credit, the fubject being, apparently, not well underftood by him. A poetical 
 
 ' A difiinguiflied French Anllt, who died in 1665. 
 
 C 
 
IV 
 
 PREFACE. 
 
 tranflation by Mr. Mafon / is a mafterly performance, and what renders this pro- 
 duction ftill more valuable and complete, is its being accompanied with elucidatory 
 notes by his friend Sir Joiliua Reynolds -, in the courfe of which the fubftance of 
 much important matter is unfolded with additional information. 
 
 Among the manv pertinent obfervations in this excellent Poem is one very ex- 
 ceptionable paflage on perfpective j in which, the Author miftaken himfelf, or pro- 
 bably not knowing, or not liking the fubject, has moft unjuftly, and incorrectly 
 remarked concerning that only certain aid to painting. As this Poem is defervedly 
 much read and in the hands of almoft every ftudent, it is but proper that fuch un- 
 found doctrine fhould be expofed. In Englifli, by Mr. Mafon, the paflage is as 
 follows : 
 
 ** Yet deem not. Youths, that perfpective can give 
 
 " Thofe charms complete by which your works fliall live j 
 
 " What tho' her ndes may to your hand impart 
 
 " A quick mechanic fubftitute for art^ 
 
 *' Yet formal, geometric fliapes flie draws; 
 
 *' lience the true genius fcorns her rigid laws : 
 By nature taught he fl:rikes th' unerring lines, 
 Confults his eye^ and as he fees defigns." 
 
 
 Sir Jofhua's good judgment could not let fuch a paffage pafs without cenfure 
 and amendment, which he has done In exprefs terms, but he might have faid 
 much more, and it remains to be wiflied he had given fuller fcope to his remarks 
 on the erroneous conception and dangerous tendency of thefe verfes. What he 
 has faid is replete with the m.oft accurate judgment, and is of great fubftance : 
 " Frefnoy, he fays, was not aware that he was arguing from the abufe of the art 
 *• of Perfpedlive, the bufinefs of which is to reprefent objeds as they appear to the 
 " eye, or as they are delineated on a tranfparent plane placed between the fpedlator 
 
 a Mr. Mafon, in an Introdudlory Preface to his tranflation, addrefled to SirJ. Reynolds, has thefe verfes on Dryden. 
 
 When Dry DEN, worn with ficknefs, bowV. w ith years. For very bread defcended to tranflate : 
 
 Was doom'd (my friend, let pity warm thy tears) And he, whofe fancy, copious as his phrafe. 
 
 The galling pang of penury to feel. Could light at will expreffion's brigJitell blaze. 
 
 For ill-plac'd loyalty, and courtly zeal. On Fresnoy's lay employed his ftadious hour; 
 
 To fee that laurel, which his brows o'trljiread. But niggard there of tlut melodious pow'r, 
 
 Traniplanted droop on Sh adweli.'-; barren head. His pen in hade the hireling talk to dole. 
 
 The bard opprefs'd, yet not fubdu'd by fate, Transfonn'd the ftudied llrain to carekfs profe. 
 
PREFACE. V 
 
 « and the objea. The rules of Perfpective, as well as all other rules, maybe 
 " injudicioully applied ; and it muft be acknowledged that a mifapplication of them 
 " is but too frequently found even in the works of the ynoji confiderahle artijls. It is 
 " not uncommon to fee a figure on the foreground reprefented nearly twice the 
 *' fize of another which is fuppofed to be removed but a few feet behind it; 
 " this, though true according to rule, will appear monftrous. This error proceeds 
 *' from placing the point of diftance (vanifliing point) too near the point of light, 
 *• by which means the diminution of objedls is fo fudden, as to appear unnatural, 
 *•' unlefs you fland fo near the pidlure as the point of diftance requires, which 
 *' \vould be too near for the eye to comprehend the whole pidttire; whereas, 
 *' if the point of diftance is removed fo far as the fpedlator may be fuppofed to 
 " ftand in order to fee commodioufly, and take within his view the whole, the 
 " figures behind would then fufter under no violent diminution. Du Piles, in 
 " his note on this paflage,* endeavours to confirm Frefnoy in his prejudice by 
 " giving an inftance which proves, as he imagines, the uncertainty of the art. 
 " He fuppofes it employed to delineate the Trajan pillar, the figures on which, 
 *' being, as he fays, larger at the top than at the bottom, would countera£t 
 *' the effects of Perfpedtive. The folly of this needs no comment ; I fliall only 
 " obferve, by the bye, that the fadl is not true, the figures on that pillar being 
 *' all of the fame dimenfions :" 
 
 *' Yet deem not, youths, that Perfpedtive can give 
 
 ** Thofe charms complete by which your works can live." 
 
 It would be a vain expe(5lation indeed, and fuch a one as I am perfuaded 
 was never formed, to imagine that linear perfpedtive could give thofe charms 
 Complete by which alone their ivorks (Painters) Jloould live. If their works pof- 
 fefted no other charm than linear correctnefs, they would be of little value, 
 and not likely to charm, or live long. To look, ths^t Perfpective fhould find 
 the true contour of regular objects, and allift in defcribing irregular ones, is 
 all that was ever wifely hoped from it, and all that it can impart. 
 
 " What tho' her rules may to your hand impart " 
 
 *' A quick mechanic fubftitute for art." 
 
 Thefe verfes are abfolutely devoid of fenfe ; yet It may be perceived what is en- 
 deavoured to be intimated. By art is mennt intuition, or genius ; and it wifhes 
 
 a Notes by Du Piles, to Dryden's tranflatlon of Frefnoy 's Poem. 
 
vi PREFACE. 
 
 to fay that intuitive genius is preferable to mechanic fkill ; and that it is better 
 to poiTefs a fine imagination, even w^ith error, than a plodding correctnefs with- 
 out tafte. 
 
 *' Yet formal geometric fhapes fhe draws." 
 
 What has Perfpective, in a general fenfe, to do more particularly with 
 formal geometric jl:apes^ than with any other figures ? Are the rules and princi- 
 ples of that art applicable only to the Cube, the Titraedron, the Icofaedron, &c.? 
 Becaufe, in treating exprefsly on this fubject, it is befl explained by apply- 
 ing its inflructive lefTons to regular objects, as being mofl vifibly fenfible of its 
 influence, is it to be inferred, that when known to its fullefl extent it flill 
 refls attached an appendage to architecture only, and has no further applica- 
 tion ? Who fo concludes has very confined notions indeed of its pervading 
 power, which equally governs irregular as regular objects, and has as much 
 influence in the drawing of the human form, as in drawing a regular piece of 
 architecture, or, 2iS texmcdihyYveinoy, formal geometric Jhapes. 
 
 *' Hence the true genius fcorns her rigid laws ; 
 « By nature taught he flrikes th' unerring Hues, 
 ** Confults his eye, and as he y^-^J- defigns." 
 
 That pleafing flattering word, Genius I what mifchief has It done ! and is 
 
 here given in a very deluding fenfe, to the undoing of the Pupil, who is 
 
 -hereby led to conceive what he would otherwife probably never have had 
 
 the boldnefs to imagine. Sir Jofhua Reynolds had, no doubt, obferved many 
 
 inflances of the mifguidance of that fatal word ; and, in his fecond difcourfe, 
 
 places it in the very light it fhould ever be confidered ; as a fomething to be 
 
 formed and flrengthened by reafon, but not to foar beyond it. He fays, 
 
 «' There is one precept, however, in which I fliall only be oppofed by the 
 
 " vain, the ignorant, and the idle. I am not afraid that I fhall repeat it too 
 
 " often. You muft have no dependance on your own genius. If you have great 
 
 *« talents, induftry will improve them ; if you have but moderate abilities, 
 
 . »« induftry will fupply their deficiency. Nothing is denied to well-dire£led 
 
 ** labour : nothing is to be obtained without it. Not to enter into metaphy- 
 
 " fical difcuffions on the nature or effence of genius, I will venture to aflert, 
 
 *' that afhduity unabated by difficulty, and a difpofition eagerly direfted to 
 
 *' the objeft of its purfuit, will produce effects fimilar to thofe which fome call 
 
 " the refult of natural powers" 
 
PREFACE. 
 
 vu 
 
 A fine talent by nature will ftill do little without cultivation ; and it is not 
 an eafy matter to draw as we fee. To draw as we fee, with any tolerable 
 corredtnefs, is the refult of knowledge and long attentive pradiicej and even then do 
 we feldom flrike the unerring line. According to Reid and other minute invefti- 
 gators of the human organs, fight is the mofl: deceptive fenfe we have, and par- 
 ticularly requires the aid of experience and judgment. I will now clofe my remarks 
 on this extraordinary pafTage, which merited not fo much notice but for the general 
 worth of the whole Poem, efleemed the mofl brief and jufl in its precepts that 
 ever was penned. 
 
 A fmall treatife on painting was publiflied in 1764 by Count Algarotti,- wherein, 
 among various fubjefts, feparately treated on, as of confequence to the compleat- 
 ing a painter's education, is a chapter relative to perfpective ; and fo extremely 
 judicious are the obfervations, as to the ufefulnefs and neceifity of a perfedl know- 
 ledge of that art, and fo forcibly is it there pointed out, that no thinking Artifl 
 can read them without being ftruck with their truth, and determining, if not 
 already acquainted with fo ufeful an information, to obtain the knowledge imme- 
 diately. I cannot better fecond that Author's arguments, they fo perfectly agree 
 with my own, than by tranfcribing them. He fays, " The ftudy of Perfpedlive 
 " (liould go hand in hand with Anatomy, as not lefs fundamental and necefiary. In 
 *' fail, the contour of an objedt drawn upon paper or canvas, reprefents nothing 
 *• more than fuch an interfedtion of the vifual rays fent from the extremities of it 
 ** to the eye, as would arife on a glafs put in the place of the paper or canvas. 
 ** Now, the lituation of an objedl at the other fide of a glafs being given, the de- 
 *' lineation of it on the glafs itfelf, depends entirely on the fituation of the eye on 
 " this fide of the glafs, that is to fay, on the rules of perfpedlive ; a fcience, \vhich, 
 " contrary to the opinion of moft people, extends much farther than the painting 
 " of fcenes, floors, and what generally goes under the name of quadratura. Per- 
 " fpedlive, according to that great mafter Da Vinci, is to be confidered as the reins 
 " and rudder of painting. It teaches in what proportion the parts fly from, and 
 ** lefl"en upon, the eye ; how figures are to be marlhalled upon a plain furface, and 
 ** forefliortened. It contains, in fliort, the whole rationale of defign.. 
 
 " Such are the terms, which the mailers, befl; grounded in their profeffion, have 
 ** employed to define and commend perfpedive ; fo far were they from calling It 
 " a fallacious art, and an infidious guide, as fome amongfl the moderns have not 
 ^ blufhed to do, infifting that it is to be followed no longer than it keeps the high. 
 
 d 
 
Vlll 
 
 PREFACE. 
 
 " road, or leads by eafy and pleafant paths. But thefc writers plainly fliew, that 
 *' they are equally ignorant of the nature of perfpe£live, which, founded as it is 
 *' on geometrical principles, can never lead its votaries aftray, and of the nature 
 ** of their art, which, without the affiftance of perfpeftive, cannot, in rigour, ex- 
 *' pedl to make any progrefs, nay, not fo much as delineate a fimple contour." 
 
 All mufl: unite in opinion with this informed writer, and agree that the ftudy of 
 perfpe(flive fliould go hand in hand with anatomy as being not lefs a fundamental 
 information ; he might have faid more fundamental, for without the afliflance of 
 perfpedtive, a knowledge of anatomy would be half ufelefs ; as how could any 
 particular exertion of the mufcular frame be expreffed without juft delineation ? 
 obtainable only from a thorough knowledge of Perfpective. Leonardo Da Vinci 
 was precifely of the fame opinion, and in his treatife on painting, among nume- 
 rous pertinent obfervations on the art, he expreflly fays, " Thofe who venture on 
 " the practice, (of painting) without firft qualifying themfelves in the theory, 
 *' are like mariners putting out to fea without either helm or compafs, ignorant 
 " what courfe to take. The practice ought always to be built on a rational theory, 
 *' of which perfpective is both the guide and the gate j and, without which, it is 
 ** impoffible to fucceed, either in deligning, or in any of the arts dependant thereon." 
 
 Leonardo Da Vinci wrote a treatife folely on perfpective; but this, if ever 
 publifhed, I have never feen, but make no doubt, it was confined in its informa- 
 tion and principles, comparatively to what is now known and practifed. Yet was 
 the knowledge of it then thought materially effential ; in what light would it have 
 been efleemed, perfected as it is at prefent ? My fubject needed not that I Ihould 
 have quoted opinions in fupport of its ufefulnefs, but I have chofen thofe great 
 authorities to corroborate and give weight to my own obfervations on it ; for, as Sir 
 Jofliua Reynolds truly obferves, " we are never fatisfied with our own opinions, 
 " whatever we may pretend, till they are ratified and confirmed by the fufirages 
 *' of the reft of mankind," 
 
 It is common to hear it advanced, as an apology for not knowing perfpective, 
 that the ftudy of it is dry and uninterefting, and that in many cafes it is not to be 
 depended on. Allowance muft ever be made for difference of tafte and opinion : 
 but with all due deference, I fliould deem the fl:udy of anatomy much more dry 
 than that of perfueftive ; yet with what patient application will a ftudent in paint- 
 ing, emulous of fame, appropriate two, three, four, years of his time to acquire 
 a competent information in that neceflary branch of his art. I would alk for what 
 
PREFACE. 
 
 JX 
 
 purpofe is fo much time fpent over fkeletons and anatomized human bodies ? The 
 anfwer would mod affuredly be, to be correcT: in the outlines; and that horn 
 a knowledge of the caufes of action and its effects, appropriate expreflion may 
 be given in every pofition, and that, without the aid of a model, and even 
 whe'i-e a living model would be imperfect, from langour of attitude. If then luch 
 labour is neceffary to arrive at the knowledge oi v^h^t pould be drawn, (hould^that 
 art be neglected which teaches how to exprefs thofe forms, and ho'-^^ to tranlimt 
 them to the canvas ? The acquirement of the former information is ufelels 
 without a knowledge of the latter, of which a competent inlight might be ac- 
 quired in three, or at moft in fix, months. That perfpeftive is not to be depended 
 on, is an unjuft allegation, it is infallible. From injudicious proceeding its delmea- 
 tlons may fometimes be diftorted, but that is not to be attributed to the deficiency 
 of the art, but to the want of judgment in laying down the proper preliminaries. 
 That painter is alfo greatly miftaken, who imagines that prefpedive is not 
 equally applicable in the delineation of the human form, as of right lined figures. 
 From a want of it, fliameful enormities are committed ; forefliortened limbs made 
 too long, a figure extended on the ground, feet or head foremoft, in a foreHiortened 
 pofition, not reprefented its jaft length, often twice the length it fhould be, and 
 fometimes thrice, of which I could point out but too many inftances in works, 
 not of inferior artifts. The portrait painter even, frequently fhews his deficiency 
 in perfpedlive, by making, as the profeffors would fay, his heads out of drawmg ; 
 the off-fideofthefacelarger than the near; one eye higher than the other; the 
 nofe not in the middle of the face, when not fo in the original; and like inftaiices 
 of want of correftnefs in the fight : but he muft not exped to have the compaffes m 
 the eye, who has not long held them in his hand. It may be allowed, that great 
 incorredtnefs is feldom committed, by an attentive, experienced artift ; it may be 
 admitted, that the eye by much pradtice, and nice obfervation, may become fo cor- 
 recl as to render it little liable to great errors; but one twentieth part of the time, by 
 long praaice employed to arrive at fuch critical difcernment, fpent in acquiring a 
 competent knowledge of perfpeftive, would make an artift of genius much earlier, 
 and infinitely more, corred and declfive. 
 
 To every painter fome knowledge of Archltedure Is abfolutely neceffary ; he 
 cannot produce the auxiliaries of buildings to his pictures without it; andthe higher 
 are his aims the more informed fhould he be in this great aid to his citt&s. 'Tis 
 lamentable to obferve the deficiency manifefted in this particular, 1 will ufe the 
 
X ■ PRE F. A C E. 
 
 words of Sir Jofliua Reynolds, *' in the works of the moft confiderable artifls," being 
 as well applicable to their deficiency fhewn in knowledge of architecture as 
 perfpedtive. Their pedeftals, their capitals, and bafes of pillars, their archi- 
 traves, imports, &c, from their total want of profeffional accuracy, expofes them, 
 with concern I have obferved it, to the ridicule of the builder's apprentice. The 
 architedlure of an hiftorical piece, or fubje£l of a whole length portrait, may not 
 be a firft-rate objecSl, nor a fecond, nor a third-rate confideration j it may be thrown 
 to any diftance of importance, at pleafure ; all I mean to dwell on is, that it is 
 thought proper to be introduced, then, if introduced at all, though ^f/>/ down * to 
 any pofiible degree next to obliteration, it fliould be properly delineated, by 
 poflefling the chara£ler of the kind of archited:ure intended to be reprefented. 
 
 The French painters, in general, (hew a laudable attention to their aiding 
 concomitants, be they in what department they will ; a fine inflance, among many, 
 is fliewn in that truly great performance, the portrait of Lewis XVI. by Callet, 
 where the ftyle and correftnefs of the architecflure, and the truth of the prefpeftive, 
 are a reproach to mofl Britifh productions of the fame nature ; which, to be rid of 
 that great trouble, are conflantly backed by a curtain, or troubled landfcape, or 
 clouded fky, even when the fijbjects are the portraits of noblemen or fenators ia 
 their robes, or ladies in drawing-room drefles. 
 
 Theftudy of perfpective combines that of architecture along with it, becaufe the 
 preciiion of architectural fubjects moft obvioufly expreffes its effedls. The acquire- 
 ment tlierefore of a knowledge of perfpective has a double advantage, uniting two 
 informations, without the help of which, an artift is necelTarily compelled to 
 wander in uncertainty; and to feel his way, as do the blind, uncertain of their path. 
 
 And here I cannot avoid remarking on a new proceeding that has lately been 
 adopted, and is dally gaining ground, as it were to the exclufion of ^// necejjity of 
 the introduftion of architecture, or the effect of perfpective in hiftorical fubjeds, 
 where it would be a proper and almoft indifpenfable requifite ; and this is, the 
 practice of crowding three, five, or ten, or more, Herculean figures into the fmall 
 compals of the frame, fo crammed upon one another that fufficient room is not 
 given for action; and the whole appears a fcene tranfacted in a clofet, and that 
 of no greater compafs than from eight to ten feet fquare; which fmall extent of 
 platform has been thought, by fome, fufficient fpace for exprefiing the ceremory 
 of a public execution, or grandeur of a coronation. 
 
 ^ A technical term of painting, implying duUnefc of tint, fliunning of infpeilion, . 
 
PREFACE. xi 
 
 In fcenes of great extent, whether reprefenting tranfactions within or without 
 the walls of a palace, orcaftle, appropriate architecture, well introduced, produces 
 grand effects, ^ as may be ieea in many of the works of the Roman and Venetian 
 fchools. Indeed moft of their great painters were great architedls. I could rea- 
 dily draw out a long lift, but the few following names are of fufficient authority 
 and celebrity, to inftance that a combination of the two arts is not at all detrimen- 
 tal to either. Leonardo Da Vinci, Raphael, Julio Romano, Hans Holbien, 
 Vafari, Paolo Veronefe, Michel Angelo, Rubens, Domenichino, Frefnoy. 
 
 Many have a notion that perfpe6live, not only merely relates to architedlural 
 fubjedts, but to them fimply when.they are reprefented as receding in the pidlure, 
 and exhibiting in a fmall fpace of a plane placed diredt before the eye, the appear- 
 ance of great depth of ftrudure as retiring farther and farther off, particularly in 
 infide fubjeds ; as looking down the aifles of churches, long galleries, and the like ;. 
 in which cafes, the nearer the eye is to being in the plane of the extent looked at,, 
 the fliorter will be the fpace required in which the depth of the fubjeft will be to 
 be delineated, and the greater and more fudden the apparent convergency of horizon- 
 tal lines. Such delineations appearing to the not well-informed in the fubjed of 
 delineation, unpleafing pidlures, and not being able to reconcile to their minds, 
 what is, apparently, fo repugnant to truth, I have heard it obferved that fuch 
 fubjedls were too much in perfpedlive, when it was only meant to imply, that the 
 point of view was taken too clofely to the plane of the building, to have a fatis- 
 fadory, and pleafing picture of the object.. To fay any fubject is drawn too much 
 in perfpective, is tantamount to faying, it is too well, or too naturally, reprefented. 
 
 Among the various informations and acquirements forming a polite and liberal 
 
 education, as well of a lady, as of a gentleman, the art of drawing ever did, and 
 
 a One of the greateft painters of the prefent day, I know, entertains veryjuft, and, I believe, original 
 ideas, as to the applicable introdudion of archite£ture into hiftorical compofitions. When the fubject is 
 of a folemn kind, as a funereal or facred proceffion, the architefture, he confiders, fliould be of few 
 parts, grave, maffive, and very little ornamented, with its horizontals in a parallel dire£lion, or nearly 
 fo, with the picture; in fubjeils of lefs gravity, the architedlure may admit of more divifion, be lighter 
 and more ornamented, and a quicker declination of horizontals may be more congenial; in fcenes of 
 mirth and feflivity, the architecture may he fevered, various, light, and ornamented. To the feeling 
 mind I cannot better inltance what I underftand of thefe notions than by drawing a parallel to them. 
 from poetry, and Pope's Eflay on Criticifm furniflies me with an admirable one. 
 
 When Ajax ftrives fome rocks' vaft weight to throw, 
 The lint too labours, and the words move flow : 
 Not fo, when fwift Camilla fcotirs the plain. 
 Flies o're th' ujibending corn, and fkims along the main, 
 
 e 
 
xii PREFACE. 
 
 always will, hold a diftinguilhed place. The certain and general principles for 
 attaining that elegant accomplifliment, which perfpective affords, are abfolutely 
 necelTary to be known, to draw even the flighteft Iketch from nature with pre- 
 clfionj and to judge with truth the works of others. The defire of attaining to 
 great excellence in any art would be confiderably checked, if there were not 
 to be found admirers fufficiently informed in their judgment, as to be well 
 able to difcriminate difference of excellence. The praife of having done well, is a 
 powerful inducement to further improvement. 
 
 Di-awing, in my opinion, is a vehicle of communication among mankind, as 
 neceffary to be fomewhat informed in, as the art of writing. The pen may ex- 
 prefs our fentiments, but not always our ideas and conceptions ; at times, that 
 can alone be done by the pencil. A mechanic is required to execute a new and 
 fingular piece of work; it is impoffible he can thoroughly conceive it without a 
 draft, the which, not being able to give, is a fpecies of ignorance nearly as great 
 as the not being able to write; and a deficiency that many an intelligent pcrfon 
 has mortifyingly and detrimentally experienced. The moll: laboured defcription 
 of fccnes, conveys not half fo perfect an idea of their form and effect, as a few juffc 
 lines of the pencil. Drawing is an univerfal language, comprehenfible to a very 
 lavage, and plainly fpeaks to every eye. No perfon therefore, dehrous of a liberal 
 education, fhould be deficient in a tolerable acquaintance with the firff principles 
 of delineation, perfpective. 
 
 few who take upon them the tafk of teaching drawing, are qualified for the pro- 
 feffion they engage in. In Landfcape drawing, the pupil is fet to copy houfes, 
 trees, &c. after a promifcuous manner, to refemhle as nearly as they are able thofe 
 of their originals ; but without being made acquainted with any fixed principles of 
 delineation m general. They advance from fimple to complex fubjects, and, when 
 capable of making a tolerably decent copy in colors, are looked upon to be greatly 
 ikllful; though at the fame time they are as incapable of doing any thing original, 
 or of taking a view from nature, as if they never had handled a pencil. They 
 are made to draw flant lines to reprefent horizontal ones ; to make parallel lines 
 tend to a point of union ; ovals to reprefent circles ; acute, or obtufe angles to re- 
 prefent right ones ; but without being fhewn the reafon, or having the caufe de- 
 monftrated to them, why they do lo. 
 
 It is common for perfons after long inftructlon in drawing, under what are termed 
 able maflers, and after they have obtained great proficiency in copying, to requeft 
 being informed how they are to take a view ; to do which they feel themfelves as 
 
PREFACE. 
 
 xm 
 
 incapable, as would be their pencil without the guide of ihe hand and judgment. 
 This would not be the cafe had their mailers, from time to time, inculcated the 
 principles of perlpective, by giving familiar objects, as chairs, tables, or other 
 furniture, or fmall models which they might furnifli, to be drawn as they would 
 appear in different places and politions j and after defcanting on, and correcting 
 the fkctches of them, proceed with their pupils to delineate the fame exactly by 
 rule, from determined ftations. The folid knowledge that would be thus inftUled 
 and ingrafted on the more pleafurable part of the art, would fo deeply fix the 
 whole, as would render it permanent and readily ufeful, whether in copying, 
 compofuig, or drawing from actual nature. 
 
 The whole of my Theory, if it can be called one, is contained in the introduc- 
 tion. I have there briefly explained the nature of, and how to produce perlpective 
 delineations of given, or known objefts, from determined flations. After the 
 Introduftion I proceed to the pradice, where, by the clearefl, and fimplelt me- 
 thod that I could devife, I have traced the fubjeifl, in regular progreflion to the 
 end of my propofed defign. To the refletfling mind 'tis needlefs to obferve that 
 the number of examples given might exceed all bounds, were endeavour made 
 at introducing every poflible cafe that might be fuggefted. In purfuance of my 
 plan the moft prominent features only have been the obje£l of mv attention ; fu- 
 bordinate ones, and repetition, mufl be left to the care and praftice of the fludent. 
 
 That I might make this work as ufeful and as compact as I well could, and 
 that it might contain In Itfelf every information neceflary to the profecution of 
 the fubject, I have prefaced the practice of Perfpective with feme problems and 
 obfervatlons on practical Geometry; giving fuch only as are indifpeniibly necef- 
 fary to enable the lliudent to draw correctly the fchemes required in the practice 
 of perfpective delineations. This I have done, as I confider it extremely dif- 
 couraglng, and deflructive of the end required, to tell the reader, who opens a 
 book for Ibme pleafmg and neceflary Information, that he has firft fomething elfe 
 to learn, as a prior knowledge, and which is not there to be obtained, before he 
 can comprehend what he Is in fearch of, and delirous to know. And this is ftill 
 more repulfive, when probably the fufficlency of fuch prior knowledge is fo tri- 
 vial, that it could all be exprefled in a few pages ; to avoid the little addition of 
 which, the ftudent Is turned back, and left to fearch for the mentioned books 
 without guide or direction of how much, or how little of it, it is necefliuy he 
 fhould make himfelf acquainted with ; a circumflance fo difcournging as fre- 
 quently to end In a total neglect of both. 
 
XIV 
 
 PREFACE. 
 
 Without a good fhare of ingenuity and refolution, 'tis Impofllble to become 
 thoroughly acquainted with any art or fclence by felf fludy, from book alone. 
 In the firft place, what is there faid, if not clearly intelligible at firfl, exprelTes 
 but the fame on a fecond reading, nor is it placed in any new light on a third ; 
 and the ftudcnt is left to ponder and work his way, as his genius and his patience 
 fults : but let it be obferved, no information obtains fo deep a root as that we give 
 ourfelves. 
 
 With information and inclination competent to advance, all difficulties will 
 fpeedily vanlfh, all clouds of darknefs will difperfe, and a bright and clear prof- 
 pect open to the view ; there may indeed a few fwamps and brambles obfliruct 
 the path and Impede progrefs ; but thefe I fliall not only endeavour to re- 
 move, but will place fuch Ifep-ftones and finger-pofts in the way as will enfure a 
 certain road, and leave little chance of being bewildered, or loft in a mire. 
 Should my traveller be led unexpectedly into a path apart from the main road, 
 he may reft aflured it will be to notice a profpect by the way that otherwife 
 might have efcaped his obfervation, and that he will be brought a gainer there- 
 by, to the place whence he ftarted ; his mind expanded and eager fur further dif- 
 covery. Through the whole I will be the companion of his travels, nor will I 
 enforce my principles by harfh or feverc means, but ufe him as a friend that I 
 would wilh to inform. To drop the metaphor, I will do my endeavour to ad- 
 vance ftep by ftep unto the end of my purfuit, with a careful attention to the ca- 
 pacity of my ftudent ; advance not any thing I cannot prove, nor leave aught, if . 
 pofiible, not clearly explained and inveftlgated. All controverted points I fhall 
 keep to be dlfcufled at the laft, they having nothing to do with true and juft re- 
 prefentation, may be looked into, or not, at the option of the reader ; though 
 it does not behove me to pafs them unnoticed. 
 
 How far I have fuccceded in my endeavours at fimplifvlng and generalizing 
 my fubject, the public, who are now become my judges, muft determine. How 
 far I have jufdy exprefled my conceptions, or how fatisfactorily conveyed to 
 others a fourcc of great pleafure to mylclf, I cannot fay ; but of this 1 am aflured, 
 that the ftudy and practice of perfpectlve may be made as entertaining as any 
 branch of painting whatever, except coloring, and giving relief of light and 
 fliade, which Is the laft thing a painter has to ftudy, and which he can never be 
 Hud to have acquired. 
 
INTRODUCTION. 
 
 EVERV thing we fee is feen perfpedlively ; whether it be a houfe, a man, or 
 beaft, or tree, or fliip, or plains, or hills, or water, or all together. It will ap- 
 pear a ftrange cbntradidion to advance, but which in a few words I hope to make 
 clear and manifeft, that no objedl whatever appears as it is, in any one point of 
 view ; that is, prefents a figure to the eye fuchas we know it to poflefs, but one 
 objea alone excepted -, which objea is a globe. A globe in every point of view, 
 and to every eye at the fame time looking at it, and in every diredion, appears 
 a globe, or fpherlcal body bounded by a circular line. Every other objedl affumes, 
 apparently, a different form in every change of pofition, or different point of 
 view whence it is feen. A circle, for inftance, the mofl perfect of plane figures, 
 never appears a circle but in one point of view, and that is, when the eye is per- 
 pendicularly over the center of it: in every other fituation its appearance is an oval, 
 more or lefs extended, the more or lefs the eye is in the direftion of its plane ; 
 like figures A, B, and C : when the eye is in the direiflion of the plane" of the 
 circle, then is its appearance a right line, as the line D. 
 
 Parallel right lines never appcui pmallel ^ confequently a 
 fquare can never appear a fquare. 
 
 There is no one capable of making ferious reflexion, and of 
 drawing confequences from certain principles, but muff be 
 fenfible and admit, that of two equal heights, one placed nearer 
 the obferverthan the other, that that which is farther off will ap- 
 pear lefs than the one that is nearer. Apparent diminution 
 of fize, is the reafon for concluding diftance of objeifls : we do 
 not fcruple to fay of two men, or of two fliips, of known equal ' ''^ ' 
 
 dimenfions, that one is farther off than the other, becaufe one appears lefs than the 
 other i and that one is much farther off, becaufe it appears much lefs. 
 
2 INTRODUCTION. 
 
 This principle being adrriltted, the confequences take place in every degree of 
 diftance, however great, or however fmall. It the eye of a fpedlator be at E, 
 (Fig. 1 , Plate 1 ,) looking at a height, as AB, and an equal height be at CD, farther 
 from the eye than AB, then will the nearer height AB, appear to the eye fome- 
 what higher than the equal, but more dlftant, height CD. For Vvhich reafon, 
 parallel right lines, as was before advanced, can never appear parallel, not 
 even when they are dlredt before the eye, as the lines AB, and CD. Fig. 2. For If 
 the eye be oppofite the middle between the extremes of the lines, fuppofe op- 
 pofite the point E, then would the diflance of the two lines at E, as FG, appear 
 greater than the fame height AC, Or BD, at the two extremes ; becaufe they are 
 equal heights feen at greater diftances. Confequently the parallel fides of a fquare 
 can never appear parallel, nor the figure be feen as it really is : But more or lefs cur- 
 ved, according as the eye is nearer or more remote from the parallel lines regarded. 
 Now the bufinefs of drawing, that is, of drawing perfpecftively, is to de- 
 lineate things as they appear, in every poflible diredtlon that they can be prefented 
 to the eye ; and not as they are, or as we know them to be. Thus of a book, 
 fuppofed placed In various pofitions on a table, as Fig'. 3, 4, 5, and 6, which, 
 though all corre£t delineations of the fame objed:, are neverthelefs all different in 
 their reprefentations, exprefilng the book as ken in as many different pofitions. 
 If a bafon is delineated, as ftanding on a table, it is mofi; commonly reprefented 
 as Fig, 7, which may be truly its appearance from a certain point of view, and fatif- 
 fadlorily indicate the real form, in the lituatlon intended, to mofl beholders ; yet is 
 neither the bafon, nor the table it is reprefented ftanding on, fuch figures as the 
 table and the bafon are really known to be i for the tops of both are known to 
 be truly circles ; yet in their reprefentations they are made ovals, and ovals very 
 much extended. 
 
 Let a fquare box, which, for particular reafons, we will fuppofe of cubical form, 
 that is, having every fide a fquare, be required to be delineated. It is often fatisfafto- 
 rlly reprefented, as Fig. 8, with one fide a fquare, and the top not In the kafl like 
 a fquare, but which has the appearance of a fquare horizontally fituated. Or a re- 
 prefentation may be given, as Fig. 9, with two fides and a top feen, of which one 
 fide only fliall adually be a fquare, the other fide, and top, very different figures, 
 yet appearing the reprefentations of fquares fo placed. Or a cubical form may be 
 reprefented, as Fig. 10, when neither fide nor top fliall be adtual fquares, yet all do 
 appear as fuch, and the whole together conveys a juft idea of the obje^l intended to 
 
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 E< 
 
 C A 
 
 B 
 
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 _rf,..,fo, .•^,i<iJ*~/ 'y/,.„^'-«^Jin. /a. 
 
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INTRODUCTION. 3 
 
 be reprefented : and notwithftanding the three delineations differ fo efTentially 
 from each other, yet do they all, and each, convey the idea of the fame form, 
 but differently pofited. 
 
 Now this effedl could not be obtained, by making the reprefentation of each 
 fide of the objedl fcen, a fquare, the better to indicate a fquarej for fuppofe one 
 only fo reprefented, as A, Fig. 1 1, (and one only, of the fame objed, can be 
 truly fo) the top, B, will not appear a fquare as placed horizontally, and at a diftance 
 from you, by being made a fquarej neither will the fecond fide, C, appear a fquare, 
 as placed at right angles with the other, by being made a fquare ; but altogether 
 will have the appearance of three fuperficies, all in a vertical plane, and have 
 no femblance of a folid body; not even when affifted with the effe(ft of lioht and 
 fhade; as Fig. 12. for the linear delineation not affeding the eye as the contour of 
 a folid body, the three fquares will appear but as one fuperficies, varioufly Ihaded. 
 
 What has been faid of the above particular figures, may be applied to any and 
 to every figure : a man, a tree, a fliip, or any form that exifts. Thus when a 
 man is reprefented with one leg longer than the other, or one arm longer than 
 the other, it is not to be inferred from thence that one leg, or one arm, becaufe 
 not cJrawn at full length, is meant to reprefent an arm, or leg, fnorter than the 
 other ; but that the leg or arm fo reprefented, is fecn, as painters exprefs them- 
 felves, forefliortened, or contracted in its manner of prefentation to the eye ; 
 and fo of every different pofition. A tree, in one point of view, fhall appear of 
 very different figure to the fame tree in another point of view; io of a fliio ; 
 and fo of every objecft of art or nature. 
 
 It is really ffrange, though not unaccountable, that though we tuvcr fee 
 objeds as they ^r^", but always as they appear, that is, perfpedlively ; yet in 
 drawings of houfcs, what are termed geometrical drawings, appear, to the manv, 
 to be the moft fatisfaftory reprefentations of them. 
 
 For the fatisfadion of the uninformed in this particular, I will briefly explain the difference tivit fubfifts 
 between thefe two modes of reprefentation, geometrical and perfpedive ; that the terms geometrical and 
 perfpeftive drawing, may be immediately and clearly iinderftood in future on the mention j and after a few ob- 
 fervations thereon, proceed with my fubjeft. 
 
 By a geometrical reprefentation, as of a houfe forinffance, is undcrftood, that 
 the whole, and every part of it, is drawn according to the ffriCt rules of geometry : 
 that is, that every circle be drawn a true circle ; every femi-circle a true femi- 
 circle ; every fquare be made a true fquare, with its oppofite fides parallel, and. 
 its angles right ones ; and that all parallel lines, in every direction, be really made 
 
4 INTRODUCTION. 
 
 parallel. Under all which agreements. Fig. 1, Plate 2, is a geometrical elevation 
 of a houfe, wherein may be obferved that the circles are true circles ; the fquares are 
 true fquares ; that all its windows, intended to be equal, are made equal and alike j 
 and that all horizontal and vertical lines are ftriiSly parallel to each other. Fig. 2, 
 is the geometrical elevation of the end of the fame building. Such delineations 
 are what are termed geometrical drawings, and are fuch as are implied when re- 
 ference is made, in this work, to drawings of objedts as they are. 
 
 Aperfpedtive drawing of a houfe, is the reprefentation of a houfe as it appears, 
 when viewed from any particular ftation. Fig. 3, is a perfpeftive reprefenta- 
 tion of the before-explained geometrical drawings, in which it may be obferved 
 that there is no one figure delineated like unto the originals of which they 
 are the reprefentations. Circles and femi-circles are reprefented by ovals and 
 half ovals ; fquares are defcribed of the figures of lozenges, or more properly of 
 trapeziums; none of their angles are right ones, fome being very obtufe, and 
 others very acute ; none of its parallel lines, except the vertical ones, are paral- 
 lel ; neither are any two of its correfponding windows of a fize, though in- 
 tended to reprefent equal and alike windows. And though this be the univerfal 
 language of nature, and the only prefentations ever offered to our eyes, yet are 
 they not fo v>'ell comprehended in general as are geometrical delineations ; which, 
 though it may appear paradoxical to allert, are abfurd delineations, and no repre- 
 fentation of any real objedl at all. 
 
 I would not have it fuppofed that I mean to imply, there is no utility in geometrical drawings; my 
 meaning here is, only relative to their not being reprefentations of exiting forms as they appear. 
 
 Now though geometrical appearances, in real objedts, never can be feen, and 
 perfpedtive ones always are feen, yet do the firft, in reprefentation, feem more 
 fatisfadtory to the untutored eye than the other ; which, overlooking the appear- 
 ance of objedts, immediately reverts to the thing fignified ; and knowing that 
 houfes in reality are equally high at their extremes, and that their tops are level, 
 and parallel to their bottoms, immediately conclude the former to be true repre- 
 fentations, and the latter erroneous conceptions, which, though frequently com- 
 mitted, cannot be defended or accounted for. 
 
 If it be pofitively true that thefe irregular figures take place as the reprefenta- 
 tions of others of truly regular forms, is it to be concluded there is fome deter-" 
 minateprecifeform of reprefentation, from certain confequences ? or is it all random 
 work, and left to the guidance of the eye and reafon only? The whole is govern- 
 ed by rule, and there is a determinate mode of procedure, upon infallible prin- 
 
S^. 2. 
 
 INTRODUCTION. 5 
 
 ciples ; by which, knowing the pkn and form of the objedV, and diftance and 
 height of the eye that views it, aperfeft delineation fhall be effeded ; which may 
 fo impofe upon the eye, as to be miftaken for the objeft itfelf. I will now 
 enter on this important fubjedl, but prev.ioufly it will be neceflary to explain 
 feme iiitrodudlory matter, upon which the certainty of effeding this defirablc 
 end is grounded. 
 
 The truth of perfpedive reprefentations depends upon an eftablifhed and 
 certain principle in optics, that vijloji, through the fame medium, is co7iveyed in 
 right lities to the eye. If the attention of the eye be directed to any particular 
 fpot, it obtains its perception, by a ray cf vifion, or of light, extending 
 
 in a right line between the obje£l and the eye : thus, the £ 
 
 eye at E, fig. i, upon looking at the point A, forms, whatisg^^— 
 
 termed in optics, a ray of vifion, or vifual ray, EA, ex- 
 tending in a right line between the point of obfervance and 
 the eye; which line of vifion it is contended, is a right 
 line ; and fliould any other obje£l, as B, intervene between a,., 
 
 the firft point. A, and the eye, fo as to touch the vifual.r::-- 
 ray, it would efte<5tually hide the point A from' view of the 
 eye at E. To prove that a ray of vifion direfted from 
 
 the eye to any particular point, is a right line, and not a curved one, as EGA, the 
 following fimple experiment may eafily be tried, which, anfwering, will in- 
 conteftibly eftablifli the fad. Place any height, as AB, (Fig. 'i.) before the eye, 
 at E ; halfway between the fight and the firft height AB, place a fecond height, 
 as CD, fo placed, that the other may be feen immediately behind it. Then 
 direding the eye to the bottom of the objedl, mark the place where it will 
 appear (which it will do) to touch the firft height, as at /^ ; then direft the eye 
 to the top of the far objeft, and mark where it will appear to touch the firft 
 height, as at a ; then if the fpace comprehended between a and b, be but half 
 the height of AB, it will be clear that the vifual rays EA and EB, direded 
 from the eye at E, to the points A andB, are right lines. 
 
 To my reader converfant in geometry, further proof need not be given of the 
 certainty of the vifual rays EA and EB being right lines, than has juft now 
 been ftated. The line ^ ^ is half the line AB, but the line AB is parallel to ab, 
 and twice as far from the point E ; then will the lines E ^ A, and E ^ B, be right 
 lines, and the triangles Y, a b, and EAB, be fimilar. 
 
 D 
 
6 INTRODUCTION. 
 
 It would be entirely foreign to the purpofes of perfpe£llve, to enter more oft 
 the fubject of optics ; the eftabliflunent of this fiiigle fa£l, paves the way to the 
 certainty of all delineation on planes. To prove that rays of vifion are fubjefl to 
 refraftion, as theypafs through mediums of different denfities, would be entirely 
 irrelevant tothe prefent purfuit, which has only one medium of optical pervicity 
 under confideration. Air ; and to that alone we are to be confined. Neither 
 would it be of any account to the prefent inquiry, to inveftigate the nature 
 cr eflence of light ; for whether it is material, or immaterial, is perfeftly unim- 
 portant here. On fuch points of contention it is neither my province, nor my in- 
 clination, to dwell: it only regards the fubjedlin queftion to eftablifli, not by what 
 7}ieans vifion is performed, but, that it is conveyed in right lines from the eye, 
 the eye and the objeiS being in the fame medium of light ; of which I hope 
 demonftrativc, but of which I am certain, (the enquiry anfwerlng the propo- 
 fition) pra£lical, proof has been given. 
 
 On the certainty of the diredl procedure of the vifual rays from the eye, it is, 
 that we are capable of calculating the exaft apparent dimenfions of objefts, as they 
 are more and more remote from us. Not that this calculation is of any par- 
 ticular fervice in perfpeilive delineations, jbut only as it obtains inconteftible 
 proof of what othervvifc might remain doubtful, the exaft proportion of dimi- 
 nution that does take place ; and which is, in the inverfe ratio of the fquares 
 of their dijlcmces from the eye that regards them. If an object be at a certain 
 difi^ance from the eye, it will appear four times the dimenfions of an equal 
 objedl feen at twice that diftance ; nine times the dimenfions of an equal body 
 placed at three times the diftance ; fixteen times as large as an equal body at four 
 times the diftance ; and fo on, inverfely as the fquares of tlie diflances ; that is, 
 Inafmuch as the fquares of the diftances increafe, in the fame ratio do their appa- 
 rent magnitudes diminifh. 
 
 If a fquare, as ABCD, be placed before the eye, it will cover, and hide from 
 view a fquare of four times its dimenfions, at twice the diflance, as FGHI: 
 confcquently, an equal fquare, at twice the diftance, will appear but a fourth 
 part the dimenfions of the firfi:, as any one of the four fquares marked on 
 FGHI. The difiance is 2, the fquare of which is 4, the inverfe then is only a 
 quarter, or a fourth part. At three times the diftance of tiie firft fquare from 
 the eye, it will cover a fquare of nine times the dimenfions, as KLMN ; of con- 
 fequence an equal fquare there, would appear but a ninth part the fize; the 
 fquare of 3 being 9, the inverfe of which would be but a nintli part. At four 
 
INTRODUCTION. 
 
 times the diftance, it would hide a fquare of iixteen times its dimenfions, as the 
 fquare OPQR, determining an equal Iquare there placed, to appear but a fix- 
 teenth part its fize ; the fquare of 4 being 16, the inverfe is but a fixteenth 
 
 
 
 
 
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 ^""^ 
 
 
 
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 part. So the proportion, or ratio, would go on to infinity, agreeably to the in*- 
 verfe of the fquares of the diftances; if at five times the diftance, but a twenty- 
 fifth part ; and, if at ten times, but a hundredth part. 
 
 Probably the invefligation of this curious circiirpflance may be aided by an 
 
 where 
 
 examination of the following diagram 
 
 .■^«^->s 
 
 9V 
 
 are three equal fquares, X, Y, and Z, placed dired before the eye at E, each 
 having one corner touching the fame vifual ray to the eye, K F A E ; of con- 
 fequence, being all vertical, and parallel to each other, their tops and near per- 
 pendicular fides, are all in the fame planes of vifion. The fquareY being twice tlie 
 diftance from the eye at E, that the fquare X is, appears, to that eye, but a 
 fourth part the dimenfions of the firfl fquare ; as is manifeft by the vi-fual rays 
 FE, GE, and HE, which pafilng the plane X, touch it in the points A, g, and 
 h, determining the fquare A g h i, as its apparent magnitude, when compared 
 with the fquare X ; which fquare A g h i, is but a fourth part the fquare X ; 
 for the line A h, is but half the line A C, and A g, but half A B ; of confe— 
 quence then the fquare A gh i, is but quarter of the fquare A BC D, or fuper- 
 
8 INTRODUCTION. 
 
 fides X. In the fame diagi-am, the fquare Z is four times the dlftance from, 
 the eye that is the fquare X ; on which account its apparent dimenlions are, 
 when compared to the fquare X, but a fixteenth part of the fquare X, as is clearly 
 evident by the vifual rays K E, L E, and M E, which, interfeding the fquare 
 X, determines thereon, a fquare equal a fourth part of the fquare Agh i, and con- 
 fequently but a fixteenth part of the fquare X ; an apparent diminution agree- 
 ably to the proportion intimated, being itiverfely as thefquares of the dijfances. 
 
 ^ .DEFINITION 
 
 I. A Visual Ray. Is an imaginary right line extended from the eye, to any 
 particular point, the objeft of the eye's regard, or contemplation. 
 
 It is curious to obferve the play of the eye, while it is employed in minutely 
 furveying any particular objeft, orobjedls; to remark its gradual (hiftlngs as it 
 changes the immediate fpot of contemplation to the regarding of another, or 
 others. It will naturally refult from this confideration, and the knowledge of 
 vifual rays being right lines, that no two fpots can be fo near, but that the di- 
 rection of the eye will be changed, and a new vifual ray be formed, in the fepa- 
 rately examining the one and the other. Obferve but the dial of a watch ; and 
 the motion of the flfifting of the eye will not only be felt as it pafles from re- 
 garding one hour to another, but it will be fenfibly felt as it glides by the minutes; 
 evincing in its progrefs a fubtlety of motion, fuperior tu the mechanlfm of the 
 delicate machine it contemplates. 
 
 From the fhifting of the eye, while employed in examination of any obje£l, or 
 number of objefts, it may be figured that while contemplating the borders of a 
 circle (as the minutes of the dial of a watch), there would be generated a cone of 
 vifual rays, of which the eye is the apex, or point, and the dial the bafe ; as Fig. 1 , 
 Plate 3. And it muft of courfe be refledied, that, as the objefts of contempla- 
 tion differ in figure, fo mufl vary the body of the collection of rays proceeding 
 from the eye in their examination. As, fuppofe the objeCl a fquare fuperficies, 
 fee Fig. 2. then will there be generated a pyramid of ra_ys; if it be a triangle, 
 then is there another pyramid formed, having a triangular bafe, as Fig. 3 ; or, 
 the objeCt being a folid, as Fig. 4 ; or the figure may be a man^ or beaft, as 
 Fig'. 5. and 6. it matters not what, on the eye's regarding them all around, 
 there will be formed a body of vifual rays, of which the contour of the 
 cbjedt regarded, be it what it will, is the bafe, and the eye the apex. 
 
TLATE 5. 
 
 ^/u/.i 
 
 _^w</fc»i .^,//,j/,./ /„/r,„ia , «fc/fe ,~^'i T MfO . 
 

 .«»^.< ■^./■^^:^Ay//yj„„.,^^,^^^^„^,,, .^, .^ 
 
INTRODUCTION. 9 
 
 DEFINITION 
 
 2. Visual Rays. Are any number of imaginary right lines proceeding from 
 
 the eye, to any object the fubjedt of its contemplation. 
 
 If the pyramid of vifual rays proceeding from the eye while contemplating an 
 obie£t be cut by a plane making a feftion of thofe rays, the figure that would be 
 generated on the plane by fuch feftion, would be what is termed a perfpeftive 
 reprefentation of that objeft ; which feftion would be varied in figure and In 
 dimenfions, accordingly as the plane making it, was inclined one way or ano- 
 ther and accordingly as it was taken nearer the eye, or nearer the objeft. Pa- 
 rallel fedtions would be fimilar figures, and all otherwife than parallel, diflimilar. 
 
 Thus of the cone of vifual rays, proceeding from the circle ABCD, Fig. i. 
 Plate 4 ; the fedion e f, made by the plane FGHI, being nearer the eye than 
 41 b, made by the parallel plane KLMN, the former figure, though fimilar, is 
 fmaller ; and the fedion c d, made by the inclined plane OPQR, is different in 
 figure from thofe made by either of the two vertical planes. So of the pyramid of 
 rays proceeding from the cube ABCD, Fig. 2; the feftions made by the parallel 
 planes FGHI and KLMN are fimilar, but differ in fize from each other, and in 
 figure from that made by the plane O P ^R on account of its inclined 
 
 pofition. 
 
 DEFINITION 
 
 3. A Perspective Delineation. Is a linear reprefentation of any obje£t or 
 
 objeas, as they appear to the eye that regards them : and is fuch a figure 
 as may be fuppofed to be made by a plane making a feCtion of the body 
 or pyramid of vifual rays direfted from the eye to the objefts, while con- 
 templating of them. Which delineation, being fo tinted as to refemble 
 the local colours of the real objeds, and having the effed of light and 
 fhade, will convey a lively idea of the real objeds, and at the fame 
 time indicate their pofition and diflance from the eye of the obferver. 
 A Perfpedive reprefentation of any objed, or multitude of objeds, is fuch a 
 reprefentation as would appear to be made on a plate of glafs, placed between 
 the eye, and the objed or objeds of examination. A view feen through the 
 window of a room, is, as it appears on that window, a perfpedive reprefenta- 
 tion of that view ; and if the fight could be kept confined, and the hand at the 
 fame time were to trace the figures of the objeds on the glafs, where they ap- 
 pear to touch it, the pidure fo drawn upon the glafs, would be a perfed per- 
 fpedive view of the profped behind it. 
 
10 INTRODUCTION. 
 
 It muft however be obvious, that every change made in the place of the 
 eye, or the pofitlon of the tranfparent plane, muft make a difference In the- 
 figure and dimenfions of the fedlon of vilual rays ; If the plane of glafs be 
 placed near the eye the fcillon will be fmall ; and as the glafs is removed 
 nearer to the obje*5l, the feftlon, or reprefentatlve figure, will proportionably 
 increafe : alfo, .the plane of glafs. may be fo pofited, as to produce very 
 dlftorted figures Indeed, but of that in another place. 
 
 Inclinid feilions of the pyramids of rays, that is, not vertical ones, are Sometimes taken, as fubjefts of 
 curiofity ; but feldom as objcifls of utility. As fubjefls of piflures they are univerfally vertically taken, and, 
 until the conclufion of this work, when fpecialiy treating on fuch fubjcfls, they will uniformly be fo 
 confiJered. 
 
 Suppofe, while the eye is fixed looking through a fight-hole as at E, (Fig. i, 
 
 Plate 5.) at an objeft, as A B C D F G, a plate of glafs were placed vertically 
 
 between the eye and the objeft ; as the plane H I K L. And fuppofe the face 
 
 ■ of the plane of glafs, towards the eye, to have been finely dufted over with 
 
 l^alr-po\^der ; not fo as to render it impervious to the fight, but fo, that theob- 
 
 ^^e£ts might neverthelefs be dlfthnSlly feen through it. Keeping the eye fixed at 
 
 the fight-hole, a fleady hand could then trace on the glafs the contour of the ob- 
 
 je6t,-.qs It would appear through that glafs, and would mark the figure ab c dfg. 
 
 Now it is the bufinefs of the rules of perfpeftive to find fuch figure, on an 
 -opaque furface, as paper, from fome certain data given or known, as would, when 
 obtained, and properly placed between the objcftand the eye, affecl the eye the fame 
 as the one traced on the glafs ; for the proof of which, the figure being out, the 
 real object fliall exadly appear through and fit the aperture ; as in Fig. 2, the 
 pbjeit does, through the aperture a b c dfg, to the eye of the obferver at E. 
 
 Having the two extremes of a right line, the whole line is obtained, by 
 drawing it from one extreme to the other ; therefore to find the perfpedlve of 
 the figure A B C D F G (Fig. 3.) it is only necefl'ary to find the points of interfec- 
 tion of the vifual rays E A, E B, E C, ED, &c. from the vifiblc angles of the 
 objeft, as they would pierce the plane H I K L, in the correfpondlng points 
 abcdfgy the lines then being joined together, in their refpeftlve directions, 
 as Is there done, the whole figure is obtained, which Is the reprefentatlon of 
 tlie contour of the obje<ft required to be delineated. 
 
 Thus, I hope, I have clearly fhewn what Is meant by perfpe<5llve reprefentations. 
 -I will next proceed to trace a.fimple method by which they may be obtained, and at 
 the fame time will endeavour to explain the infallibility and truth of the procefs. 
 
Flatk r. 
 
 
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 4 
 
 F7<;.y. 
 
 I^ 
 
 D 
 
 H 
 
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 Ff'n. .'J 
 
 K 
 
 Loii,h,ri l'i,/:li:^linl In Jama- .lUtlioti .l.iii ■ i.Wn 
 
INTRODUCTION. re 
 
 As It is certain that the apparent figure of every object is changed by any 
 variation of the place of the eye, fituation of the objeft, or polition of the in- 
 tervening plane on which the reprefentation is required ; it of confequence 
 follows, that to give a perfpeftive delineation of any object, the Point of View 
 muft be fixed, the pofition and place of the Plane of Delineation muft be 
 determined, and the fituation and dimenfions of the Original Object, 
 known. With tliis data premlfcd, a perfpeftive delineation of any objeft, or 
 multitude of objefts, may be obtained, with fuch certainty and correflnefs, that 
 the figures drawn^ being cut out, and the plane on which they are delineated, 
 fixed in its flated place, the original cbjeft or objefts would be found to fit and 
 fill the aperture-, without the fmallefl poflible variation. 
 
 DEFINITIONS. 
 
 4. Point of View, or Point of Sight. Is the fixed place of the eye of the 
 
 Obferver, viewing the object or obje£l:s to be delineated. 
 
 5. Plane of Delineation, or Picture. Is the plane of canvafs, or paper, 
 
 upon which the delineation is made, or intended to be drawn. 
 
 6. Original Object, or Objects. Is any objeft or objefts, to be drawn ; as 
 
 a houfe, a fhip, a man, or all, or many of them, together. 
 y. Original Lines. Are any lines that are tlie boundaries of Original 
 Obje^s, or of planes in thofe objeiSs. 
 
 8. Horizontal Planes. Are any planes placed truly level ; that Is, to which 
 
 the gravity of the plumb-line is truly perpendicular. 
 
 The floors, cielings, &c. of every houfe are endeavoured to bs made horizontal, and are alvvays 
 fo confidered in perfpeftive delineations of regular Buildings. 
 
 9. Horizontal Line. In perfpedlive, Is a line on ihcplane of delineation, level 
 
 with the eye of the obferver or point of view ; and is fuppofed ob- 
 tained by an horizontal plane paffing through the eye of the 
 obferver, produced till it cuts the plane of delineation. 
 
 10. Vertical Planes, Are planes perpendicular to ilf(5r/zo«/<7/ P/^wj. 
 
 The upright walls of a houfe, its doors, windows, &c. are always coniidered to be truly vertical, being 
 ever endeavcu:«d to be made fo. 
 
 Let It be required to find the perfpective reprefentation of a cube, fuppofed 
 placed perpendicularly over the fquare A B C D, Fig. 1. Plate 6, as it woivld 
 appear on a plane of glafs flanding vertically on the line G L, to the eye of 
 an obferver, elevated one inch and a half over the flation point, S. 
 
12 ^^INTRODUCTION. 
 
 Draw S G parallel to A B, and S L parallel to A D ; alfo draw the vifual 
 rays S A, S B, S C and S D ; produce the Hue B A till it touches the line G L 
 in the point I, and draw S O perpendicular to G L. Then, on a plane of paper 
 or canvafs as GHKL, Fig. 2, draw a line VZ, parallel to GL, and make it 
 one inch and a half above GL ; VZ will be the horizontal line. Mark a point at 
 V, and another at Z, as far diftant from each other, as are the points G and L in 
 the plan, Fig. r. Take the diftances G a, G I?, G c and G ^, where the vifual 
 rays interfedl the line G L (Fig.i.) feverally in your compnfles, and mark them 
 off on the line V Z (Fig. 2.) at i, 2, 3, and 4, and draw fine perpendicular lines 
 through the points. Take the diftance GI (Fig. i.), and mark it off at V I 
 (Fig. 2.) and draw a vertical line through the point I ; upon which line mark the 
 height of the cube, equal to the length of one of its fides, in the plan, as O P. 
 Then are all the neceflary fteps taken for obtaining the reprefentation required; 
 which is done by drawing the lines O V and P V (Fig. 3.) a Z and e Z ; J"V 
 and c Z, cutting each other in the point J, and completing the figure ah cdfg. 
 Which figure will be the reprefentative figure of a cube, as it would appear to 
 an obferver regarding it fituated on the fquare A B C D, (Fig. i.) whofe eye 
 was one inch and a half above the point S. 
 
 If the drawing upon the plane GHKL (Fig. 3.) was placed perpendicu- 
 latly over the line G L, as is done (Fig. 4.) by turning the moveable plane 
 GHKL upright on the line G L, the relation it then has to the ground plan 
 will be more clearly difcernable, and the united operations and coincidence of 
 both, more readily feen ; and where it may be noticed that were the figure 
 abcdfg cut out, a folid cube (landing on the fquare A B C D, would 
 appear exa£lly to fit the aperture, to the eye of a perfon elevated, one inch 
 and a half over the point S, with his eye oppofite the point O in the horizon. 
 
 DEFINITIONS. 
 
 1 1 . Ground Plane. Is the plane upon which the Obje£ls to be drawn are placed ; 
 
 as alio whereon ftands the Obferver and Plane of Delineation. 
 
 N. B. The Ground Plane, in perfpedlive enquiries, is confidered an infinitely extended level, or horizontal, plane. 
 
 12. Ground Line, Is the line in which the Plane of Delineation refts on the 
 
 Ground Plane. 
 
 13. Station Point. Is a point on the Gror<!«^P/<7W perpendicularly under the 
 
 Point of Sight, or Point of Fieiv. 
 In the procefs of perfpeftive delineations, the horizon, or horizontal 
 line., is a confideration of the greateft importance, inafmuch, as it regulates 
 
I'l.ATK VI . 
 
 ,1 M-./.lmrs.Vali.m .lonl&,K 
 
-4 
 
INTRODUCTION 
 
 13 
 
 and governs every part of the work, whether it be the reprefentation of 
 buildings, or human figures, or both, or with numerous other objecfls com- 
 bined. Accordingly as the horizontal line is placed higher or lower, does the 
 drawing of the whole pidlure vary, the entire of the work being governed by it. 
 
 Between the Horizontal line 2iX\6.ih& Ground line, or bottom edge of the Pidlurc, 
 is comprehended the reprefentation of infinity of level ground ; that is, were 
 the Ground plane to be infinitely ftretched out, beyond the plane of delineation, 
 
 it would all appear under the horizontal line. 
 
 tH 
 
 iy 
 
 — c 
 
 "-B ' A G S 
 
 Let the line A S reprefent a fedlion of the ground plane ; and let G H repre- 
 fent a fedtion of the plane of delineation ; let E be the place of the eye of an ob- 
 ferver ; S will, of confequence, be the ftation point. Draw the line E O parallel 
 to A S, cutting the line of the pidlure G H, in the point O, the place of the 
 Horizontal line ; then ivillthefpacebet'weeji G andO, on the piSfure, or plafie of de- 
 lineation, he the reprefentation of the level ground plane, continued infnitely towards 
 B, beyond the plane of the piClure. 
 
 The fpace of ground from G to A, is a certain diftance ; by drawing the vifual 
 ray A E, the plane of delineation is cut in the point a, giving the fpace a G for its 
 reprefentation on the pifture. Suppofe the reprefentation of a greater length 
 were required, as G B ; the vifual ray B E being drawn, determines and gives h G 
 for its reprefentation on the pidlure ; and fo on of any length that might be re- 
 quired, it would always be obtained -by drawing a vifual ray from the diftance 
 defircd, to the eye, cutting the picture ; but no point on the ground line could be 
 ib far diflant, that a vifual ray from it could fall in with the line O E, becaufe the 
 line O E is parallel to the ground line. Did the line of vifual ray, as E c, differ 
 but ever fo little from the line O E, it would if produced, fomewhere cut the 
 ground line S B, lengthened out ; but no point, however far diftant, could be af- 
 fumed in the ground plane, that a vifual ray from it could fall in with the line 
 O E; becaule two parallel lines, though produced infinitely, could never meet; 
 
 d 
 
14 
 
 INTRODUCTION. 
 
 Si-g-. 
 
 ^ 
 
 Horizon 
 
 ^ 
 
 wherefore the fpace between G and O, as was advanced, comprehends the repre- 
 fentation of infinity of level fpace under the horizon. 
 
 When any level plane is below the horizon, 
 
 then the top of it is feen ; the more it is ^ 
 
 depreffed below the horizon, the more is its ^^ ^ ^^^^^ /^ 
 
 true figure difcernable ; as alfo will be the 
 
 cafe the more it is elevated above the horizon ; 
 
 and when a level plane is in the plane of the 
 
 horizon, then is its appearance but a right line ; 
 
 as is exprefled in Figures i and 2. 
 
 From what has been before obferved of two 
 equal heights, one placed nearer the eye of ^3~'-'~~2^ \~ 
 
 the obferver than the other, that the nearer 
 
 height appears higher than the farther; it will of confequence follow, that if a 
 fquare plane or parallelogram, as the front of ahoufe, be placed before an obferver, 
 one end nearer the eye than the other, that in confequence of the nearer vertical 
 angle appearing higher than the farther, the horizontal lines of the top and bottom 
 will appear to decline towards one another, on the fide of the farther angle 3 and 
 muft of courfe, if continued in the reprefentation, meet in a point, Thefe points 
 of union or meeting of inclined lines, have been denominated by the beft writers 
 on perfpective, the vanifliing points of thofe apparently inclined lines. 
 
 DEFINITIONS. 
 
 14. Vanishing Point, Is a point on the plane of elineation, which is the 
 point of union or point of convergency that two or more lines will have, which 
 are the reprefentations of two or more parallel lines iii aa original objeil, placed 
 inclined to the plane of delineation. 
 
 This definition and the following (the 15th) and all the obfervacions relating to them, (hould be carefully and 
 thoroughly conhdered ; as the juilly underftanding of them is matter of the utmoft importance : 'tis therefore, 
 that the StuJentis requelled to be particularly earneftin the confideration of them, and if not fully comprehended 
 enafirftperufal, to- rend them over again and again, and ponder on them, till they are thoroughly conceived. 
 
 15. Vanishing Line, Is a line on the picflure, or plane of delineation, fup- 
 
 pofed obtained by a plane paffing through the eye, parallel to any 
 
 plane in an original objeft, and produced until it cuts the pifture. 
 
 Confequently the Horizontal line is the Vanijhtng line of all horizontal planes ;. 
 
 and all horizontal lines, or lines laying in horizontal planes, will have their. 
 
 vaniJJjing points in the horizontal line.. 
 
rr..irE.7 
 
 jI 
 
 A 
 
 A'»^^, ./i/Ciw^^./^-X""*' ■ '^•'^^" /'" ' f-tf'o . 
 
INTRODUCTION. rj' 
 
 And the 'oanijljing points of all lines whatever, will be fomewhere in the lines 
 that are the vanijhing lines of the planes thofe lines are in. 
 
 And farther, all parallel lines in an original objedl or objedls, that are fituated 
 parallel to the plane of delineation, can have no vanifliing point, but muft all„ 
 ab are the originals, be drawn geometrically parallel, on the plane of delineation. 
 
 '■To find the vaniJJnng point of a line, inclined to the plane of delineation ; draw 
 a line from the eye of the obferver, parallel to the line of which the vanifliing point is- 
 requlred, till it cuts the pidlure orplaneofdelineat on; the point wherein it touches 
 thepidture is the vanifliing point of that original nnc, and of all lines parallel to it. 
 
 Let the line GH (Fig. i. Plate Vil.) be the diredlion of a front of a building 
 on the ground plane, ftanding inclined to an obferver at the ftation S ; and let the 
 line XV be the diredllon of the plane of delineation ; draw S V parallel to G H ;, 
 alfo draw the vifual rays S G, S H. It muft be clearly evident that the angle of 
 the front of the houfe, ftanding perpendicularly over the point G, will appear 
 higher than the equal height at the farther angle, over the point H ; of con- 
 fequence, the top and bottom horizontal lines of the building will appear inclined,, 
 and to have a tendency towards each other on that fide where the upright angle 
 appears the lefler, and therefore muft be fo reprefented on the plane of deli- 
 neation. The point wherein they would meet, if produced, would be a point 
 in the horizontal line perpendicularly over the point V in the ground line, at the- 
 height of the eye of the obferver, as is exprelled by the point Z,. in the Diagram 
 below, (Fig. 2.) and which point is obtained by being the interfedlion of a line 
 drawn from the eye parallel to G H, (Fig. i .) produced till it touches the plane of 
 delineation XV, in the horizon at V. Which point would be the point of their tendeficy^ 
 and comprehends infnity of fpace hetiveen it, in the horizon, and the point I, the- 
 intcrfecling point of the line GW produced till it cuts the ground line. The angle 
 G will appear to interfe(5l the plane of delineation in the point g ; and the angle 
 H will appear to do the fame in the point h ; and the apparent height of each, 
 according to any fixed height of the building, is determined as in the diagram. 
 below. Where, the height being fet up on the interfeding line of the building, 
 AB, and lines being drawn from thofe points to the vanifliing point Z, de- 
 termines the heights ab and cd, as the apparent and comparative heights of' 
 the two extreme angles of the building ; and the whole plane, were it con- 
 tinued on infinitely, would concentre and vanl(h in a point ; as at Z, 
 
i6 I N T H O D U C T I O N. 
 
 For however extended might be the line G H towards K, a vilual ray could 
 not be drawn from any point of the extended line G K that could poffibly fall in 
 with the line S V, becaufe the line S V is parallel to G K. Wherefore the fpace 
 from I to V, is the reprefentative fpace on the plane of delineation, for the infinite 
 extention of the plane over the line G K. How trifling foever might be the 
 variation of the vifual ray, as S a, from the line S V, were S a produced, it 
 would fomewherc meet the extended line G K, which could not be the cafe 
 with the producing of the line S V, becaufe it is parallel to G K; and parallel 
 lines, though produced infinitely, will never meet. 
 
 A full illuftration of all the foregoing obfervations and conclufions will be 
 found on furvey of the figures, Plate 8, where may be obferved (Fig. i) that the 
 lines A B, CD, E F, and L K, being the reprefentations of parallel lines, the 
 originals of which were in planes inclined to the plane of delineation, have 
 the fame vanifliing point, Vj and being the reprefentations alfo of horizontal lines, 
 have their -oanip'ing point in the horizontal line. The lines F K, 'D G and B H, 
 being alio the reprefentations of parallel lines, have likewife a common point of 
 tendency, or vanifliing point, S ; and, as before, being all horizontal lines, have 
 tlieir vanifliing point in the horizontal line, which is the vanifliing line of all ho- 
 rizontal planes, confequently all lines laying in horizontal planes have their va- 
 nifliing points in the horizontal line. Upon the fame reafoning the lines C E, 
 D F and I K, being alfo the reprefentations of parallel lines, have, in confequence, 
 a common vanifliing point, as Rj and the parallel lines FI and KG, have a 
 like mutual tendency in the point T. But it may be remarked that the horizontal 
 lines F K, D G and B H, and the inclined lines D F, I K and F I and K G are 
 lines all in the i^ime inclined plane B D F I K G H; wherefore, agreeably to the 
 principles before ftated, that the vanifliing points of all lines laying in the fame 
 plane, will be fomewhere in the vanifliing line of that plane ; thofe three diffe- 
 rent inclinations of lines will have their vanifliing points in the fame right line : 
 fuch may be obferved is heie the cafe. The line RST is the vanifliing line of the 
 plane B D F I KGfl; being the line that would be obtained by a plane through 
 the eye parallel to the original plane, of which that is the reprefentation, and pro- 
 ducing it until it would cut the pidure, and the three vanifliing points of the three 
 different diredlions of the lines in that plane, are all in that line, as R, S and T. 
 
 The line R S T is not the vanifliing line of the plane B D F I K G H only, 
 it is the vanifliing line alfo of all planes parallel to that plane ; and is there- 
 
FZ.4TE 8 
 
 .j&rri^n-.^^^£^£^^^^ €y ^f fti/'^ ,. f^s^l^n-^r/i . f^oo 
 
INTRODUCTION. i; 
 
 fbre the vatiifhing line of the parallel end of the fame houfe, and all lines lay- 
 ing in that plane will have their vanifliing points fomewhere in that linej fuch 
 is the cafe with the line C E, which has its vanifliing point at R ; for the lines 
 CE and DF, are parallel lines, and tiiough the boundaries of different planes, 
 they are alfo in the fame plane, DCEF ; and will therefore have a common 
 vanifliing point ; which they have, at R. 
 
 Fig. 2. is another reprefentation of the above objedt, hut with this difference of 
 pofition, that one plane of the houfe is confidered as having been placed paral- 
 lel to the plane of delineation ; wherefore the lines A B, C D, E F and L K be- 
 ing all parallel to the plane of delineation, will have no point of declination, or 
 common tendency, but will all be drawn geometrically parallel to each other. 
 But the lines LE, NC and O A being perpendicular to the plane of the piclure, 
 becaufe at right-angles with the others, will have their point of tendency diretftly 
 oppofite the point of view, or point of fight ; becaufe, on the principle of finding 
 the vanifliing point of lines, by a line being drawn from the eye, to the pidure, 
 parallel to them, it will of courfe be there, as at Y ; and a vertical line through 
 Y, will be the vanifliing line of the plane O N L M E C A. The flant lines of 
 the roof F D, EC, and L M, being parallel, though in different planes, will 
 have a point of common tendency in the fame vanifliing line, as X; as will alfo 
 the parallel lines L N and E M, at Z. 
 
 Thus I have brought the inveffigation of my fubjedl to an end j and fliall here 
 conclude what I may term a whole, but brief theory, of perfpe£tive delineation 
 on planes. I do not however imagine it will be thoroughly comprehended, on 
 a firfl: perufal, by thofe who were before totally unacquainted with the fubjedl; 
 nor do I confider it will on a fecond, without fome pradlice ; but which, I 
 make no doubt, before having gone through the following work of pradice, will 
 be clearly and fully underftood. 
 
PRACTICAL GEOMETRY. 
 
 P 
 
 REVIOUS to entering on the Pratfllce of Perfpedive Delineation, it is 
 requifite that the fludent be acquainted with a fufficiency of pradlical geometry, 
 to be enabled to execute, without delay, what may be required in the procefs of 
 perfpe£i:ive drawing. In this feclion have been colleded fuch problems on that 
 fubjetft as are abfolutely neceflary j they are of general ufe, and the mofl: 
 facile conftruction of them has been carefully endeavoured. Should prac- 
 tical geometry be already familiar to the reader, this divifion may he pafled, 
 only performing the laft requifition, as it contains the principal preliminary 
 fleps relative to the operative lines for finding the perfpective forms of objects 
 from determined ftations. 
 
 To know fomething of angles, their kinds, how to eftimate their magni- 
 tude, and compare them to ench other, is not only requifite in moft mathemati- 
 cal refeachcs, but of advantage even in the common purpofes of life. 
 
 By an Angle, in geometry, is meant the inclination, or the mutual ten- 
 dency, which two lines have to each other that touch at one extreme, and' 
 then feparate, leaving a fpace between them.. 
 
 Q^;^/ 
 
 B 
 
 E 
 
 Mathematicians refer to a line, or to many lines, by letters, or other fymbols, 
 being placed at their extremes; and identify them, by calling them the lines of fuch 
 fymbols or letters ; as of the three lines, Fig. i, which may be denoted the lines AB, 
 CD, and EF. By this fimple means diftinfl; reference is made to different lints- 
 where many are confufcdly mixed together ; and iiifercnces and confequences are 
 drawn relative to them, with the utmoft perfpicuity and exactitude ; as of the 
 three lines AB, CD, and EF ; aflerting, that if the line AB is longer than CD, 
 CD is alfo {hotter than EF, EF being longer than AB. Or, it may be faid, that 
 the line AB is parallel to EF, and that CD is inclined to them both. An angle 
 is referred to by three letters, or other fymbols ; one being placed at the vertex, 
 or junction of the two lines forming of it; as H, Fig. 2, and one at each other 
 extreme of the lines, as G and K ; to nominate which angle, and convey a fenfe 
 of the fame to others, it is read the angle GHK, or KHG, always naming the letter at the vertex 
 of the angle, between thofe which refer to the other extremes of the lines. 
 
/^1-r/-: .0 
 
 B 
 
 ^- 
 
 ^Zi 
 
 'f^- 
 
 _^&«!//fv/ .'^f/'//.»/f^f/ /'t/ yhj*ir\j . f/ff//f/e /fifi. f.Fr/>. 
 
PRACTICAL GEOMETRY. 1-9 
 
 Angles, formed by right lines, are of three kinds only^ viz. Right Angles, [Plate o,"! 
 Obtufe Angles, and Acute Angles. When one of the Knes forming of an 
 angle is perpendicular to the other, tlien is fuch an angle faid to be a right 
 angle; fuch is the angle ABC, Fig. i, Plate 9, the line AB being per- 
 pendicular to the line B C. When the lines have a greater degree of ex- 
 panfion than a right angle, fuch an angle is faid to be an obtufe angle, as the 
 angle D E F, Fig. 2 ; and when- they have a lefs degree of expanfion than a 
 right angle, fuch an angle is faid to be acute, as the angle G H IvFig, 3. 
 
 The magnitude of an angle is computed by the portion it comprehends 
 of a circle, ufing the angular point as the centre to revolve the circle upon. 
 For the general admeafurement of angles, the circumference of a circle is di- 
 vided into 360 equal pa^rts, called degrees ; a divifion univerfally^afTented to ; 
 and an angle is faid to contain, or to be an. angle of as many degrees as fall 
 within the expanfion of the two lines. 
 
 If two lines, one perpendicular to the other, crofs each other, there are formed. 
 four angles, all right angles. By the croffing of the perpendicular lines AC 
 and B D, (Fig- 4j there are formed four right angles, and ufing the point of 
 their common interfeclion, E, as the point to revolve a circle around upon, each 
 angle will of courfe contain a quarter of that circumference ; and the whole 
 circumferejKe being divided into 3 60 equal parts, each rjght angle, (all right 
 angles being equal,) muft contain a quarter of 360, that is 90 degrees. A right 
 angle is a determinate one, and there can be no variety of them ; but of 
 obtufe and acute angles there may be many, of various magnitudes. 
 
 The circle ABCD, Fig. 4, is divided into 360 equal parts. The angle AEF, is 
 an acute angle of 20 degrees ; the angle AEG an acute angle of 50 degrees ; and 
 fo on to any number fhort of 90. The angle AEO is an obtufe angle of i3o. 
 degrees, and the angle AEL an obtufe angle of 170 degrees, and fo on to any 
 number Ihort of l80> at which period the expanfion of the two lines would fall 
 into one right line, as AEC. For the greater accuracy, in the eftimating of 
 angles, each degree is fubdivided into 60 equal parts, called minutes ; and each, 
 minute into 60 equal parts, called feconds ; fo the meafurement of an angla 
 may be a certain number of degrees, minutes, feconds, thirds, 6cc. 
 
 An angle is not enlarged by lengthening of the lines forming of it ; for the 
 angle ABC (Fig. 5.) is flill the fame and not at all increafed by extending 
 qf the lines to D and E. An angle is eftimated only by the degrees of iiicli- 
 
20 PRACTICAL GEOMETRY. 
 
 rPlate 1 J^^'^''^^ which one line forming it has to the other ; and that incUnation is not 
 increafed by lengthening of the lines ; for the line DB has no greater, but the 
 fame inclination to AB that any portion of the line has ; and the angle DBE 
 and ABC are one and the fame angle, and would flill be fo were the lines 
 lengthened out infinitely. 
 
 This may be more clearly perceived in Fig. 4, where the angle aEf is the 
 fame with AEF ; and aEg with AEG, &c. For, each contains fimilar portions 
 of the curve of their refpedlive circles ; confequently an equal number of 
 degrees. By attentively examining the figure, it will be fully comprehended 
 that the magnitude of angles is afteited only by the degree of inclination which 
 the lines have to each other, however (hort they are, or however long. 
 
 It is not my intention to give a complete fyftem of Pradtical Geometry ; 
 that would form an extenfive work of itfelf. I purpofe to give only that 
 fufficiency of it as will enable the Student in Perfpedlive to draw his figures on 
 true principles, and corredtly. 
 
 A Point may be defined to be the extremity of a line ; a line, curved, or 
 ftraight, the extremity of a furface ; and a surface, plane, or irregular, the 
 boundary of a folid. 
 
 A Right Line, is the fhorteft line that can be drawn between two ex- 
 treme points. A Curved Line, is a line that lays indireft between its ex- 
 trea.e points. Lines are faid to be parallel when the perpendicular dif- 
 tance between them is in every part equal. Curved lines are parallel when 
 they are oppofite portions of concentric curves; and Concentric Circles 
 are fuch as are llruck upon a common center j as are the circles ABCD, 
 EFGH, IKLM, Fig. 6. being ftruck upon the common center O. In which 
 circles, the portions BC, FG, and KL, are parallel. 
 
 An Arc is any portion of a circle, as the arc PQRST, Fig. 7. 
 
 A Chord of an arc, is a right line drawn from one extent of an arc to the 
 other, as the line PT of the arc PQRST, Fig, 7. 
 
 An Ordinate, or Ordinates, is a line, or any number of lines, dropped 
 from an arc, or curved line, perpendicularly to the chord of that arc, or 
 curved line, as the lines Qa, Rb, Sc, Fig. 7. which are dropped from the 
 curve PQRST perpendicularly to the chord PT. 
 
 An Angle has already been defined; page 18. 
 
PRACTICAL GEOMETRY. 21 
 
 Problem I. To make an angle equal to a given angle, from a given point, [Plate 10.] 
 in a given line. 
 
 ABC, [Prob.i. Plate 10.] is the given angle, anJE the given point in the line EF\ 
 With one leg of the compaffes fixed on the vertex B, of the given angle, 
 with the other defcnbe the arc AC; with the lame extent of compafTes, and 
 with one leg fixed in the given point E, defcribe the arc, FD, indefinite ; then 
 extend the compafles from A to C, and apply that meafure from F to D, . 
 making the arc F D equal the arc AC; draw the line E D, then Will the 
 angle DEF, be equal to the angle ABC. 
 
 Nste. For greater accuracy in meafuring, or making equal angles, let the expanfion of the com- 
 pafles be as great as the angle to be meafiired, or the compafles will well allow. 
 
 Prob. II. To draw a line from a given point, parallel to a given line. 
 GH is the given line, and I is the given point. 
 From the given point I, draw a line as 1 H at pleafure, touching the given line, 
 in a point at H ; make the a gle H I K, equal the angle GH 1, by Problem I, 
 and the line IK will be paruUei to t e line GH. 
 
 Prob. IT. To bifed, or to divide, a given line into two equal parts. 
 LM is the given line. 
 With an extent of compafies greater than half the given line, on each of its 
 extremes L, and \1, defcribe two arcs croffing each other in the points a and b ; 
 draw the line a b which will bii.£t, or divide the line LM into two equal parts. 
 
 Prob. IV. To Dife£l, or divide, any given angle into two equal div.fions. 
 
 NO? is the given angle to be divided. 
 On the vertex O of tue given angle, defcribe an arc, as NP ; with tlie fame 
 or any extent of compa-Tes greater than half that arc, on the points N, a. 1.1 P^ 
 defcribe two arcs interfecling each other at c ; then draw the line O c, which 
 will bifedt the angle NOP. 
 
 Definition . A right line is Jaid to be perpendicular to another right line ichen it 
 does not incline to cither /ide, but makes a right angle on both Jides of 
 the line. And this, be the two hues pqjited as they 'u:i!l, iziiihout 
 regard to --ivhat is really horizontal or vertical, 
 
 » Throughouc thefe Problems, the given requifites, liich as lines, angles, &c. ere drawn with. 
 ftout lines ; the opeiau/e !ine«, or lines of the procefs, are all dotted j a:iJ the required iiaes, or the 
 lines obtai.ied, are expiefied by fine lines. 
 
 F 
 
it PRACTICAL GEOMETRY. 
 
 [Plate 10.] Prob. V. To draw a right line perpendicular to a given right line, from 
 
 a given point in that line. 
 RS is the given line, and T is the given point. 
 On each fide of the given point T, fet off equal meafures, as T R, and T S ; 
 then, with any greater meafure in the compalles, on the points R, and S, de- 
 fcribe two arcs interfecting each other in the point d ; draw the line d T, 
 which w^ll be perpendicular to the line RS. 
 
 Prob. VI. At the extreme point of a given right line, to draw another 
 right line perpendicular to the given line. 
 VX is the given lifie, and X the given point. 
 
 Afliime any point, as the point e, at pleafure, but let it be fomewhere about 
 midway between the line given and the line required, and fixing one leg of 
 the compaffes in that point, extend the other to the point X, from whence the 
 perpendicular is required, and draw the curve VXZ Indefinite ; then applying a 
 ruler to the points e, and V, where the curve touches the line V X, draw 
 the right line VeZ, touching the other extreme of the curve in the point Z, 
 and draw the line XZ which will be perpendicular to the line VX. 
 
 The foregoing propojition is a very I'feful ojie, and ivo'rthy of particular cotzjide- 
 r at ion. If from each extreme of the diameter of a circle, lines be drawn meetijig 
 in the circumference, the angle that ivould be formed, would be a right angle ; 
 and of confequence the lines one perpendicular to the other. Thus in thefemicircle 
 ylBCDE, Fig. 7, if two lines AB and BE, be drawn, meeting in the point B, the 
 angle made, the angle ABE, will be a right angle : alfo the angle A C E is a right 
 angle, fo is the angle ADE ; and fo would a?7y angle be which extended the 
 diameter, and ivhfe vertex touched the circumference. 
 
 In Problem VI. before performed, the curve VXZ is a femicircle, of which 
 
 VZ is the diameter -, and the angle VXZ is an angle extending the diameter, and 
 
 •whofe vertex touches the circumference, co?ifequently the angle VXZ is a right angle. 
 
 Prob. VII. To draw a line perpendicular to a right line, from a given 
 
 point out of that line. 
 
 FG is the given line, and H is the given point. 
 On H, the given point, with any opening of the compalles greater than the 
 dillance of the line, draw an arc, as FG, cutting the given Hue in the two points 
 
PRACTICAL GEOMETRY. 23 
 
 F and G. Then with the fame, or any opening of the compaffes greater than [Plate 10. 
 half the fpace between the two points F and G, defcribe two arcs oa the other 
 fide of the line, interfering at f, and draw fH, which will be perpendicular to FG. 
 Prob. VIII. To divide a line proportionally, as another is divided. 
 
 I K is the line required to be divided in tbefatne parts, proportionally^ as is the 
 line LM in the poijits g and h. 
 
 Place the two lines parallel to each other, and at any diflance at difcretion, as 
 IK; draw the lines L/and MK, touching the extremes of the given lines, and pro- 
 duce them till they meet in the point N ; then draw the lines hN and gN, cutting 
 the line I K in the points i and k, the points required. The divifions made on the 
 line IK will be proportionally to each other, and to the whole line, as are the 
 divifions in the line LM, to one another, and to the whole line. 
 
 Def. a Square /j<7 ^adrilateral whofe oppofite fides are equal and parallel, and 
 its four internal angles all right ones. 
 
 Prob. IX. To conftrudl a Square on a given line. OP is the given litie. 
 On either "extreme of the given line, O or P, fuppofe O, draw a perpendicular 
 line, as O R, (Prob. VI) make the line OR equal to the line O P, and with the 
 fame meafure in the compaffes, on the points P and R, draw two arcs inter- 
 fering each other at S -, then draw the lines S R and S P, which will complete the 
 Square O R S P. 
 
 De f. a Regular Hexagon, is afx equal fided right lined figure, having 
 fix internal angles, which fhould alfo all be equal. 
 
 Prob. X. To conftruft a regular hexagon on a given line, for a fide. 
 T V is the given line, for a fide of the hexagon. 
 On the two extremes of the given line T and V, with the length of the line 
 TV in the compaffes, defcribe two arcs, as TmW, and VmZ, interfering each 
 other at m ; on which point m, with the fame meafure in the compafles, defcribe 
 the circle T Z X Y W V, and flill with the fame meafure, on the points 
 Z and W, mark the circle in the two other points X and Y, and draw the lines 
 TZ, ZX, XY, YW and WV, which will complete the hexagon T Z X Y W V. 
 
 Note, a fide of a regutar hexagon, is the chord of the fixth part of the circumference of a circle cir- 
 cumfcribing of it. 
 
 Def. a Regular Octagon, is an eight equal fided, right lined figure, 
 having eight internal angles, ii'hich fiould alfo all be equal. 
 
24 PRACTICAL GEOMETRY, 
 
 [Plate lo.] Proe. XI. To conftrud a regular odlagon, on a given line, the dimenfion 
 
 of one of its fides. 
 
 AB is the given line for the fide of an oEiagon. 
 
 Produce, or lengthen, the line AB, both ways, towards I and K, and on the 
 points A and B, draw the perpendiculars AE and BF indefinite (Prob. V.) Bi- 
 fe£l the right angles EAI and FBK (Prob. IV.) by the lines AC and BH, which 
 lines make each equal to the given fide of the odlagon AB. Draw CD and HG pa- 
 rallel to AE and BF, and make themalfo each equal to AB ; lafiily, make the lines 
 AE and BF, each equal to CH, and draw the lines DE and FG, which will 
 complete the octagon ACDEFGHB. 
 
 As an oftagon is a figure of very frequent occurrence in buildings, often forming the ground plan 
 of apartments, and, as commonly as the circle, fliaping the bows or projefling ends and fides of rooms ; I 
 have defire therefore, to give as corred and expeditious ways of conftructing it, as poflible, and probably 
 the following maybe found more {o^ than the one juft defcribed, when fuch method can be followed. 
 Note, — It often happens that an oftagon is required to be conftrufted in a given fpace, that is, its dia- 
 meter or breadth is given, and not a fide. When that is the cafe, the bufinefs is foon ac- 
 compliflied, by firft making a fquare of the diameter, and proceeding as follows. 
 
 Prob. XII. To conftruct an octagon on a given line, its diameter or breadth. 
 
 jLO is the given line for the diameter of an oSlagon. 
 On the given line LO firfl conflruct a fquare (Prob. IX.) as LMNO, and draw 
 the diagonals LN and MO, Interfecting each other in the point k ; then on the 
 four angles of the fquare, with themeafure of one half of a diagonal in the com- 
 pafl'es, defcribe the four arcs ckh, b k e, d k g, and fka, cutting the fides of 
 the fquare in the points abcdefg and h; laftiy, draw the lines ab, cd, ef, and 
 gh, which will form and be fides of the odtagon required, abcde f gh. 
 
 Jffrcm afiy point within a triangle, tifo right lines are drawn to the extremes of 
 any fide of that triangle, thofe lines form a larger angle than the remaining twofdes 
 of the triangle. 
 
 In the triangle ABC, (Fig.iS) let a point, as D, be alTumed, and draw the lines 
 DBandDC; then will the angle BDC, be greater than the' angle BAC. By drawing 
 the lines AE and AF, refpcftively parallel to the lines DB, and DC, the circum- 
 ftance will be manifeft, for the angle E A F is equal the angle BDC, the lines 
 being parallel ; but the angle AEF is greater than the angle BAC, which expands 
 but the portion from a to b of a circle meafuring of it, while the other extends 
 from c to d ; wherefore the angle BDC, equal the angle E A F, is greater 
 than the angle BAC; agreeably to the premifes ftated. 
 
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PRACTICAL GEOMETRY. 25 
 
 Thefe are all the geometrical problems I think neceflaryto the profecuting of [Plate 10.] 
 pradtlcal perfpealve delineations ; (hould the fludent wifti for farther, or more 
 ■complete information, on this fubje^:, I mufl refer him to the Work pvib- 
 iiflied by my Father, entitled, " a royal road to geometry ;" where 
 will be found a complete body of Geometry, both elementary and pradical, 
 fully and clearly inveftigated ; and alfo a comprehenfive and brief theory of 
 menfuration of luperficies and folids, with fome of the mofl commonly uleful 
 properties of the ellipfis or oval, pleafingly illaftrated. 
 
 Proposition 14. Draw the following perfpeftive fcheme. 
 
 As a confirmation of acquaintance with pradical Geometry, and of the ufe 
 of the compares, it is required to draw the following fcheme, which muft 
 be done with facility, as it is the previous ftep to drawing any regular perfpec- 
 tive delineation, according to the praftice of the following work. 
 
 On a given line, as A B, conftruft a fquare, as A B C D, (Prob. 9) draw a 
 line GL, at pleafure, touching the angle A of the fquare. Through a pointy 
 as S, aflumed on this fide the line G L, draw a line, as X Z, parallel to the line 
 G L. (Prob. 2). From the point S, draw a line as S O, perpendicular to the 
 line GL. (Prob. 7). Alfo from the point S, draw the lines S G, and SL, feve- 
 rally parallel to the fides of the fquare, A B, and A D, by making the angles 
 GSX and LSZ refpedively equal tothe angles BAG and DAL. (Prob. i.) 
 And laftly, draw the Une SE bifedling the angle G SL. (Prob. 4). Which line 
 will be parallel to the diagonal of the fquare, AC. 
 
 Li the courfe of drawing perfpedive delineations of houfes, &c. continual 
 mention and reference muft be made to plans and their component parts, with 
 which the ftudent will be confidered to be well acquainted ; but left that 
 fhould not be the cafe, it is necefiary he be inftrufted as to what is meant 
 and exprefled in a plan of a building, and informed how the fame is read by 
 architefls and others, acquainted with their indications. 
 
 A plan of a houfe is commonly explained or defined, as being the figure, 
 marked out on the ground of the external boundaries, and internal divifions of 
 the apartments of a building, either in actual exiftence, or intended to be built. 
 In one refped fuch is a juft definition, but in general, much more is exprefled 
 in plans than merely the fituation, fize, and figure, of the apartments j both 
 to fLew the proprietor what he is to exped, and that the builder may fully 
 
 G 
 
a6 PRACTICAL GEOMETRY. 
 
 '^' comprehend what he is about to ered. A plan, as moft generally drawn,. Is 
 
 properly an horizontal fedlion of a building at a ftated height ; or it is the fi- 
 gure, which the top of the walls would exhibit, when raifed all to the fame level 
 a few feet above the ground, if looked at from above direftly down upon them ; 
 whereby many incidents in the flru£ture are exprefled, that cannot be marked 
 out in the trenches, or even take place, fome four, five, or fix, feet above ground. 
 
 [Plate 1 1. j This will be better underftood by reference to fenfible figures. To 
 thofe who are converfant in Architedlure, the Elevation (Fig. i, Plate ii,) 
 would be nearly pictured in the imagination from the mere infpedion of the 
 plan ; Fig. 2 ; but the plan, Fig. 2, is not the figure that would be cut out in 
 the ground, as fhaping the foundation to the building ;fuch would be fimply as 
 Fig. 3, exprefling little more than the length and breadth of the apartments, 
 and thicknefs of the walls, more information could not be gathered from it. 
 Whereas, from the plan. Fig. 2, is underftood that in front there are two pillars 
 ftanding in a recefs, with a door between them, and a niche in the middle of 
 the pier on each fide ; alfo, that in each end of the apartment, within, there is a 
 window, that there is a chimney in the middle of the crofs- wall, with a door on the 
 right leading into another apartment, and a recefs for a falfe door on the other, 
 fide the chimney, to be uniform with the real door ; that the lines i, 2, 3, 4, 5, 
 &c. exprefs an ai'cendlng flight of ilalrs ; that A is the half-landing, on which 
 -there is a window to light the ftaircafe, and that the dotted lines imply the 
 returning flight to the next ftory : all which is clearly gathered and immedi- 
 ately underftood from infpeftlon of the plan fimply, with other minute par- 
 ticulars ; fuch as the number of fteps that condudl into the dwelling, implied 
 by the lines marked a, b, c, that they fall' within the pillars, that there is 
 intended a plinth around the building exprefled by the double line around, 
 that there Is meant a bafe to the pillars, and fuch like minutia ; anJ to the- 
 whole there is affixed a fcale of feet, proportionally to the plan la^d down, by. 
 means of which the dlmenfions, that is, the lengths and breadths of apartmcnrs,. 
 maybe knowii, and the breadths of doors, windows, fire-places, ftairs, and. 
 treads of ftairs, &c. may be accurateJy meafured.. 
 
 Such delineation is undoubtedly an horizontal feftion of the walls, takea 
 fome fix or feven feet from the ground ; fomewhere about the height of the 
 line BC, Fig. i. Indeed tlieie are particulars exprefled that caruiot bei 
 noticed till the building is raifed confiderably higher, as the window D, on tha 
 
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PRACTICAL GEOMETRY. 27 
 
 half landing, and the completion of the ftair-cafe to the fecond ftory. [Plate ii."| 
 All of which may flill be better conceived from infpedion of the perfpedive 
 delineation, Fig. 4, reprefentiiig the ftru(fture as raifed fome feven feet 
 above the ground level, and of which the plan, Fig. 2, is the geometrical or 
 ichnographical proje£lion. 
 
 I have been thus particular to avoid all delay from the want of fuch 
 neceffary information ; and for the more certain affurance of having no 
 impediment to check advances, I will defcribe how a ftair-cafe is read 
 from its geometrical plan. Fig. 5, is the plan of a ftalr-cafe, fhewing the 
 fpace of ground it occupies, and the number and breadth of the fteps. Fig 6, 
 is the geometrical elevation of that ftaircafe, fliewing its relation to the plan, 
 and the height and diredlion of the flight of fleps to the flory above, to 
 which they condu6l : the heiglit of the fteps is regulated to the height they 
 are intended to mount to, and the breadth, 10 the convenience of the tread and 
 the fpace allowed to contain the whole in. 
 
PRACTICAJL PERSPECTIVE. 
 
 XF the ftudent has attentively perufed the Introdudlion to this work, and fully 
 comprehends it, he will be ably qualified to proceed to the pradlice of what is 
 there inveftigated ; at the fame time he will enjoy the fatisfatlion arifing from 
 knowing perfedlly what he is about to do, and of being convinced of the truth of 
 the rcfult. Should he have neglcded, or from previous knowledge have no 
 occafion for, that examination, he will here, merely have to perform as directed, 
 placing implicit confidence in his inftrudlor that he will not lead him aflray. 
 
 The fbudcnt is particularly requefted, that he reft not fatiifieJ with only following me through my own 
 diagrams and defcriptions; it is requifite that he draw them out himfe f, to a much larger fcale; nor be content 
 with performing each cafe once only, but to pra>ftife them twice, or thrice, varving their pofitions, and atten- 
 tively following the general rules given for their proper delineation ; by which procedure his Knowledge will 
 not only be ftrengthened, but the practice will become eafy and familiar. He (hould alio obferve to proceed 
 ftep by flep, as direfted, nor draw one line but as told; then will all confufion vanifli, mifunderftanding be 
 avoi.led, and the whole be clear and fatisfaiSory. 
 
 Difgufl is but too often conceived at the multiplicity of lines exhibited 
 in works on pcrfpediive delineations, refledlion not being made, that every line of 
 the whole example, and every needful procefs requifite for the completion of 
 that example, are there obligated to remain, that the fame may be fecn and 
 done by the fiudent ; but in his performance much the greater part need only be 
 drawn in pencil, and obliterated when the end required is obtained; and this of 
 every procefs from firfl to laft; thereby avoiding all neceffity of confufion of 
 operative lines, they being removed like as the fcafl^blding is taken from about 
 a building as it is completed. 
 
 As my entrance on this fubjedl is different from any that has hitherto been 
 made public, I deem it fomewhat incumbent on me to give my reafon for deviating 
 from the beaten track j and it is briefly, that I think, before a ftudent is capable 
 of executing the minutiae of this art, he fliould firff comprehend and pradtife it 
 upon a general and broad bafis. I am therefore induced, in the firlf place, 
 to give a number of examples for the delineation of the various fimple forms of 
 buildings, from the proper requifites given or known. In the fecond I fliall 
 exemplify the different parts of buildings, as doors, windows, fiepS; pcdefials. 
 
PRACTICAL PERSPECTIVE. . 29 
 
 bafes, and capitals of columns, cornices, vafes, &c. And in the third, I fhall 
 combine the two former parts together, in the reprefentation of regular, and 
 fome difficult, pieces of Architecture ; and conclude with the leading principles 
 for calling of Ihadows from a given place of the light. I purpofe alfo, in an 
 Addendum, to touch upon the fubjed: of refledlions on water, and plane mirrors, 
 fhowing their pofitive and only true attainment by the rules of perfpe(5tive ; and 
 a critical inquiry into fome circumftances of difpute relative to diftorted repre- 
 fentations of objeds, ariling from injudicious proceeding, but from no error or 
 fallacy in the rules of perfpedive delineation. 
 
 Before the practice is begun, I think it expedient once more to draw the 
 attention to the principal definitions of terms ufed in the procefs of perfpedlive 
 delineations; and that they may be the more certainly underftood, and more 
 deeply imprefTed on the mind, I fliall make reference from them to a fcheme, 
 which will, I am of opinion, with a little refledion, clearly (how their relation 
 and unity, beyond almoft a poflibility of mifunderftanding. 
 
 DEFINITIONS*. 
 
 r rlate 12' I 
 
 1. Original Object, or Objects. Is any objed:, or number of objeds, 
 
 propofed to be delineated; as a houfe, a fhip, a man, or all, or 
 many of them, together. 
 In Figure i, Plate 12, the houfe ABCDFHK, is the original ohje&. 
 
 2. Original Lines. Are any lines that are the boundaries of orio-inal 
 
 objeds, or of planes in thofe objects. 
 The lines A B, EC, CD, &;c. are original lines, being the boundaries of the 
 original ohjeU ABCDFHK. 
 
 3. Ground Plane. Is the plane upon which the objeds to be drawn are 
 
 placed; and is always confidered a boundlefs level plane. 
 The plane X, is \.\\g ground plane, whereon ftands theobjedt ABCDFHK. 
 
 4. Point of View, or Point of Sight. Is the fixed place of the eye of the 
 
 obferver, viewing the objed: or objeds to be delineated. 
 E, The eye of the obferver, is the point of view, or point of Jight. 
 
 5. Station Point. Is a point on the ground plane, perpendicularly under 
 
 the point of fight, or eye of the obferver, and exprefi!es the ftation 
 whence the view is taken. 
 S, is the flat ion point, being a point on the ^roz^wi ^5/^/?^ perpendicularly 
 under the eye of the obferver, at E. 
 
 * Thefe definitions refer alfo to my Appnratus. 
 H 
 
30 PRACTICAL PERSPECTIVE. 
 
 [Plate 12. ]6. Plane of Delineation, or The Picture. Is the canvafs or paper, 
 upon which it is intended to draw any objedt or number of objetfts. 
 The plane G I K L, is the plane of delineation ; but in the cxtenfive fenfe 
 of the word, the plane of delineation is confidered a boundlefs plane, 
 however circumfcribed may be the draft thereon made. 
 y. Horizontal Line, or the Horizon. In perfpedive delineations, 
 is a line on the ■plane of delineation, in every part level with the 
 eye of the ohferver, or point of view. 
 V Z, Figure i, is the horizontal line, on th^ plane of delineation GIKL. 
 The horizontal line is fuppofed obtained by the interfedlion of a plane 
 paffing through the eye of the obferver, parallel to the ground plane, produced 
 till it touches the plane of delineation. . 
 
 The mere infpedtion of the diagram, Figure 2, cannot fail of giving 
 thorough infight as to what is meant by the horizontal line, and how it is 
 fuppofed obtained. FGHI is t\\& plane of -delineation, ABCD the horizon^ 
 tal plane ^dii^Wig through the eye of the obferver touching the plane of deli" 
 ncation in the line B C, which is the horizon, or horizontal line. 
 S. Centre of the Picture. Is the point on the pi<flure, perpendi- 
 cularly oppofite the eye of the obferver or point of view ; and is 
 confequently always fomewhere in the horizontal line. 
 O, in the horizontal line. Figure i, is the Centre of the Figure, being per- 
 pendicularly oppofite the eye, at E. 
 o. Vertical Line. Is a line drawn through the Centre of the Piclure 
 perpendicular to the horizon. 
 PR, Figure i, is the vertical line, being drawn perpendicularly through 
 the Centre of the PiBure, O. 
 
 Kote, the vertical line determines how nwch of the view lies to the right, and how much to the left, of the 
 eye of the obferver. 
 
 ro. Distance of the Picture. Is the dire<ft: line between the eye of 
 the obferver, and the centre of the piclure. 
 E O, Figure i, is the dijlancc of the pi&ure, or plane of delineation GIKL. 
 II. Ground Line. Is the line made by the plane of delineation, touching the 
 ground plane. 
 G L, Figure i , is the ground line of the plane of delineation GIKL. 
 iJ. Intersecting Point. Is a point made on ^^ plane of delineation, by 
 the producing of any line in an original objcB, till it touches 
 ihs plane of delineation. 
 
PRACTICAL PERSPECTIVE. 31 
 
 The point T, Figure i, is the interfering point of the original line B A. [Plate iz.J 
 
 13. Intersecting Line. Is a line made on the plane oj delineation, by the 
 
 producing of any plane in an original objeSl, till it touches the 
 plane of delineation, or where, if produced, it would touch it. 
 The line WT, Figure i, is the interfeEling line of the original plane 
 ABCDNj being the line, where that plane, if produced, would touch 
 the plane of delineation. 
 
 14. Vanishing Point. Is that point, on the plane of delineation, to which 
 
 two or more lines will converge, which are the perfpedlive re- 
 prefentations of two or more parallel lines in an original objed, 
 placed inclined to the plane of delineation. 
 The point V, Figure i, is the vanifiing point of the line A B, being 
 effeded by the line E V being drawn from the eye of the obferver parallel to 
 it, and produced till it touches the plane of delineation, in the point V. 
 For the fame reafon, V is the vanifliing point of the line C N; it is alfo 
 the vanifliing point for any other line that is parallel to the line CN, as BA; 
 all parallel lines having the fame vani/hing point. The point Z, Figure i, 
 is- the vani/hing point of the line A K, being obtained by a line drawn from the 
 eye parallel to the line AK, and produced till it touches the plane of delineation. 
 The point Z is alfo the vanilhing point of the original lines D F, and N H. 
 
 Note, There will be as many different vanifhing points of lines in the delineation of an original obje<a as 
 there are different direftions of lines in that original objeft. 
 
 The point I, Figure i, is the vanifliing point of the parallel original lines 
 DN and FH; being cftcded by the line EI being drawn from the eye parallel 
 to them till it touches the plane of delineation. And for. die f^uiie reafon Q is 
 the vanifliing point of the line C D. 
 
 In the procefs of perfpeclive delineations, the plan of rhe objeft being draw« out, the pkce of the various 
 vanifliinf points of horizontal lints is found on the ground line, whence they are tran ferred to the horizon 
 bv perpendicular lines over tnem ; as may fee feen, Figiu-e 3. Where fuppofe S the ftation of an obferver, and 
 E the point of view ; the lines S A and S B may be the direiSion of lines finding the yanifliing points of any 
 orioinal lines, and being transferred pei-pendicularly to the points C and D in the horizon, anUver the fame as if 
 thev had immediately been obtained from the eye by means of tlie lines E C and E D. The tfFeas of the fame 
 procefs may be obferved in Figure a, where the points F and I are transferred to the horizon perpendicularly, 
 i.T the points B and C ; the fame as if they were effected onllv. horizonlal plane by the lines EB and EC. 
 
 15. Vanishing Line. Is a line on the pitlure, fuppofcd made by a 
 plane pafling through the eye of the ohfcrvcr parallel to any 
 original plane, and produced till it torches the pJclure. 
 The line VZ, Figure i, is the vanijhing line of an horizontal plane, and of 
 
 all horizontal planeaj being effeded, by being the uiterfe<5lion of a plane pafling 
 
32 PRACTICAL PERSPECTIVE. 
 
 (|Plate t2.] horizontally through the eye, or parallel to an horizontal plane. The vertical 
 iinelVG, is tlte vanifiikg line of the original vertical plane ABCD N, being 
 the line where a plane pafiing the eye of the obferver parallel to that plane, 
 would touch the plane of delmeatiofi. 
 
 There will be as niany different 'vanifiifig fines on tlie plane of delineation as 
 there are different pofitions of planes in the objed: or objedts ; and all parallel 
 planes will have the lame vanijJ^ing line. Alfo all lines lying in the fame plane 
 will have their -vanijhing points in the vanifiing line of that plane. 
 
 All planes or lines in an original obje£f, which are fituated parallel to the 
 
 flane of delineation, can have no vanijhing lines or vanijJnng points on 
 
 the plane of delineation. 
 
 1 6. Visual Ray. Is an imaginary right line, implying a ray of 
 
 vifion dired:ed from the eye, to any point, the objedt of its 
 regard or contemplation. 
 E A, or EI, &c. Fig. i, are vifual rays, being right lines from the eye 
 to the points A and I. 
 
 A number of vifual rays diredled to every part of an objeft, muff form 
 a pyramid of rays, of which the eye is the apex, and the objed: the bafe. 
 
 17. A Perspective Delineation. Is fuch a delineation as may be 
 
 fuppofed to be made by a plane making a fetftion of a body or 
 pyramid of rays proceeding from an eye, while contemplating an 
 obiecft, or many objecfts. Such a figure, or fuch figures, obtained 
 by the rules of perfpedlive, is called a perfpeftive delineation. 
 The feftion of a pyramid of rays, producing a perfpeftive projection, is moft 
 commonly confidered as being taken between the objed; and the eye; but the 
 fedion of rays may be taken when they are extended beyond the objed, in 
 which cafe fuch a fedion is called a projeded perfpedive rep re fen tat ion of the 
 objed. The latter cafe gives fuch a figure of the contour of the objed, as 
 would be made by the fhadow of it from a torch being put in the place of the 
 eye of the obferver ; as may be diftindly feen. Figure 4. Where G may be 
 confidered the place of the eye, or torch ; H I the objed ; abed, the inter- 
 vening plane; and K L M N the exterior plane beyond the objed. The fec- 
 tion of the rays h i, on the plane abed, is called the perfpedive or fcenographic 
 projedion; and the fedion m n, on the plane KLMN, the projeded per- 
 fpedive reprefentation, or fliadovv by torch light. 
 
 1 
 
Pi.. til'. Ml . 
 
 y. 
 
 r .".In Ptthluhed irs- Jttiue.''' .V.Utfn ./.j/i ■.' /.t't»t> . 
 
PRACTICAL PERSPECTIVE. 33 
 
 To know perfpedtive, is to know the rules fo to delineate objedls, as to 
 exprefs their apparent leflcning, as they are more and more remote. The appa- 
 rent leffening of objedls, and their change of form, is the filent language of 
 nature indicative of diftance and variety of pofition. Perfpcdive, according to 
 the elegant and corred: definition of Addifon, is, " the fcience by which things 
 are ranged in pidure, according to their appearance in their real fituation." 
 
 The fituation of the objeds being given, with the place and pofition of the 
 plane of delineation, and height and diftance of the eye of the obferver; the 
 delineation of the objedls is truly determinable by rule, and may moft mecha- 
 nically be perforrned, as follows : 
 
 EXAMPLE I. 
 
 Let it be required to find the apparefit form that a cube would exhibit, ij 
 when placed over the fquare ABCD {Fig. i, Plate 13), its bafe, it was viewed 
 by an eye elevated two inches perpendicularly over the ftation S, and Juppofing the 
 ■plane of delineation tofiand vertically over the like GL. 
 
 Firfl, I would advife the Student to place a cube before him in the pofition 
 ftated, and recommend that a fketch of its appearance be made by the eye alone, 
 as corredly as he can, which will for certain be a form agreeable to the figure 
 below. In {ketching, particularly of regular objeds, judgment fliould ever 
 
 [Plate 13.] 
 
 direct the hand ; as here, the eye being elevated fomewhat above the cube, the 
 top of it will, of confcquence, be feen, and, in the pofition fiated, will appear 
 nearly of the form of the delineation G CD E, and whatever may be the height 
 of the near angle of the cube in the drawing, as A G, the more remote angle, 
 C B, being to repreicnt an equal height feen at a greater diftance, lliould be 
 made fomewhat lefs than A B. In which cafe the horizontal lines of the top 
 and bottom, GC and A B, will be inclined to each other, and would, if pro- 
 duced, meet; and being horizontal lines, or the reprefentations of horizontal 
 lines, would meet fomewhere in the horizontal line. Suppofe the line VZ the 
 place of the horizon, V would be the point of their union or tendency, 
 
 I 
 
34 PRACTICAL PERSPECTIVE. 
 
 called their vcviifl^ing point . For the fame rcafon the angular line EI^", fliouM 
 alfo he aiade Icfs tlian the angle A B ; and the point of tendency of tl:e horizon- 
 tal lines GE and A F, would alfo he in the horizon, at the point Z. The figure 
 required, therefore, will nearly refemble the figure here drawn, the figure 
 ABCDEF\ 
 [Plate 13.3 Clearly co underftand what we are about to do, is the nrft and furefl ftep to 
 compafs the end defired. We are now going to obtain, by mechanical procefs, 
 the figure that the contour of a cube would make flanding over the fquare 
 A B C D, to the eye of an obferver raifcd two inches above the point S ; the 
 pofnt S, and the bafe of the cube, ftanding on the fame level plane. 
 
 Knowing the figure of its appearance from the fketch, we will now obtain its 
 prccife form, according to principle, with ruler and com.pafies ''. Draw the ne- 
 ceffary operative lines (Fig. 14, Plate 10); Through the llation S, Fig. i, draw 
 the line X Y, parallel to the diredion of the plane of delineation, G L ; then the 
 lines SG and SL, refpedively parallel to the lines AB and AD of the 
 bafe of the objed:, which lines, produced to the plane of delineation, determine 
 the vanijhtng points of the horizontal lines AB and AD, and of all horizontal 
 lines parallel to them. Draw the line S O, perpendicular to GL; which line 
 being the perpendicular diredion of the eye to the plane of delineation, deter- 
 mines the point on the pidure to which the eye fhould be diredly oppofite to 
 view it when donej and Ihows how much of the objed is on the one fide, and 
 how much on the other, of th« point of view, Laftly, draw the vifual rays 
 SB, SC, and SD, cutting the plane of delineation in the points b, c, and d. 
 
 Thus much is necefi^ary for the preparation of the plan ; the pidaire% or plane 
 of delineation, is prepared, as follows. (See Figure 2.) Firft, draw the 
 
 ' I would recommend the Student to have three or four cubes, of about three inches fquare, and advife 
 that he apply them before him agreeably to the cafes as they occur, and firft (ketch their appearance by the eye 
 and hand alone, and after, perform the fame by rule. 
 
 ' The Student fliould here put paper on his drawing-board, and fet the very examples himfelf as 
 they occur, and to a larger fcale. In the prefent inftance, he (hould place the fquare of the bafe of 
 the objeft A B C D ; then draw the line of the plane of delineation G L, fix his ftation, S, and proceed with his 
 drawing exaftiy as direfted in the procefs. Among many good advantages that will attend the fo doing, will be 
 one, not the leaft, that of his not having a confufion of lines at one time; for, drawing them only as directed, 
 evtry thing will be clear and devoid of confufion. It is otherwife with all the diagrams in the work ; the prefent, 
 for inftance, includes four diftinft Examples that will be feparately treated on, and has all the neceffary lines drawn 
 that relate to them, exhibited at once to view. 
 
 ' The pifture fhould be made on a paper feparate from the pUn, though here they are done all on one, to 
 ihow their connexion the more clearly, and fox want of room. 
 
PRACTICAL PERSPECTIVE. 35 
 
 ground line G L, and, parallel to it, and two inches above it % as flated, the [Plate 13.J 
 horizontal line, VZ. Mark on the horizon the point O, to which the eye is 
 iuppofed to be perpendicularly oppolite, to view the pidlure when done. Every 
 other preparation is taken from the plan, and may be done in the order follow- 
 ing. Set off the diftances of the vanifliing points O G and © L, Figure i, on 
 the horizon, Figure 2, at © V and ©Zj alfo the feveral diftances ©b, © c, 
 O A and d, Figure i, at ©b, © c, © A, and © d, on the ground line of the 
 pidture, Figure 2, through which points draw fine perpendicular lines, indefi- 
 nite, which lines I will call vifual lines, and thus proceed. 
 
 As the near angle of the objed:, A, touches the plane of delineation, it is clear 
 that that angular line, in the reprefentation, will be the fame height as the objedt ; 
 that is, equal to the length AB or AD in the plan. Figure i. Take therefore 
 the length from A to B in the compaffes, and apply it on the perpendicular line 
 A B, Figure 2, and draw the lines B V and BZ ; alfo A V and AZ, which 
 cutting the other vifual lines in the points e, f, and h, i, determines the 
 two perpendicular fides of the cube A e f B and A B h i. Then draw the lines 
 h V and f Z, interfedling each other in the point g, in the perpendicular line 
 g c ; which will complete the whole linear reprefentation of the cube A e f g h i. 
 If the delineation A e f g h i were placed upright over the line G L (Figure i), 
 the line G L of the one, placed exadlly on the line G L of the other, and the 
 points b, c, A and d of the one, over the points b, c, A and d of the other, a 
 folid cube put on the fquare A B C D would exad:ly fit the figure A e f g h i, 
 were it cut out, and viewed by an eye elevated two inches over the flation 
 point S''. 
 
 EXAMPLE II. [Plate 13.] 
 
 Let it be required to find the form that another cube "would exhibit, when 
 placed by thejide of the Jirjl, and viewed from the fame ft at ion and point of view. 
 
 The fquare B EFC, Fig. i , is the bafe of the fecond cube, and being pofited in 
 the fame diredion, and parallel to the ftrft, the fame preparatory lines will {&x\t', 
 there only remains to draw the vifual rays ES and FS cutting the ground line 
 GL in the points x and w. 
 
 • In this diagram it is two inches, but in that made by the Student it may be to three or four times the fcale, 
 that is, fix or eight inches, or any height at pleafure. 
 
 ^ The Student, provided with cubes, is advifed to try this little experiment, when he has completed his 
 drawing, and he will find it perfcdly fatisfaftory. i 
 
36 PRACTICAL PERSPECTIVE. 
 
 [Plate 13.] The fame preparatory lines on the picture (Figure 2) will alfo ferve in this 
 cafe. VZ will be the horizon, and Y, and Z, will be the vanifliing points of 
 the horizontal lines. Take the diftances O w and x, Figure i, in the com- 
 pafles, and apply them at o w and © x, Figure 3, and draw the perpendicular 
 vifual lines pw and n x, indefinitely. 
 
 The two cubes being in contad. with each other, the angle over B is common 
 to them both; and becaufe in the fame direction, the lines B V and A V, Figure 
 2, being drawn, determine the fide ekmf; which fide being obtained, draw 
 then the lines m Z and g V, interfe<fling,at n, and the figure of the fecond cube 
 is determined, and is the figure e k m n g o. The fide e f g o, being in contaifl 
 with the firft cube, cannot be feen unlefs the bodies were tranfparent. 
 
 EXAMPLE III. 
 
 // is required to find the figure that a cube would exhibit, if, placed over the 
 fquare BEFC, Figure 1, // was viewed by an eye two inches above the fiat ion 
 S, the plane of the picture fianding perpendicularly over the line G L. 
 
 Note, The Student is defired to pay particular attention to this propofition, and view it as a new example 
 under the ftated premifes. 
 
 Draw the lines SG and SL parallel to the fides of the object BE and BC, 
 in order to obtain their vanifliing points, G and L. Draw the vifuul rays E S, B S, 
 FS, and CS, cutting the ground line G L in the points x, b, w, and cj and 
 produce the line of the objedl, E B, till it interfedls the ground line in the point 
 A. Lafily, draw the line S O perpendicular to the line G L. 
 
 Prepare the pidlure. Figure 2, by drawing the ground line G L, and parallel 
 to it, and two inches above it, the horizontal line V Z. Fix the point O in the 
 horizon, the point oppofite the point of fight-; and alfo the point O in the 
 "•round line, diredlly under it. Set off the diftances of the vaniihing points G 
 and L, Figure i, at V and Z, Figure 2; alfo the feveral difiances O x, 0b, 
 Q w, and c, Figure i, at O x, O b, © w, and © c, Figure 2, and draw fine 
 perpendicular lines, in pencil, through them. 
 
 Becaufe the near angle of the objed: is at a diflancc from the pidure, it will 
 not be reprefented on the picture, its full height ; that is, equal to the real height 
 of the objed: ; that is done only when the objedl touches the plane of delineation ; 
 
 » That point, on the pifture, is often called the centre of the picture, meaning thereby that the point 
 of fight (hould be direftly oppo'te it, at its proper diftance ; and for the future, for the (ake of brevity, it fliall 
 be fo called, throughout the work. See Definition S. 
 
PRACTICAL PERSPECTIVE. 37 
 
 as it did in the firll: example at the angle A. Its reduced height therefore, [Plate 13.] 
 agreeable to its diflancc from the picture, muft be obtained ; and which is very 
 rciidily done as follows : 
 
 . If the plane of the objcdl, in the dired:ion of the line E B, Figure i, were 
 continued forward, it would touch the plane of the pi6lure in a perpendicular 
 line over the point A, and would there mark its height. Let that be done, by 
 producing the line EB to A; then fet off the diftancc Q A, Fig. 1, at A, 
 Fig. 2, and draw the line A B, Fig. 2, indefinite. The line A B is the interftdting 
 line of the plane of the objert in the diredion of the line B E, Fig. i (Def. 1 3). 
 
 Proceed on the picture in the following manner ; on the interfering line A B, 
 make A B equal the heii;ht of the objcdl, and draw the lines BV, and A V, 
 which, crolling the vifual lines bf and xm, determine the plane e k m f , 
 for the reprelentation of the plane of the objedl over the line E B, Fig. i , 
 from which part the whole figure is foon obtained. By drawing the lines f Z and 
 e Z, the plane e f g o is determined, and drawing the lines m Z and g V, the 
 top of the cube, fin ng, is found, and the whole figure, e km n g o, is completed, 
 which is m the linear reprelentation of the objedt. Pvcflecflion will immediately 
 point out» that the figure but jufl: now obtained, mufh be the fame with the one 
 found by the fecond example, which was done by means, of the angle ef, of the 
 firfl: cube; 'tis only fiippofing the firfl taken away, and the fecond left by itfelf. 
 
 When neither fide ot the objecfl touches the plane of the pidure, it is immate- 
 rial, as to the performing of the operation, which fide is produced for an intcrfedl- 
 ing line J choice only fhould be made of that which will leaft interfere with the 
 work. In the example, jufi: performed, the fide E B was produced for an in- 
 terfedion, as at A, but the fide B C might as well have been produced^; let it 
 be fo done, as at K, Fig. i, and mark off the difiance © K, at K, Fig. 2, 
 where make the height K M equal the height of the objed:, that is, equal to , 
 the height A B, and draw the lines M Z, and K.Z, which will fall in with the 
 before-found lines f g and e o, and form the plane e f g o ; from which the 
 ■whole figure could readily be completed, as may be obferved from infpedlion. . 
 
 EXAMPLE IV. 
 
 // is required to give the reprefentation of a cube as being placed dircBIy upon 
 the one found by the former example, that is, upon the cube (ianding on thefquare 
 B E F C, under the premifesjlated, with thelajl example. 
 
 The fame preparatory lines in plan and pidure, with the lafl:, will ferve in 
 
 • The Student is deCred to draw the whole figure by means of that interfeftion, that he may be convinced 
 of the truth of either procefs, and of the coincidence of both. 
 
 K 
 
38 PRACTICAL PERSPECTIVE. 
 
 [Plate 13.] this example. In Fig. a, lengthen the vifual hnes km, e f , and og, to p, q, 
 and r ; then proceed as followb : 
 
 Set up the height of the cuhe on the interfering line A B H, Fig. 2, above 
 the height of the firft, that is, make B H equal B A, and draw the lines H V, 
 and q Z cutting the vifual lines in the points q, p, and r, giving the figure 
 fmp q r g for the contour of the required cube; which rifing above the horizon, 
 the top is not feen, and the horizontal lines p q, and q r, decline to their vanifhing 
 points V and Z. 
 
 The Student is advifed to place three cubes, agreeably to the difporition of the three cubes forming the group, 
 figure 2 ; and, having fo placed them, to draw their appearance by the hand aiid eye, as nearly as poffible frojn 
 the fame point of view ; afterwards to draw them as one example correctly by rule. 
 
 The linear rcprefentations only, of the cubes have been defcribed, but the affiflance of (hade has been given, 
 that their forms might be the better difccrned ; and the Student is advifed to colour each of his operations, as they 
 are pt-rformed. A double advantage will thereby be obtained, that of embodying his linear figures, and gaining 
 a freedom of fliadowiiig and tinting at the fame lime. 
 
 If it fliould be fiiggefled, of what advantage can the drawing of cubes placed 
 in fuch or fuch pofiticns be ? I can only anfwer, that, from the fimplicity of their 
 forms, they are given as firft examples ; but though fimple, they may neverthe- 
 lefs comprife the forms of irregular and pii^urefque figures, as well as regidar 
 and formal ones, of which Figure 3 may ferve as an inftance, and is given to 
 intimate that a fubjed: of difficulty may be derived from a fubjeft of much 
 apparent fimplicity. 
 
 There can be but two ways of placing a cube, in a vertical pofition, to the 
 plane of delineation, and thofe are, either with both fides inclined to it, as has 
 already been four times done, or with one fide parallel to it, and the other, of 
 confeqiience, perpendicular to it. Inclined pofitions have been given ; we will 
 now proceed to delineate a parallel one. 
 
 [Plate 14.] EXAMPLE V. 
 
 7/ is required to find the appearance that a cube would make, on the plane of 
 delineation, when placed with one fide parallel to that plane. 
 
 Let the fquare A B C D, Figure 1, Plate 14, be the fituation of the cube ; the 
 line G L, the pofition of the plane of delineation, parallel to the face of the 
 cube over the line A B j and let S be the ftation of the obfcrver. 
 
 If the face B A of the cube, touched the plane of dehneation, it is clear, a 
 fquare, equal to the fquare A B C D, Figure i, would be the reprefentation of 
 
Pi.Aric XliJ 
 
 iiroilini fiin* 
 
 K X 
 
 "b "W- 
 
 «■ A 
 
 Z.mhat TiiMi')hc,i I;,- J.1II..' Jf.itiiii ft*. I.»- 
 
PRACTICAL PERSPECTIVE. 39 
 
 that fquare ; but it is at a little dif^ance from it ; confequently, thougVi it will berpj^tg , . ^ 
 a fquare, as being a parallel fecflion of the pyramid of vifion, it will be a fome- 
 what fmallcr fquare than the face of the cube, and fmaller in jufl: proportion to 
 its diflance from the picflurc. To afcertain which, it is ncceffary to have an 
 interfedtion of fome plane of the obje(!l: with the pi<flure, as of A D in the point 
 I. Draw the line S© perpendicular to the ground line G L, © will be the 
 vanifliing point of the line A D and of all lines parallel to it ; alfo draw the 
 vifual rays AS, B S, C S, and D S, cutting the ground line, in the points 
 b, c, a, and d. 
 
 Prepare the picture (Figure 2), as follows: Draw the ground h'ne G L, 
 and parallel to it, and at any height at pleafure, the line Y Z, for the horizontal 
 line. Mark the point ©, the centre of the pidure, on the horizon, and alfo 
 the point © perpendicularly under it, on the ground line. Set off the feveral 
 diftances of the vifual interfedtions, © b, © c, © I, ©a, and © d, Fig. i, 
 at ©b, ©c, © I, © a, and © d. Fig. a, and draw fine pencil lines perpendi- 
 cularly through them, upwards on the pidlure. 
 
 The line drawn through the point I, is the interfering line, on which mark 
 the height of the cube, as I K, equal to a fide of the cube in the plan, as A B, 
 Fig. I, and draw the lines K © and I ©, Fig. 2, cutting the vifual lines a n, 
 and d i, in the points n, i, and e, k, forming the plane e n i k, as the reprefenta- 
 tive face of the cube, over the line A D in the Plan. Parallel to the horizon 
 draw the lines n g and e f, determining the fquare e f g n, as the reprefentative 
 fquare over the line B A in the plan. Fig. 1. Laftly, draw the lines g © and 
 i h, interfedling in the point h, forming the figure ngh i, as the top of the 
 cube, and giving the figure e f g h i k, as the linear reprefentation of the whole 
 cube, under the premifes ftated. 
 
 EXAMPLE VL 
 
 Figure 3 reprefents the plan of three redangular folids, placed fide by fide, 
 forming the general figure E F H K. 
 
 li is required to find their reprefentation, fuppofing them to fand with both 
 faces inclined to the plane of delineation, ivhich is given in the place and dire^ion 
 of the line GL, and S is the fat ion of the obferver. 
 
 Draw the preparatory lines ; firft the line W X, parallel to the ground line G L, 
 then the line S© perpendicular to it; alio the vifual rays FS, PS, N S, E S, 
 MS, and KS, cutting the ground line in the points e, f, g, h, i and k; and pro- 
 duce the face of the objed FE, to B, for an interfedlion. Laftly, draw the 
 
49 PRACTICAL PERSPECTIVE. 
 
 [Plate 14.] lines S V, and S R, rcfpedively parallel to the two f.ices of the objed E F and 
 EK, to obtain their vanilhing points. 
 
 It will be obferved, that there is not extent enough of paper foi- the line of the pifture, G L, and the line S R,, 
 to come in contaft ; in fuch cafe an expedient muft be ufed. Take any portion of the diftance of the picture 
 S 0, fuppofe half, as at m, and draw the line ni L parallel to S R ; then will the diftance © L be half the diftance 
 of the required vanifliing point. Should the line at half the diftance not come within the limits of the paper, then 
 let a third or a fourth of the dillance be taken ; the parallel line being r'rawn, will give a proportional diflance of 
 the vanifliing point. 
 
 Let the line B C, Fig. 4, be the direction of the plane of the pi(flurc, let A be the flation point, A C will be 
 the diftance of the piifVure. Let A B be the direftion of a line finding a vanilhing point at B. Divide the dil- 
 tance of the piclure into two equal parts at D, and draw the line DE parallel to AB ; then will the diftance C K 
 be /ui!f the diftance C B. Take a third part of the diftance A C, at F, and draw F G parallel to A B; then will 
 G C be a tiirj part of the diftance B C. Thus whatever portion is taken of the one, drawing the pa'jllel line 
 will give a like portion of the other, for the triangles formed are firailar, and the correfponding fides will there- 
 fore be proportional. 
 
 Prepare the piftiire^ Fig. 5; that is, draw the horizontal line YZ, and the 
 gxound line GL, parallel to each other, at any diliance at pkafure. Fix on the 
 point , in the horizon, for the centre of the pidure, and draw the vertical line 
 O . Set off the diftance of the interfcdling point B, Fig. 3, and of the viftial 
 points ©e, © f , © g, © h, © i, and ©k, at A, and © e, © f , © g, © h, ©-i 
 and © k, Fig. 5, and draw the vifual lines through them. Laftly, let off 
 the diftance of the vanifliing point V, Fig. 3, at P, Fig. 5, and the diftance of 
 the vanifliing point Z, Fig. 5, at twice the diftance © L, Fig. 3''; and proceed, 
 in the following manner : 
 
 On the interf.ding line A C% Fig. 5, fet up the height of the objed, U'hich 
 fuppofe AB, and draw the lines AP and BP, cutting the perpendicular vifual 
 
 * Preparation of the piftiire, always implies, firft, dc-termiiiiiig the diftance of the horizontal and ground lines 
 (Def. 7 and 11). Secoidlv, the fi\ingon the centre of the pi£lure (Def. 8), and drawing the vertical line 
 (Def. ..)). Thirdly, the fetting off thedillances of the vanifliing points (Def. 14), and fetting off the diftances of 
 the interfeftions of the vifual rays, with the ground line, in the plan, on the ground line of the pifture ; and this 
 is dcfired to be underftood and done in fuuire, on the being told to prepare the pifture. 
 
 ' It is abfoiutely necefiary, without having retourfe to a very troublefome procsfs, which fhall be given in the 
 courfe of the »vork, to have the places of the vanifliing points, on thepiflure, that the relative lines may be drawn 
 in true direftion to them. When the paper, or drawing-board, is not long enough to receive them on it, a piece 
 miift be added, as here, or a lath muft be fixed to the board ; where, placing a pin in the vanifhing points, a ruler 
 may be laid to them, and the work may be done with as much accuracy, as were they not above a foot diftar.ce. 
 
 ' The Student will obftrve, that when by reference one courfe of the alphabet has been exhaufted, I have been 
 of necelTity reduced to begin another ; by which the fame letter will be fometimes twice or thrice repeated in the 
 fame pbte; but by being ufed in parts remote from each other, it is hoped all confufion will be avoided. J 
 think fuch proceeding better, than having recour'e to Italic, or Greek letters, as forae authors have done ; by 
 which, the Student, not acquainted with Greek charaders, is quueal a k)fc vjhat to call thcni. 
 
PRACTICAL PERSPECTIVE. 41 
 
 lines, and determining the figure abed, for the reprefentation of the face of theC^-^te 14.J 
 obje<a over the line EF, Fig. 3 ; then draw the lines d Z and a Z, which will 
 obtain the plane of the end of the objea: ad no; and laftly draw the lines c Z 
 and nP, interfering at m, and completing the figure abcmno; the figure 
 required. By drawing the lines x Z and v Z, the whole figure is divided into 
 three parts, agreeable to the three rectangles in the plan, Fig. 3. 
 
 EXAMPLE VII. 
 
 // is required to Jind an equal and like figure to one of the foregoing, as if placed 
 on the fecond of the three figures of the lafl example. 
 
 As this example introduces no new pofition of plane in the original objeft, 
 the fame preparatory lines will anfwer, as in the former example; and as all 
 the vifual lines are already drawn, it is necefiTary only to heighten them. 
 
 On the interfeding line AC, Fig. 5, fet up the height BC equal BA, and 
 draw the line CP; determining the plane vxpq for the front of the required 
 reprefentation ; after, draw the lines pr and q s to their vanifliing point, Z, 
 giving the plane v qs t, as the other fide of the objecH: ; to which the top is added 
 by drawing the line s P, fhaping the figure q p r s, for the top; and completing 
 the form v x p r s t, the reprefentation required. 
 
 The top of the objeft q p r s, Fig. 5, being very near the horizon, is, of confeqiience, very little feen ; had the 
 objeft been higher, ftill lefs would have been vifible; had it fallen in with the horizon, that is, had B T and not 
 B C been the height of the obje<?t, none of the top could have been feen, but its reprefentation would have been 
 a line in the direftion of the horizon. 
 
 Fig. 6 is meant to fhow what the compound of the two laft fimple 
 examples might involve; and is introduced to encourage the Student in his 
 purfuit, by giving a foretafte of the refult of his labours, and to inftance that 
 while he is applying rules and principles upon, feemingly, very uninterefting 
 objedls, the fame extend to and embrace irregular and pidurefque ones. 
 
 Hitherto the examples have united as few different diredtions of planes, form- 
 ing a folid figure, as could well be given ; they may be fuppofed to have been 
 buildings with flat or no roofs; it is now my intention to introduce other di- 
 rertions of planes, as inclined roofs ; and thefe in fome variety. 
 
 Roofs are of various kinds, but two only are neceffary to be obferved upon 
 here, and thefe are what are called gable-end roofs, and hipped roofs. A gable- 
 end roof, is when the end walls of the building go perpendicularly up to the 
 point of the ridge, and the ridge extends from end to end of the building. 
 
+z PRACTICAL PERSPECTIVE. 
 
 [Plate 15.] The upper part of the er,d walls are therefore of a triangular form, to the depth: 
 the roof Hants down. ABCDE, Fig. i, Plate 15, reprefents the end wait 
 of a gable-end roof; CDE being the triangular part formed by the roof. A 
 roof is faid to be hipped when the ridge comes Ihort of the extent of the building 
 and flants down on every lide; AEFGH, Fig. 2, may convey the idea of a 
 hipped roof; and both one and the other be further explained by Fig. 3, where- 
 the line IK indicates the ridge of a gable-end roof, and OP the ridge of a hipped, 
 one ; and OM and P N the flant at the ends. A roof may have one end gable, 
 and the other hipped, and is often fo conftruded.. 
 
 EXAMPLE VIII. 
 
 It is required the reprcfentation of a quadrangular building Jituated' with each- 
 fide inclined to the pi£lure. Covered with an A" roof, each end being a gable-end. 
 
 Let the re(flangle A BCD, Fig. 4, be the plan of the building; the lir(e EF' 
 will be' the place of the ridge of the roof, extending from end to end. Let tha 
 line QL be the place of the plane of delineation, and let S be the fiiation point. 
 
 Find 0, the centre of the pidlure; alfo the points Q and L, the vanifliing 
 points of the lines AB and AD and their parallels. Produce the face of the 
 building A D to I for an interfedlion with the pidlure; and draw the vifual 
 rays interfedling the ground line of the pidlure in the points b, e, a, f, and d''.. 
 
 Prepare the pidlure. Fig. 5, by drawing the horizontal and ground lines VZ, 
 and GR, at any diftance from each other at pleafure ; fix upon the centre o£ 
 the pidlure ; and draw the vertical line 0; fet off the diftances of the 
 vanifliing points V and Z, equal the diftances of the vanifliing points 
 Q and L in Fig. 4; draw the interfedling line I L, Fig. 5 ; and all the 
 vifual lines through the points b, e, a, f and d; taken from their refpedlive places 
 and diftances b, e, a, f, and d, Fig. 4; and proceed as follows : 
 
 On the interfering line I L, Fig. 5, fet up the height 1 K, equal the height 
 of the building B C or HG, Fig. i and 2; and draw the lines KZ and IZ^ 
 determining the plane gmo p, for the front of the building. Draw the lines 
 
 • A fingle pitched roof is conftriifted in the form of the Roman capital letter A, and is therefore, by builders,, 
 called an A roof. A double pitched roof is, for the fame reafon, called an M roof, as it nearly refembles that 
 letter; but is more like the letter W, inverted, thus A\. 
 
 ' 'it is not neceflary to draw the vifual rays beyond their interfcftion with the ground line of the pifture : it is 
 fufficient they be drawn to there, in the direftion to the ftatloii point; for the future, therefore, they will be 
 drawn no farther, and the ftation being fixed, and exprefled on any part of the plate, it will be fufficient the vifual 
 rays be drawn to the pidure in direftion to that point. 
 
I'l.ite /4 
 
 i^' ' i\ \ 
 
 y^:.^/ ^■/:f^^.^-- <K,^^y^ r7^Ji*4^ /4'no. 
 
PRACTICAL PERSPECTIVE. 43 
 
 nr'Vand gV, determining the end of the building g h i m. It now remains to {[Plate 15.] 
 place the roof, which is readily done, but which however requires fome cir- 
 eumfpedtion in the procefs. 
 
 Place the height of the roof XD, Fig. r, on the interfeding line at I L,, 
 Fig. 5, and draw LZ, which will give the height of the roof on the angular 
 line of the building g m, at r; from which fpot it may readily be transferred to- 
 its proper place in the vifual line e k, by the line r V, which cuts the line ek 
 in the point k, the point required. From the point k draw the lines ki, and. 
 k m, completing the gable-end of the building. Draw the ridge of the roof 
 k Z cutting the end vifual line, in the point n ; and laftly, draw the line no, 
 completing the whole linear delineation of the building g h i k n o p. 
 
 It muft be carefully obferved, that whatever original plane is produced to the pifture to obtain an interfeftion, 
 that that interfeftion ferves only to obtain heights in the direftion of that plane ; whence they may be transferred 
 to o"her planes in coutacT: with it ; as in the prefent iiiflancc. The ititerleiSting lioe I L, Fig. 5, is the interfe<3ing 
 line of the plane gmop; of confequence, any original height fet up on that line can only be transferred through- 
 out thedireflion of that plane; for inftance, the height of the roof K L was transferreu by the line LZ, all 
 along that plane to its other extremity s, but the line r s is not the place of the ridge of the roof, which lies in the 
 middle of the plane g h i k m, proceeding from the point k ; but any height on the angular line g r, is eafily tranf- 
 ferred along that plane by U'eans of its horizontal vaniniing point V: by which means the height of the roof was 
 obtained by the line r V, at k. If, inftead of the plane over the line A D, Fig. 4, being produced for an inter- 
 feftion, the plane of the middle of the houfe in the direftion of the ridge of the roof, had been drawn, ,and the 
 height of the roof had been fet up on that line, it would, at one application, be transferred to its proper place. 
 
 Let the line FE, Fig. 4, be produced to P for an interfedlion ; fet off the 
 diftance P, at © P, Fig. 5, and draw the interfering line PR. On PR, fet 
 up the height of the ridge of thfe roof, equal the height X D, Fig. i, and draw 
 the ridge line R Z, which line will determine the exad ridge of the roof betweerji. 
 the proper vifual lines, and will be found to correfpond, exadly, with the ridge 
 before obtained, by the former procefs. 
 
 The roof may be found by a very different procefs*. I' do not (how it for its-, 
 beauty alone, though that is great, or for its utility either, but to manifell: the truth-, 
 of the rules of Perfpedlive, by experience of their juft coincidence. 
 
 The flant lines of the roof will have their vanifliing points on the pidure, as 
 well as any other direftion of lines in the fame objedl. The line k m. Fig. 5^ 
 being in the vertical plane ghi k m, will have its vanifliing point fomewliere in 
 the vanifliing line of that planer (Def. 15). A vertical Ime drawn through the 
 horizontal vanifliing point V, will be the vanilhing line of. the plane g h 1 k ni j 
 
 • If the Student poflefs not a confiderable degree of difcernment, and quick penetration, it will require fome 
 ferious inveftigation ere this procefs be fully comprehended, which, in truth, it is almoft impoflible to make per- 
 fectlv clear without proper apparatus, and perfoijal explanation. 
 
44 PRACTICAL PERSPECTIVE. 
 
 [Plate isOof confequence, the vanifhing points of the lines km, ki, and all lines parallel 
 to them, will be fomewhere in the vertical line G V Q X. 
 
 Two lines drawn from the eye, parallel to any two lines in an ohje&, findirg 
 their vanijhing points, will tuake the fame angle at the eye, as the lines in the 
 objedl make with each other ; for the two lines in the one inflance are refpeBively 
 parallel to the two lines in the other. 
 
 The line S Q, is drawn from the ftation S, parallel to the line A B, 
 Fig. 4, and a line drawn from the flation S, making the fame angle with 
 5 Q, as ED does with E C, Fig. i, will find the vanifhing point of 
 ihe line ED, and which point mult evidently be fomewhere in a vertical 
 line through the point Q. To obtain which point in pradlice, take the 
 •diilance of the vanilhing line it is in, that is, the length from S to Q, 
 in the compaffes, and fet off the fame on the horizon. Fig. 5, from V to W. 
 At t'he point Wmake an angle, V W X, equal to the inclination of the roof, that 
 •is, equal to the angle CE D, Fig. i, and produce the line till it interfedls the 
 vertical line through the vanifhing point V, in the horizon, in the point X. 
 The point X will be the vanifliing point of the line of the roof km, Fig. 5 ; and 
 of the line n o, parallel to it. The flant lines of the roof k m and n o, already 
 obtained, will, on application of a ruler, be found to tend to the point X, agree- 
 ably to the above ftatement. 
 
 By the fame reafoning the line of the roof k i. Fig. 5, will alfo have its va- 
 nifliing point, and in the fame vertical line G V Q. It will be found to be as 
 much below the horizontal vanifhing point V, as the point X is above it. See 
 the plate explaining the definitions, under the article Vanifliing Point; Dcf. 14. 
 
 Let the line A B, Fig. 6, be the line of the horizon ; let the line C D be the 
 vanifliing line of a v<;rtical plane, being the gabJe-end of a houle ; and let the 
 angk A BC be the angle of inclination, finding the vanifliing point of the flant 
 lines of a roof in one diredlion. Let the line B D be the line, finding the vanifli- 
 ing point of the flant lines in the other diredion, having the fame inclination to 
 an horizontal line: then will the angle A B D be equal the an^Ie ABC, and 
 the diftance A D equal the diftance A C. 
 
 EXAMPLE IX. 
 
 It is required to find the reprefentation of a quadrangular Maiding, fttuated 
 inclined to the pidture, centered with afngle hipped roof 
 
 Let the quadrangle GDHK, Fig. 7, be the plan of the huilding, the line 
 MN will reprefcnt the ridge of the roof. The former line QL may be the 
 
PRACTICAL PERSPECTIVE. 45 
 
 place of the plane of delineation, and it may be viewed from the fame ftation S. [Plate 15.] 
 
 The pofition and direction of the lines of this objed; being the fame as thofe 
 of the former example, the preparatory lines that ferved the preceding, will 
 anfwer for this. It is requilite only to draw the vifual rays MS, NS, GS, PS, 
 and KS, interfedling the pidlure in the points m, n, g, p, and kj and to pro- 
 duce the line DG, for an mterfedting point, at R. 
 
 Prepare the pidure, Fig. 8. Let the line VZ be the horizon; GR the 
 ground line; O the centre ot the pidture; and the points m, n, g, p, and k, the 
 correfponding points with m, n, g, p, and k. Fig. 7. Draw the vifual lines 
 through thofe points, and the interfering point R, and proceed as follows : 
 
 On the interleding line R E let up the height R T, equal the height of the 
 objed; H G, Fig. 2, and draw the lines T V and R V, cutting the vifual lines 
 of the front of the building in the points z and o, y and p, determining the plane 
 y poz, for the reprefentation of the plane of the front : from the angular points 
 z and y, draw the lines z w and y x, to their vanilliing point Z, determining 
 the plane y z w x for the end of the building. 
 
 On the interfering line, fet up the height of the roof TE, equal the height 
 NK, Fig. 3, and draw E V cutting the angular vifual line of the building in 
 the point e ; irom which point draw the line eZ, cutting the viiual line p a, in 
 the point a, the point of diredlion of the ridge of the roof; draw the line a V, 
 which, cutting the vifual lines through the points m and n, in the points t and 
 V, determines the exadl portion of the ridge of the roof, t v, which is the repre- 
 fentation of OP, Fig. 3, or of the ridge M N, Fig. 7 : draw the lines t o, vz, 
 and vw, which will complete the whole reprefentation required^. 
 
 In Fig. 8. If the lines a z and a w be drawn, they will form a gable-end 
 yzawx, of which the point a is the point of the gable, and will anfwer for the 
 diredlion of the ridge, whether it be a gable-end, or a hipped roof; for in both 
 cafes it lies in the middle, of the breadth of the houfe ; wherefore the Urie a V 
 anfwers as well the ridge of a hipped roof, as of a gable-end. 
 
 On examination of the plans of the two buildings, Figures 4 and 7, itvwilL 
 be obfarved, that they are placed at right angles with each other, and in contact 
 at the point D ; which being the cafe, the fecond example could have been 
 eafily accompliflied from, the firft, without need of another interfedion, or 
 other preparatory lines, than merely the additional vifual rays from the vilible 
 
 > ' The Student is particularly advifed to be fure he ferfellly underftands the procefs of thefe two examples ere 
 he proceeds farther ; as all that will follow, will, more or lefs, have relation to theni. He is recommended to 
 praftife them on a large fcale, that he may the better fee the affinity and relation the lines and planes have to 
 one another ; and to be very careful in the procefs. 
 
 M 
 
46 PRACTICAL PERSPECTIVE. 
 
 angles of the ftrudlure ; but the exemplification of this procefs fhall be made 
 part of the fubjeft of the next example. 
 
 [Plate 16.] EXAMPLE X. 
 
 Let the form ABC DE F, Fig. i, Plate 16, be the general plan of a build- 
 ing, of which, let the fquare FGCH be the plan of a tower, and the other 
 two parts A B G F and E F H D be fubordinate parts, with gable-end roofs, and 
 refting againfl: the fides of the tower. Fig. 2, is a geometrical elevation of the 
 building; IKLM the height and breadth of the tower; ON the height of the 
 roof of the lower building, and O P the height of the upright walls. 
 
 It is required to jind the reprefentation of the above building, as it Jlands 
 fojited to the platie of delineation at the line R T,frotn theflation S. 
 
 Find the vanifhing points R, and T, by lines from the ftation drawn parallel 
 to the different faces of the building ; alfo the centre of the picture ; produce 
 the line FE to X, for an interfecftion ; and draw all the neceffary vifual rays. 
 Prepare the pidure, Fig. 3. Let V Z be the horizon; © the centre of the 
 pidlure ; V and Z the vanifliing points of the horizontal lines ; G L the ground 
 line, and © the vertical line. Set off the diftances of the points b, a, g, f, n, 
 h, e, d, and X, Fig. i, at b, a, g, f, n, h, e, d, and X, Fig. 3, and draw fine up- 
 lines through them indefinitely ; then proceed as follows : 
 
 On the interfedling line X T, Fig. 3, fet up the height X Y, equal the height 
 of the walls of the building O P, Fig. 2. Alfo the height Y W, equal the 
 height of the roof PN, Fig. 2; and draw the lines Xi, Y k,andW v, to the fame 
 vanifiiing point, V; determining the plane of the building u i k m, and the 
 height of the roof on the angular line, at v. From the points v, m, and u, draw 
 the lines v Z, m Z, and u Z, obtaining the height of the roof, at o, in its vifual 
 line ; and by drawing the lines o m and o p, the whole gable-end u m o p q is 
 completed. Draw the ridge of the roof o z, cutting the end vifual line n, in the 
 point z, and draw the line 2 k ; then is the whole building over the plan 
 E F H D, Fig. I , completed ; from which the other parts may readily be projetfled. 
 Draw the lines ks, and i r, by direction to their vanifhing point, Zj alfo the 
 lines sy, and r t, by tendency to their vanifhing point, V. In the plan Fig. i, 
 produce the ridges of the two roofs till they meet, at the point K ; from which 
 point draw the vifual ray K 1, agreeable to which interfedlion, draw a vifual line 
 at 1 on the pid:ure. Fig. 3 ; to which line produce the ridge of the roof o z, 
 touching it at c; from c draw the line cw, tending to the vanifhing point Z, 
 £:utting the vifual lines of the ridge of that building in the points w and x j w x 
 
Plate XV. 
 
 Fy.3. 
 O P 
 
 I.oulon PiMithrd hv Jxmrj- Mation JanfiSw 
 
f£,4TE /6- 
 
 K 
 
 .ji„y^„ (/■„//,,..../ /y yi-^~ y-""' -/~f^ • 
 
PRACTICAL PERSPECTIVE. 47 
 
 is the ridge of the roof. Draw the hnes wy, w s, and x k, completing the [Y'hte 16.] 
 
 other building, over the plan A B G F, Fig. i. The delincaftion of the tower 
 
 is foon accompliflied : on the inteifeding line XT, make the height X T, equal 
 
 the height of the tower M L, Fig. 2, and draw the line T V, cutting the viftial 
 
 lines of that face of the tower, in the points a and i ; from the angular point a, 
 
 draw a Z, cutting the other vifual line of the tower in the point e, which will 
 
 complete the whole of the required reprefentation. 
 
 Fig. 4 is introduced to fliow to what a complicated objedt, fuch a figure, as 
 is jul^ now obtained, may apply. I will give one more example on the true de- 
 lineation of roofs, and then proceed to other objecfts. 
 
 EXAMPLE XI. [Plate 17.] 
 
 Let the figure FA BCD (Fig. i, PI. 17) be the plan of a building, the ridge 
 of whofe roof let be the line H I K ; forming a gable-end at the face A B, and 
 a hip at the end E D Let Fig. 2 be the geometrical elevation of the faid 
 building, expreffing the feveral heights ; and let P O be the height of the horizon. 
 
 // is required to find the figure fuch building would prefent, fianding in the 
 pofition and place it does, to the plane of delineation over the line V X,frorn the 
 flat ion S ; the point of fight being equal the height from P /o O, Tig. 2. 
 
 Obtain the centre of the pidlure ©, as alfo the vanifliing points of the differ- 
 ent diredlions of horizontal lines in the building V, and Zj draw all the vifual 
 rays from the vifible angles of the building, cutting the ground line in the points 
 b, h, a, g, i, k, e, t, d ; and produce the face G E to R, for an interfedlion. 
 
 Prepare the picfture, by drawing the horizontal and ground lines X Y and 
 G L, parallel to each other and diftant equal the height P O (Fig. 2) ; fix the 
 diflances of the vanifhing points, and place the centre of the picture, on the 
 horizontal line Fig. 3 at X, Y, and © ; alfo fet off the diftances of the vifual 
 interfeftions at Fig. i , at the correfponding diftances, Fig. 3, and draw the vi- 
 fual lines perpendicularly through them. 
 
 On the interfeding line, R D, fet up the feveral heights of the building R A, 
 RB, RC, and R D, equal the geometrical heights L m, rn, L W, and L M, 
 of the elevation, Fig. 2, and proceed with the delineation, as follows. The 
 height R C, on the interfedting line. Fig. 3, is the height of the upright walls; 
 defcribe it around the building, by means of the vanilhing points, to the feveral 
 vifual lines, in the points r, x, w, v, and s ; and defcribe the bottom line of the 
 building, to the fame vifual lines by means of the point R. The height of the 
 roof, from the point D, may alfo readily be transferred to its proper place, as 
 follows J Firft, to the extreme vifual line in that diredion of the wall of the 
 
48 PRACTICAL PERSPECTIVE, 
 
 [Plate 17.] building, in the point c ; whence convey it to the angular vifual line through the 
 point a, at f, by means of the vaniOiing point Y; and thence to its proper vifual 
 line through the point h, at m, determining the point of the gable-end, which 
 the lines m v, and m w, complete. From the point of the gable, m, draw the 
 ridge, m n, to its vanifliing point Y ; and the return of the ridge, n o, to its va- 
 nifliing point, X : draw the hip lines o r, and o s ; and the line n x, and the whole 
 roof will be completed. 
 
 The fhed, or lean-to, is obtained from its heights A and B; as may clearly 
 and fatisfadlorily be feen, from examination of the figure. 
 
 The truth of delineation, that is, drawing agreeably to the flridtefl: perfpec- 
 tive, is unqueftionably as requisite to be attended to in dcfcribing old and de- 
 cayed objedls, as in tracing the moft perfect. Without due attention to truth 
 in the delineation of the former, they may be moft prepofteroufly reprefented. 
 It is not becaufe being inclined, being really out of perpendicular, that they may 
 be made to incline any how; they muft be made fo with judgment. 
 
 It is an advifable method to delineate a rude objecfl, of any importance, truly, 
 as if quite perfect, and then deftroy it at pleafure, tempering the flroke of ruin 
 with the hand of judgment. For inflance, in the fubjedl but juft truly deline- 
 ated (Fig. 3), and lliown in a pid:urefque manner (Fig. 5); let it firft be 
 delineated lT:rid:ly corred:, in pencil, with every angle and boundary made per- 
 fedlly fliarp and regular, as is expreffed by the fharp lines. Fig. 4; then, with 
 the deftroying hand of time, trace the rougher figure there drawn around it. 
 The rude figure is not lefs under the governance of perfpedlive than the perfed: 
 one, but only lefs indicative of abfolute departure from truth. A tree is deline- 
 ated perfpeftively when delineated properly. "Delineate a tree agreeably to rule," 
 I was told by a gentleman* to whom I made the obfervation, and who well 
 underftood perfpedive, and much admired it. " I will, my Lord," I replied, 
 •' if you will draw its geometrical plan and elevations." 
 
 It is a very pleafurable procefs, the breaking down a regularly drawn fub- 
 je<ft into ruin ; and it is done with the more fatisfadion when it is performed 
 with confidence, fenfible at the fame time it is not random work, but that it 
 is true delineation governed by rule and judgment. 
 
 Thus far advanced, having gained confiderable information on right-angled, 
 or fquare objeds, it is now expedient to turn attention to round ones, and 
 from them make reference to many-angled ones, as hexagons and odagons. 
 
 * The late Lord Mountjoy, fo lamentably killed, <iuring the Rebellion in Ireland in 1 798, at the battle of Rofs, 
 
PLATE XX II 
 
 Fu^.i 
 
 K 
 
 D 
 
 E 
 
 V 
 
 h h a. gi 1 
 
 ^ — g ' Q 
 
 //Ic e t d. Tt. 
 
 J^UJ. 
 
 Fuj.4 
 
 
 
 Ful>:Csh:d by / .H.t/t„f, fW^/^/t^i* 
 
. PRACTICAL PERSPECTIVE. 49 
 
 I know not for what reafoa writers on perfpe(flive commonly divide the 
 fubjed: of linear delineation into two parts, which they term rcdiilinear and 
 curvilinear; there feems to be an evident impropriety in this divilion of the 
 fubject, fince the fame procefs, (imply, is followed in both cafes in determining 
 of known forms, whether bounded by right lines or curves. It is generally ob- 
 ferved on entering on the inveliigation of curvilinear delineation, that the 
 perfpedive reprefentation of a circle is a fedtion of the cone of rays, which, pro- 
 ceeding from the eye to all parts of the circumference of the circle, is made by 
 a plane cutting them in any direction : that when the fedion of rays is taken 
 parallel to the bafe of the cone, the figure of the fedtion made is fimilar to the 
 bafe whence the rays proceed, that is, a circle. When the fedlion is taken in- 
 clined to the bafe of rays, that then the figure made will be an oval ». And {o 
 they proceed till they have enumerated every different way a cone may be cut, 
 and particularized the forms that would thence be alTumed, making reference 
 to the fcience of conic fedtions, as if convinced their readers were well verfed 
 in that ingenious and elaborate inquiry. 
 
 With equal propriety it might be faid of any redlilinear figure, whether 
 right-angled or polygonal, that ^ fedlion of the pyramid of rays, formed by 
 the eye viewing it, taken parallel to the bafe, will be a fimilar figure to the 
 original, and that, taken in any other diredlion, would determine a figure 
 confiderably different and difTimilar. All this, though very true, forwards 
 the fubjedl nothing ; and the ftudent, unlefs acquainted with thefe truths, 
 mufl rely folely on the aflertion of his informer that it is fo. The fadl is, the 
 operative part of all perfpedlive delineation is by the interfedlion of right lines ; 
 that when right lines are to be obtained, by finding the extremes of them, the 
 whole line is determined, and the reprefentation of a folid bounded by planes is, 
 on that account, very foon accompliflied : but this is not the confequence 
 with refpedt to the obtaining the reprefentations of curves ; a ffraight ruler 
 will in no way coincide with a curved line between its two extreme points. 
 There is no mode of procedure for determining the apparent forms of curved 
 lines, but by finding points in the curvature, and by obtaining fuch fuffi- 
 citnt number of them, that the hand may be enabled to trace the curve 
 through ihcm with adequate corredtnefs. 
 
 ' Except in one poCtion, and that is, when>the cone of rays is cut by the plane of delineation fub-contra- 
 wifc, as it is termed ; that is, when the portion cut off is fimilar to the whole cone, then, of courfe, the bafts, 
 of tjoih, being fimilar, muft be circular. But this takes place only in inclined cones. 
 
 N 
 
so PRACTICAL PERSPECTIVE. 
 
 [Plate i8.] When the curve is irregular, as the curve A BC DEFG (Fig. i, Plate i8), 
 a point mull be aflumed at every confiderable variation in the curve, as at 
 B, C, D, E, F, G, and ordinates be dropped from them to the bafe or chord 
 of the curve AH, as B b, C c, Dd, &c. the various heights of wliich ordi- 
 nates being found, the curve may be traced through their top extreme points 
 with very fufficient corredtnefs. Nor can any other mode be followed, let the 
 curve be ever fo regular; as a circle or an ellipfis. The only difference is, 
 that the curve being regular, the points may be regularly afiumed, and thereby 
 be more eafily found ; but however regular the curve, it can be obtained only 
 by finding points in its curvature. By circumfcribing and infcribing a circle 
 •withafquare (as Fig. 2), eight points in its circumference may readily be ob- 
 tained by fimply finding the reprefentation of thofe fquares; and this, whether 
 placed horizontally (as Fig. 3), or vertically [zs Fig. 4), or inclined (as Fig. 5), 
 and, with care, the curve may be traced through them. Eight points I con- 
 lider fufficient for tracing the curvature of an oval, even of confiderable magni- 
 tude j but if not thought fo by others, more may eafily be acquired. Points in 
 the curvature of the reprefentation of an ellipfis, or oval, may alfo be obtained 
 hy circumfcribing and infcribing it with redtangles, and finding thofe recftangles, 
 as Fig. 6 : fo of a hexagon or of an 0(flagon, by circumfcribing them 
 red:angularly, and drawing the regular parallel lines from one correfponding 
 point to another, and delineating them merely, the required figure is like- 
 wife afcertained by only drawing the boundary lines from the points fo ob- 
 tained (fee Figs. "7 and 8). By finding the reilangular circumfcribing figures, 
 and the parallel lines A B, CD, and E F, of the one, and C H, IK, LM, 
 and N O of the other; the hexagon and odtagon will be defcribed by drawing 
 their boundary lines from the interfed;ing points made by the lines of the right- 
 angled figures before found, as C A, AD, E B, and B F, of the one, and 
 the lines 1 L, N K, H O, and G M, of the other. Not but that fuch figures 
 may be more fcientifically delineated by the aid of vanifhing points, as will 
 be fhown by and by, but fuch method as is now pointed out has confi- 
 derable advantages. 
 
 EXAMPLE XII. 
 It is required to Jin d the perfpe&ive reprefentation of an irregular curved line,, 
 defcribed on a plane flanding inclined to the plane of delineation. 
 
 The curve ABCDEFGH (Fig. i, Plate 1 8) is the curved line ; let it be 
 inclined to the plane of delineation, I K, in the angle H I K; and let S be the 
 flation point. The curve is fuppofed to fland upright on its chord or bafe A Ho- 
 
PRACTICAL PERSPECTIVE. 51 
 
 AfTume the points B, C, D, E, F, G, at the different variations of thc[Plate 18; J 
 curve, and draw the feveral ordinates B b, C c, Dd, 5cc, perpendicular to the 
 chord of the curve A H, and produce the chord line, or bafe of the curve, to 
 I, for an interfedtion. Find the centre of the pid;ure ©, and the vanifliing 
 point of the line A H, by the line S K being drawn parallel to it. 
 
 Prepare the pidure (Fig. 9). Let X V be the horizon, and I L the ground 
 line; I is the interfedting point, the centre of the pidlure, and V is the 
 vanifliing point. Let the vifual lines through the points a, b, c, d, e, f, g, and 
 h, correfponding with the vifual interfedions at Fig. i, be drawn. 
 
 Set up the feveral heights of the ordinates, Fig. i, on the interfering line 
 ID, Fig. 9, at G, B, E, F, C, and D, and draw pencil lines from them to the 
 vanifhing point V, which crofling the correfponding vifual lines, determine 
 the points B, C, D, E, F, and G, through which the curve required may be 
 traced with fufficient accuracy. 
 
 EXAMPLE XIII. 
 
 Tf is required to find the reprefentation of a circle lying in an horizontal 
 plane, and touching the plane of delineation. 
 
 Let the line M N (Fig. 10) be the length of a fide of a fquare circumfcribing 
 the required circle; let P be the horizontal line, and © the centre of the 
 pidlure. 'J"he centre of the pidlure will be the vanifhing point of the lines of 
 the fquare perpendicular to the pidlure, the other lines will be truly horizontal, 
 therefore be drawn parallel to the horizon. 
 
 If the Student defcribe a circle of diameter equal tlie fide of the fquare M N, and therein infcribe a fquare 
 touching its circumference, he will find the length from a to c (on the line MN, Fig. lo) equal the length of 
 the fide of the infcribed fquare (as 86, Fig. 2), which length he will divide and fet off equally on each fide the 
 middle point b ; and which is in the figure fet down for the completion of the example enjoined. 
 
 Make P equal the diftance of the pidlure, or plane of delinration, that is, 
 equal the diftance of the eye from the plane of delineation; P will then be 
 the vanifliing point of one of the diagonal lines of the fquare, and a point oi\ 
 the horizon, equally diftant on the other fide of the centre of the pidlure ©, 
 would be the vanifhing point of the other diagonal line. To obtain eight poitits 
 in the circumference of the required circle proceed as follows : 
 
 Draw the lines M © and N © ; then the diagonal line N P, cutting the line 
 M © in the point R; draw the line RS parallel to the line MN, and the 
 figure M R S N will be the reprefentation of the circumfcribing fquare of the 
 required circle. Draw the fecond diagonal M S, interfedling the firfl in the 
 
5^ PRACTICAL PERSPECTIVE. 
 
 [ Plate i3.] point g ; through which point draw the lines b g d to 0, and e g f, parallel to 
 MN, which will obtain the four points wherein the infcribed circle will touch 
 the fides of the fquare, b, e, d, and f. Let the infcribed fquare be now 
 defcribed to obtain four other points in the curvature of the circle. Draw the 
 lines a and c ©, cutting the diagonals in the points i, m, n, and o, which 
 will be the four angles of the infcribed fquare, and four points of the circum- 
 ference of the fought circle; which may very corredlly be drawn through the 
 eight points b, i, e, m, d, n, f, and o, as is fhown in the figure. - 
 
 EXAMPLE XIV. 
 
 // is required to jind the rcprefentation of a circle in a vertical plane, per- 
 pendicular to the pi£lure, the circle touching the plane of delineation. 
 
 Let the line N V (Fig. ii) be the fide of a fquare circumfcribing the re- 
 quired circle; let P © Q^be the horizontal line, and the centre of the 
 pidlure. The centre of the pidlure being the vanifhing point of all lines per- 
 pendicular to the pidure, will be the vanifliing point of the top and bottom 
 lines of the circumfcribing and infcribed fquares. 
 
 As was defired in the laft Example, if the Student defcribe a fquare within a circle of the required dimendons, 
 he will find it equal the length h p, fet off equally on each fide the middle point k. 
 
 Proceed as follows. Draw the vertical line X, which line will be the va- 
 nifliing line of the plane of the required circle (Def. 15). Make X equal 
 the diftance of the pi(fture (Def. 10), the point X will be the vanilhing point 
 of one of the diagonals of the fquare circumfcribing the required circle. 
 
 Draw the lines V and N ; draw the diagonal N X, which, inter- 
 fe(5ling the line V © in the point T, determines V T for the fide of the fquare ; 
 and drawing the line TS parallel to V N, completes the circumfcribing fquare. 
 Draw the diagonal VS, interfering the other in the point z, the centre of the 
 required circle; through which point draw the lines 1 z k, and x z f, deter- 
 mining the four points in which the circle comes in contad; with the external 
 fquare, the points f, x, 1, and k. To obtain the internal fquare draw the 
 lines p and h ©, which interfediing the diagonals of the circumfcribing 
 fquare, determine the four angles of the internal one, which are alfo four 
 points in the circumference of the required circle; the points q, r, s, v. Eight 
 points in the circumference are now obtained, viz, the points k, q, f, r, 1, s, x, 
 and V ; through which the curve may be traced with very fuificient accuracy. 
 
 The two lall Examples confidered unitedly, will ferve to exemplify the 
 do(5lrine of vanifhing lines; and the truth and infallibility of the rules of per- 
 fpettive delineation. 
 
 4 
 
JV.ATi: //f 
 
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 I 
 
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 ^^^_ 
 
 _^ 
 
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 A 
 
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 MV 
 
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 V 
 
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 / 
 
 ^^=^ 
 
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 a b c /-\ d e f g ;li 
 
 _^S>«f„ ,/t^ -,<•„/ 4yt'„«. lA./t-^ . I„f~./ 
 
PRACTICAL PERSPECTIVE. $3 
 
 When arches are in a vertical plane, and the plane of delineation placed pa- 
 rallel to the plane they are in, they muft then be truly geometrically drawn on 
 the pidlure, their decrealed dimenfions, agreeably to their diftance from the 
 pidurc, muft be obtained, which bifeded, the arch muft be ftruck on that 
 centre. But when they are drawn as fltuated in planes inclined to the plane of 
 delineation, that is, when they are the reprefentations of original arches 
 ftanding inclined to the plane of delineation, then will they vary each from 
 the other, agreeably to their place and diftance, and in juft relation thereto. 
 
 When arches are of equal magnitude, on the fame level, and in the fame plane, 
 as are the arches of a long arcade, the trouble of finding their apparent curva- 
 ture, when inchned to the pidlure, is but little, as the fame heights of the 
 ordinatcs that ferve for the finding of one ferve for all, were they ever fo many. 
 
 EXAMPLE XV. [Plate 19.3 
 
 Let the three equal arches. No. i. No. 2, and No. 3 (Fig. i, P/ate 19), 
 JlandiDg in a plane inclined to the plane of delineation, I K, in the angle R 1 K, 
 be requited to be delineated ; and let S be the Jlation of the obfcrver. 
 
 When arches are not drawn to a large fcale, three points found in their cur- 
 vature between their extremes, or fpringings, will be fufficient to trace their 
 curves through. In the arches here required to be drawn, let the points c, d, e. 
 No. I ; h, i, k, No. 2 i and n, o, p. No. 3 ; be the points of the ordinates, 
 taken all equally diftant from their centres. The vifual lines drawn from each 
 of the ordinates, alfo from the extremes of the fpan of each arch, to the ftation 
 S, will cut the plane of delineation in the points a, b, c, d, &c. Produce the 
 plane of the arches to the plane of delineation for an interfedlion at I. 
 
 Let the three arches be fuppofed to be feen below the horizon, which let be 
 equal the height I X, Fig. 2. The line XV will be the horizon, and I G will 
 be the ground line. Set off" the diftances of the interfedions of the vifiial rays 
 a, b, c, d, ficc. Fig. i, from the interfering point I, on the ground line I G, 
 Fig. 2, a, b, c, d, &c. and draw the vifual lines perpendicularly tlirougli 
 them, and alfo a vertical line through the interfering point I. 
 
 On the interfering line I X, Fig. 2, fet up the heights of the ordinates 
 taken, of the required arches, that is, make 1 1, and 1 v, equal the ordinates c t, 
 and dv. Fig. i, and draw the lines IV, t V, and v V, Fig. 2, cutting the 
 vifual lines of the ord nates, in the points i, 2, 3, No, i ; 4, 5, 6, No. 2 j 
 7,8,9, No. 3 ; through which points the curves may be drawn from the 
 fpringing of the arches with a fteady hand with fufficient accuracy, 
 
 o 
 
54 PRACTICAL PERSPECTIVE. 
 
 [Plate 19.] EXAMPLE XVL 
 
 Suppofe the arches of the lajl example •■d.cre required to he drawn above the 
 horizon, at any height at pleafure, fuppofe at the height IN, Fig. 3; the 
 horizon andjlation remaining as before. 
 
 The flation and pofition of the arches being as before, the fame vifual line^ 
 with the laft, both in plan and elevation, will ferve; it will only be neceflary to 
 heighten the vifual lines. Fig. 2, to Fig. 3. 
 
 Make Nx and N z, Fig. 3, equal the heights of the ordinates c t, and d v, 
 of the plan Fig. i, and draw the lines NV, z V, and xV, cutting the vifual 
 lines of the ordinates and fpringings in the points o, o, o, o, o, &c. through 
 which the curves may with care be traced. 
 
 Fig. 4, fhows an arcade, ftanding on piers, agreeably to the dimenfions and 
 height of the arches of the laft example. 
 
 Should the arches be unequal, as the arches of a bridge generally are, Hill the 
 fame mode of drawing ordinates, and fmding their heights according to their 
 diftancc, muft be purfued. The arches differing in dimenfions or in figure, 
 that is, being either femicircular, fegments of circles, or femi-cllipfes, will 
 caufe only a little more trouble in the operation of finding them. 
 
 EXAMPLE XVII. 
 
 Let Fig. 5, be the geometrical elevation of a bridge. Let it be fuppofed to 
 ftand perpendicularly on the line AC ; and let B be the ftation whence it is 
 viewed. Let I K be the g-found line of the plane of dr-lineation. 
 
 // is required to fnd the perfpe£live reprefentation of the above bridge^ under 
 the Jlated premifcs, f'/ppo/ing the horizon equal the height I N, Fig. 6. 
 
 Let the ordinates of the different arches be regularly ailumed; and from 
 their points of interfedion, i, 2, 3; 4, 5, 6; 7, 8, 9, en the chord line A C, 
 let vifual rays be drawn to the ftation B, as alio from the piers or fpringing of 
 the arches, cutting the plane of delineation in the points a, b, c, d, e, &c. ; and 
 let the chord line A C be produced to D for an interfedlion. Draw the line 
 B E, from the flation B, parallel to the chord of the arches, AC, for the va- 
 nifliing point of horizontal lines in that dired;ion. 
 
 Draw the horizontal line O N, Fig. 6, and parallel to it the ground line 
 through the point I. Make N O equal the diflance D E, Fig. 5, and let off 
 the diftances of all the vifual rays, Da, D b, D c, &c. Fig. 5 ; at la, lb, 
 Ic, &c. Fig. 6, and draw the vifual lines through them. 
 
PLATE XC\. 
 
 bcde f g- K X k 1 m IX o p q r 
 
 FuAtyKdbYJ-Vnllim (I,/ i J.<'m 
 
PRACTICAL PERSPECTIVE. 55 
 
 Firfl, to obtain the points in the curvature of the two fmall arches, which [Plate 19.] 
 being of a fize, and their ordinates of equal height, the operation of finding 
 the heights of the perfpedlive ordinates will ferve for both, as was fliown in the 
 laft example. Make the heights I 2, 1 3, on the interfetfling line I N, Fig. 6, 
 equal the heights of the ordinates of the fmall arches, Fig. 5, and draw the 
 lines 3 O, 2 O, and I O, cutting the vifual lines of the arches in the points 
 o, o, o, o, o, and o, o, 0,0,0; through which points the curve may be traced, 
 as is there done\ On the interfedtion. Fig. 6, make I 4, and I 5, equal the 
 heights of the ordinates of the centre arch No. i , Fig. 5 ; and draw the lines 
 5 O and 4O, cutting the vifual lines of the centre arch in the points c,c,c,c,c; 
 through which the curve may readily be drawn. I 4 and 16 are equal the 
 heights of the coping of the bridge C b and d e, Fig. 5 ; from which points, if 
 lines be drawn to their vanifhing point O, the proper vifual lines will be inter- 
 fedled, as in the figure, in the points a, a, j, a ; joining which points, by 
 right lines, completes the entire of the bridge, and, cleared of its operative lines, 
 and ihaded, would be as Fig. 7. 
 
 Thus, by finding of points in the curvature of regular or irregular lines, are 
 their apparent forms obtainable, nor can there be any other method devifed, by 
 which that end can be effetled. 
 
 EXAMPLE XVIIL [Plate 20.] 
 
 Let it be required to find the apparent form of a circular flrud.ure, part cy- 
 lindrical, part conical, in the fhape of a potter's kiln. Fig. i, Plate 20, is the 
 geometrical elevation of the given ftrudlure; its bafe, A BCD, cylindrical; its 
 fuperftrudurc, B E F C, conical. The circle a a a a, &c. Fig. 3, is the plan of 
 the bafe, and the fmall concentric circle 4444, &c. the dimenfions of the 
 circle of the top of the conical part, at E F, Fig. i . 
 
 It is required to find the apparent form of fuch a figure, from the fiation S, 
 the plane of delineation being ai \ X, and the height of the horizon being equal 
 the height AG, Fig. i. 
 
 Circumfcribe and infcribe the two circles of the plan Fig. 3, by fquares, and 
 draw vifual rays from the angles of thofe fquares to the plane of delineation. 
 Produce the diagonal of the fquares MK to I for an interfedion, and draw a 
 line from the fiation parallel to the diagonal, to obtain its vanifliing point, 
 which will be difi:ant from the centre of the pidure ©, equal the diftance S Q. 
 
 • The Student is advifed to praftife this£;(ampIeto a much larger fcale. 
 
56 PRACTICAL PERSPECTIVE. 
 
 rPlate 20. 1 A line from the ftation S, drawn to the pifture, parallel to the diagonal of the plan, would not come within 
 the limits of the plate ; half the diftance is therefore taken, at s, and the line s Z drawn. Q Zi will then be half 
 the diflance of the vanifliing point, that is, Z will be equal © s, or half O S. 
 
 Firft, to the delineation of the cylindrical bafe. The two circles of the top 
 and bottom being equal and parallel, 'tis only rcquifite to find them, and being 
 joined together by the external vertical lines, tangents ^ to them both, the whole 
 figure is completed, as is fliown, Fig. 5. 
 
 Prepare the pidure, Fig. 4. The line KK is the horizon, and LM the 
 ground line, diftant from each other equal the height AG, Fig. i. From the 
 centre of the pi(flure © , fet off the diftances of the feveral interfedtions of t!ie 
 vifual lines from the plan Fig. 3, as alfo the intcrfed:ing point of the diagonal, 
 I, at the correfponding letters b, c, e, and f, and L, Fig. 4. Draw the inter- 
 fediing line LP, and the vifual lines of the fquares through the points b, c, e, 
 and f, and make © d on the horizon equal the diilance of the vanilhing point 
 of the diagonal, that is equal twice © Z, Fig. 3. 
 
 On the interfering line Fig. 4, fet up L E, equal the height of the cylin- 
 drical bafe of the objedl A B, Fig. i ; and draw the lines Ed and Ld cutting 
 the vifual line of the exterior angle of the fquare in the points m and n, and 
 draw the horizontal lines m o and n p, to the vifual line through the oppofitc 
 angle of the fquare. Then draw the lines m©, n©, o©, and p©, and vvv 
 and r t, completing the circumfcribing fquares of the top and bottom circles. 
 Draw the other diagonals, VO and rp, which, interlecling, determines the 
 centres of each of the circles, through which centres, diameters being drawn to 
 the middle of the fides of the fquares, the four points are obtained wherein the 
 infcribed circle touches the fides of the fquare. 
 
 The diagonal lines Ed and Ld alfo cut the vifual line of the angle of the in- 
 fcribed fquare in the point 2 ; and drawing the line 2 3, and the lines 2 4, and 
 35, to Q, the internal fquare 2453 '^ determined, and four other points in the 
 curvature of the required circle are obtained ; through which eight points the 
 curve may very well be drawn. The fame is to be done of the circle above 
 the horizon, but it being fo contradled- in its appearance, from its nearnefs to 
 the horizon, the procefe of obtaining it can better be traced from infpedion 
 of the figure, than by defcription. Draw the vertical lines a If and cd, tangents 
 to the above curves, and the bafe of the figure will be completed ; the extent 
 of which will be found to be exadlly the fame with the fquare comprehended 
 
 » A Tangent to a circle, or other cun e, is a right line which juft touches the curve, and of courfe in nowife 
 coincides with it, but the curve quits it inuiiediateiy on each fide. 
 
PRACTICAL PERSPECTIVE. 57 
 
 between the points of interfedlion x and z, Fig. 3, where vifual rays from [Plate 20.] 
 the flation are tangents to the cylindrical bafe of the objedl. 
 
 To obtain the circle of the top of the objed:, draw the diagonal line Pd, iuti 
 making the height LP, on the interfcdlion, equal the height TR, Fig. 1. 
 
 The Ihort lines e, f, g, and b, are the vifual lines anfwering to the vifual in- 
 tcvicaions 0,0,0,0, (Fig. 3,) of the two fquares circumfcribing and infcribing 
 the circle of the top, which interfedlions are fet off from the centre point 
 B, the ray of the dotted vifual line in the middle of the objedt Fig. 4. Where 
 the line e interfeds the diagonal line Pd, draw the horizontal line e,b, and 
 the lines e © , and fj Q , to their vaniHiing point O. Where the line b inter- 
 feds the diagonal hne at /, draw the horizontal line / k, and the circumfcribing 
 fquare ehik will be completed. Draw the other diagonal line of the fquarc, 
 and through the centre of the fquare draw the Imes 00, and 00, determining 
 four point^I of the curve of the circle. The inner fquare is obtained in like 
 manner with the foregoing, from the lines f, and g, by which four other points 
 are had in the curvature, 3, 3^ 3^ 3' through which eight points the circle 
 may eafily be traced. The circle of the top, and the circle of the bafe, being 
 joined by the tangent lines ol>, and od, the whole required figure is completed. 
 
 EXAMPLE XIX. 
 
 Let it be required to find the reprefentation of a circular objed, of which let 
 Fig. 2 be the geometrical elevation. The bafe A B C D is the fame as the bafe 
 of the former objed, but the fuperftrudure is fomewhat different, as well as 
 more complicated ; the conical part being the form HIKE. The circular plan, 
 Fig. 3, IS as well the plan of the prefent as of the former objed, with the ad- 
 dition of two circles expreffing the dimenfions of the flructure at HL and IK. 
 The circle of the gallery is the fame, in diameter, as that at HL, and the top 
 the fame with EF of the former objed. 
 
 // is rerjidred to find the perfpeBive of the above objeSf, Fig. 3 being the 
 ■plan and ft nation 'with the plane of delineation VZ, and ?> is the fat ion. 
 
 Let each circle of the plan, Fig. 3, be infcribcd and circumfcribed by a 
 fquare; and from the angles of thofe fquares, let vifual rays be drawn to the 
 plane of delineation, and let the general diagonal, LN, be produced to P for 
 an interfedion with the pidure. 
 
 Let LM, Fig. 6, he the ground line of the pidure, and let KK be the 
 horizon. is the centre of the pidure, and g, on the horizon, is the va- 
 niihing point of the diagonal line, g being equal the diflancc V, Fig. 3. 
 
 p 
 
5S PRACTICAL PERSPECTIVE. 
 
 [Plate 2c.] The viTual lines through the points b, c, e, and I, Fig, 6, are the vifaal 
 lines from the near angles of the two fquarcs of the great circle of the bafe of 
 the object. The height MO, on the interfe<ftion, is the height of the bafc of 
 the objed:, equal the height DC, Fig, 2. The bafe of the prefent example 
 being cxadlly the fame with that of the former, it is needlefs to go through 
 the procefs of obtaining it; the pra6tice of the preceding, and infpedion alone 
 of this, will be ample information as to its attainment. MP, on the inter- 
 feclion, is the height of the circle H L, Fig. 2, The line Pg being drawn, 
 interfedls the vifual line of the angle of the fquare, determining the point 1 of 
 one of the near angles of that circumfcribing fquare ; from which point the 
 whole may be readily completed ; but which procefs being the fame with the 
 finding the circle of the gallery above, we will proceed to the defcription of 
 it, as, being more difcernible, it will better anfwer the purpofes ot both. 
 
 Draw up the vifual lines cc, and ee, the vifual lines of the two near angles 
 of the fquare circumfcribing the required circle. Make M C), on the interfe<ftion, 
 equal the height of the gallery TR, Fig. 2, and draw the diagonal line Qg 
 interfering the vifual line ee, in the point e, anfwering to the point 1 of the 
 fquare below. Draw the horizontal line of the fquare ce, and from the points 
 c and e draw lines to ©, the vanifhing point of hnes perpendicular to the pic- 
 ture. The line from the point c interfeds the diagonal in the point m, from 
 which draw the line mn, parallel to ce, completing the fquare ecmn; in 
 which, draw the other diagonal en determining the centre of the circle a. 
 Through the centre, a, let two lines be drawn through the fquare, one parallel to 
 ce, and the other in diredion to the vanifliing point ©, which will obtain four 
 points, I, 2, 3, 4, in the circumference of the circle. The Ihort lines r and t, 
 anfwer to the vifual lines of the near angles of the infcribed fquare, agreeable 
 to the vifual interfedfions r and t, Fig. 3. Thofe lines intcrfecl the diagonals 
 in the points 5 and 6, from which, lines being drawn in diredion to O deter- 
 mine the two other angles of the fquare, and points in the circle, 7 and 8 ; . 
 through which eight points let the circle of the gallery be drawn. The fquare 
 5 6 7 3, is the exterior fquare of the circle of the body of the objedt at top, in 
 ■which, four points are already determined, x,x,x,Xj and the four other points, 
 z, z, z, z, arc readily obtained from the vifual interfedions 00 of that fquare 
 in the plan Fig. 3, and the circle drawn through them ; draw the lines of 
 the conical body of the objed xk and xl. There only remains to find the top 
 circle at M N, Fig. 2. 
 
I'l^ATHXX ■ 
 
 r„l,Ull„l l;.f.,' >•■•' . <W <■<!"■ 
 
PRACTICAL PERSPECTIVE. 59 
 
 Make M R, on the interfedion, equal the height TO, Fig a. jinr! Hraw the CPlate 20.] 
 diagonal line Rg, whicli cutting the contiguous vifual line^, determines tlie point 
 d, one of the angles of the outer fquare ; from which point, the fquare dagh 
 is obtained. Th.e vifual Lnes ^/, ^,<r,d',^nfwer to the vifual interfedtions 0,0,0,0, 
 from the angles of the correfponding fquare in the plan Fig. 3, The procefs of 
 obtaining the inner circle being the fame with either of the preceding cafes, 
 the mere infpediion of the figure will fuflice as to the procefs, and convey very 
 ample information. The height MT, on the interfedion, Fig. 6, is the 
 height of the centre of the ball, equal the height TP, Fig. 2; and the line 
 Tg being drawn, where it cuts the dotted line through the middle of the ob- 
 jed:, at E, is the place of the centre of the ball in the reprefentation. Thus is 
 the whole that is neceflliry to be obtained ftridtly by rule accomplifhed ; the 
 other lines and additions to the general figure are eafily fupplied by the hand 
 and judgment. It would be perfedly irklome to obtain every minutia by 
 rule; the leading figure and features be.ng found, if the judgment cannot 
 trace the reft, little will be done by fuch a hand. 
 
 The required lines being drawn in ink, and the operative lines rubbed out, 
 the objedl will remain difencumbercd, which Ihaded, may be, as Fig. 7, not 
 unlike the light-houfe en the pier at Ramfgate, whence the idea was taken. 
 
 The mode that has been adopted to find the perlpe(5live of a circle, by ob- 
 taining eight points, regularly allumed, in its circumference, would as well have 
 obtained the rcpreientation of an odbigon, if, m place of tracing a curve through 
 each two points fo as it fhould fall in a fijwing unbroken line through the fuc- 
 cecding, they had been joined together ty right lines, chords to thofe fame 
 curves; as is fhown geometrically Fig. i, Plate 21, and perfpe£lively in [Plate ai^} 
 Fig. 2. But a ftiU more fimple method would be as before recommended and 
 fliown, Fig. 8, Plate 18, by drawing and finding the parallel lines from the 
 extremes, of the oppofite fides ; which we will now put in pradlice. 
 
 EXAMPLE XX. 
 
 Figure 3, Plate 21, is an odtagon, around which, let a fquare IKLM be 
 defcnbed J let the parallel lines C F, BG, and AD and HE, be drawn. 
 
 // is required to jind the perfpe^live appearance of the above oElagon, hy 
 jinding the circumj'cribing fquare J and the parallel lines tvithi/i, from a given 
 flation and poi/it of view. 
 
 Let the line V X be the place of the plane of delineation parallel to a fide of 
 the fquare. Let S be the Itation. The centre of the picture O will be the va- 
 4 
 
6o PRACTICAL PERSPECTIVE. 
 
 [Plate 21.] nifliino' point of ^'t- l'"es pcipencficular to the pidlure; and the diftance of the 
 picfture S O, laid down on the horizon, on each fide the centre 0, will give 
 the vanifliing points of the diagonals of the fquare. Draw the vifual rays in 
 diredlion to tne flation cutting the plane of delineation in the points 
 k,c,b, i,a,h,m, and produce the diagonal KM to N for an interfedtion. 
 
 Prepare the pidlure, Fig. 4, by drawing the ground line G L, and parallel to 
 it, the horizon, YZ. © is the centre of the pid;ure, and O Y and Z are each 
 equal the diftance of the pidiure S © in the plan, wherefore Y and Z are the 
 vanirtiing points of the diagonals of the fquare, and of all lines parallel to them. 
 The vifual lines through the points k, c, b, i, a, b., and m, anfwer to the cor- 
 rcfpoiiding vifual interfedlions in the plan. L, in the interfering point, and 
 L N, the interfering line. We will firft obtain the reprefentation of the 
 odagon as lying in the ground plane. 
 
 Draw the diagonal line LY, from the interfering to the vanifhing point. 
 The point f, where it cuts the vifual line through the point m, is the place of 
 the near horizontal fide of the fquare, fg. Draw the lines g ©, f ©, and d 1, 
 which will complete the fquare fgdl, of which, the line d f is a diagonal. 
 From the points e and e, where the vifual lines through the points a and h touch 
 the near fide of the fquare, draw the lines e ©, and e 0, crofling the oppofite 
 fide of the fquare in the points e and e; and where they crofs the diagonal d f 
 in the points v and x, let horizontal lines be drawn through thofe points to the 
 oppofite fides of the fquare, cutting them in the points e, e, e, ej and drawing 
 the corner lines ee, ee, &c. the ocftagon e, e, e, e, c, e, e, e, is completed. 
 
 het it be required to find the appearance of the fame oBagon, as feen elevated 
 above the horizon, dire^ly over the one found on the ground plane ; fuppofe equal 
 the height LP 0/7 the interfeEiion. 
 
 Draw the vifual lines of the ground figure up to Fig. 5. Where the diagonal 
 
 line PY croflTes the near vifual line in the point a is the place of the near fide 
 
 of the fquare around the odiagon, and the horizontal line ab \% that fide. 
 
 Draw the lines bQ), «0, and cd, completing the fquare ^j/^r 7, Where the 
 
 vifual lines, through the points a and h below, crofs the fide of the fquare ab, 
 
 at 0,0, let lines be drawn to the centre, , crofiing the oppofite fide of the fquare 
 
 cd, in the points 00 j and where they crofs the diagonal line in the points m 
 
 and n, let horizontal lines be drawn through thofe points to the other fides of 
 
 the fquare, cutting them in the points 0,0, and 0,0; the remaining fides of the 
 
 odtagon at the corners being joined together, the whole oragon o, o, o, o, o, o, o, o, 
 
 is completed, as required. 
 
t^. 
 
 .>^. 3. 
 
 Jjdr/'. ^y 
 
 K D 
 
 E T. 
 
 ,^t,,An> .'AA/tit/Cf./ /-^ y.t^^fn.. J(i(r/V>M /"'.vwC-* 0*e*f> . 
 
IPP 
 
PRACTICAL PERSPECTIVE, 6i 
 
 Thus, at whatever height required, the proccfs of finding the figure is with [Plate 21. J 
 facihty performed: as fuppofe at the height LO, on the intcrfedlion ; tht 
 diagonal hne OY being drawn, cuts the near vifual hue, Fig. 6, in the points, 
 whence is drawn the fide of the fquare e z ; from which the whole may be 
 completed by the fame procefs as before fliown in Figures 4 and 5. 
 
 The diagonal vanifning points Y and Z are as well the vmiilhing points of 
 the corner fides of the odeagon, as of the diagonals of the fquare j for thofo 
 fides of the o<Stagon are parallel to the diagonals (fee the plan, Fig. 3) ; they will 
 therefore have the fame vanifhing points. In the figures jufi: obtained, if a 
 ruler be applied to thofe lines, they will be found to tend corredly to their fe- 
 veral vanifliing points; to which they are continued, in the figures, by dotted 
 lines agreeably to their direction. Thus will the ufe of thofe vanilhing points 
 contribute to the correcftly delineating the figure, and at the fame time illullratc 
 the truth and beauty of the rules of perfpcdlive. 
 
 Joining the correfponding points of the 0(flagons, above and below, by 
 perpendicular lines, a folid figure will be formed, like to Fig. 7, or like 
 to Fig. 8 ; where the rules, but jull: performed, are exemplified in an appro- 
 priate figure, and which is a view of the light-houfe on the North Foreland near 
 Margate. 
 
 Thus by a Very fimple method may, apparently complicated figures be 
 obtained, with the utmoft corrednefs and facility. Thus may a hexagon be 
 defcribcd ((ec Fig. 7, Plate 18), and foof any other regular polygon. 
 
 I will give one more example of general figures, more complicated than any 
 that has hitherto been defcribed ; and after performing it, will proceed to 
 give fome general rules, governing the procefs of taking views, whether of 
 fingle or many objeds. This fhali clofe the firfi: divifion of my fubjedl, whicii 
 fliall be refumed again with an inquiry into many interelling particulars and 
 minutiiP, whereby a more intimate knowledge cannot fail of being obtained. 
 
 EXAMPLE XXI. [Plate 22.] 
 
 Let Figure i, Plate 22, be the general plan of a church., which, like moft 
 country churches, let be compofed of feveral parts. Let A BCD be its 
 body; EFGH its tower; IKLM, and M L N O, be fubordinate parts of 
 the building; and let abed be the porch. Let Fig. 2, be its geometrical ele- 
 vation ; the ends and meafuremcnts A B and B C, anfwering to I M and M O 
 in the plan Fig. i ; and the points of the roofs D, l£, and F, Fig. 2, anfwering 
 to the lines of the ridges Q R, T V^ and P L, Fig. i . 
 
62 PRACTICAL PERSPECTIVE. 
 
 [Plate 22.3 // is required lo fnd the perfpe&ive reprefe/ttation of the above building, on 
 the plane of delineation Y Z, the Jiation being at S. 
 
 Find the vanifliing points Y and Z, of the horizontal lines of the building by 
 the lines S Y and S Z being drawn from the ftation parallel to them. © is the 
 centre of the pi(5tiire. Draw the vifual rays from the vifible angles of the ob- 
 jet^t, in dire<ilion to the ftation S, till they interfe(5t the plane of delineation. 
 
 When a complicated objeft it to be drawn, that is, when it is compofed of many parts, it neceflarily gives 
 life to a number of vifual rays for the precife detentiination of tliofe parts, and the whole together will form 
 an apparently confufed number of lines. But the eye that views them properly fees no confufion in them ; it 
 views them as the eye of the adronomer views the itarry hemifphere, placing each duller, and arranging each 
 Uraggling brilliant in its proper fign. 
 
 To avoid confufion of rays in a very complicated object, it is advifable to ufe different coloured inks ia the 
 claffing of the rays, as alfo diilerent degrees of flrength of thofe colours to particularize different parts. 
 
 In the delineation of fuch an obje(5t as the prefent example, the firft confi- 
 deration is the choice of a proper interfedlion j for although any interfecflioii 
 will do, one fliould be chofcn, which fliould unite moft parts in its diredtion, 
 with the greatefl: exadtnefs and lead trouble. In the prefent inftance, none feems 
 fo eligible as the diredlion of the roof PL M, which let be produced to W. 
 
 In the pidure, Fig. 3, G L is the ground line; let G V be the height of 
 tlie horizon, the line VX will then be the horizontal line. ©, in the horizon, 
 is the centre of the pidlure, from which, place the diftances of the horizontal 
 vanifiiing points ©V, and ©X, equal the diflances ©Y and ©Z, Fig. 1. 
 AB, Fig. 3, is the interfering line, and all the vifual lines on the plane of de- 
 lineation are drawn agreeably to their interfedlions on the ground line in the 
 }>lan. 
 
 On the interfecling line, the height A C is made equal the height AG of the 
 elevation. Fig. 2 ; and the lines C c and A a being drawn in diredtion to the 
 vanifhing point V, determine the height ac, the height of that part of the 
 building on the viiual line anfwering to the ray from the point M in the plan 
 Fig. I. Through the points a and c draw the lines de and bf to their vanifii- 
 ing point X, determining the plane bdef, the reprefentation of the plane 
 AG lie. Fig. 2; the vifual lines bd and fe anfwering to the rays from the 
 points I and O, in the plan. Draw the lines dh and bg tending to their 
 vanilhing point V, to the ray from K in the plan, completing the plane bghd. 
 On the interfedlion, make the height AD, equal the height of the roof N E 
 of the elevation Fig. 2, and draw D i in diredlion to V j through i draw the line 
 kl, to the vaniOiing point X, touching the vifual lines of the roofs in th« 
 
PRACrrCAL PERSPECTIVE, 65 
 
 points k and 1; draw the lines km, mh, kd, k c, 1 c, and le, which will [Pbteaa.J 
 complete the whole of the ftrudlure over the plan IKN O, Fig, i. 
 
 The height of the roofs of the low buildings is equal the height of the up- 
 right walls of the body of the ftrufture, as is fhown by the line P R, in tb.e 
 elevation Fig. 2 ; wherefore, the line m o, and the return line o n, may be drawn 
 to the vifual lines correfponding with the interfecftions from the angles A and B 
 of the plan. Alfo, from the angle g, the line gs may be drawn, which will de- 
 termine the lines sr, rt, and tp, of the porch. Make AE, on the interfedion, 
 equal the height of the roof BF in the elevation, and draw the line E V, de- 
 termining the ridge of the roof between the two vifual lines from the points 1' 
 and L of the plan. Draw the lines of the gable end vo and vz; the point z is 
 obtained by the line om being drawn to its vaniflaing point X, cutting the 
 vifual line from the angle D of the plan, in the point z. 
 
 Make A G and A F, on the interfedtion, equal the heights of the tower, BO, 
 and B M, of the elevation, and draw the lines G V and F V, cutting the vifual 
 hue from P in the plan, in the points a and 6 ; through which points draw the 
 lines ac and ef, to their vanifhing point X; and the lines cd and eg, to their 
 vaniiliing point Vj the points g, e, and y, being in the proper vifual lines 
 from the angles of the tower F, E, and H, in the plan. Complete the tower by 
 drawing the lines Jg, de, ae, and af. 
 
 The prcfent example was contrived to elucidate the general pradlice of vanifli- 
 ing points, which are as well to be obtained of other pofirions of lines, as hori- 
 zontal ones. It is not always that the vanifliing points of inclined lines are re- 
 quired, but they arc often iifeful, and fomctimes abfolutely necefTary. In the 
 geometrical elevation, Fig. 2, the lines MO, P F, G D, IE, are all parallel 
 lines, as alfo are the lines OF, FR, EH, and DI; and though fituated in 
 different, yet they are in parallel planes, and will therefore have a common va- 
 nifliing point. A line drawn perpendicularly to the horizon through the vanifhing 
 point X (Fig. 3), as LO, will be the vanifliing line of the plane of the end of 
 the church over the line IG of the plan, alfo of the end of the body AD, like- 
 wife of the fide of the tower EH. And a line drawn through the point V 
 (Fig. 3), perpendicularly to the horizon, as G M, will be the vaniihing line 
 of the planes over the lines (Fig. i), IK, A B, ab of the porch, and FK 
 of the tower J and all lines in thofe planes, or the boundaries of thofe planes, 
 will have their vanifliing points fomewhcre in thofe vanifliing lines ^ 
 
 To obtain the vanifhing points of the inclined lines of the roofs and tower, 
 
 ' This circumftance of finding the vaniOiing points of inclined lines was/before treated on in Examnle 8,^, 
 Fig. 5, Plate 15 ; but here it is more fully exemplified. 
 
64 PRACTICAL P E R S P E C 'f I V E. 
 
 1_ Plate 22. J proceed as follows: take the diilance of the vanifhing point, Z, from the ftatioa 
 S, in the compalTes ; that is, take the length of the line S Z, and apply it on 
 the horizon from X to H. At the point H make an angle with the horizontal 
 line, equal the angle of the roofs a. Pc, Fig. 2; the curve K I, and the diflance of 
 it from the centre H, being equal to the curve a< , and diftance of it from its 
 centre P; then is the angle KHI equal the angle of the roof aPc, Fig. 2. 
 Produce the line H K to Q ; Q will be the vanilhing point of the line ea of the 
 tower, alfo of the parallel lines ov, d k, and cl; which, though obtained by 
 a different procefs, will all be found, by application of a ruler, to tend truly to 
 that point, as is Ihown by the dotted lines in tl-e example. 
 
 A like procefs being performed of the diflaace of the vanifhing point Y, 
 from the flation S, will obtain the vanifliing point of the fan^e inchnation of 
 lines in the other planes of the objedf. Take the length S Y in the compaffes^ 
 and fct it off on the horizon, from V to N. At the point N, make an angle 
 INT, on the horizon, equal the angle KHI, that is, equal the angle of inclination 
 of the roof, aPc, Fig. 2. The line NT produced to M in the vanilhing 
 ■ line G M, will be the vanilhing point of the line Je of the top of the 
 lower, alfo of the lines W3, and y^, of the porch (the inclination of the 
 roof of the porch being the fame as the other roofs of the body of the church), 
 as is Ihown by the dotted lines in the example. The walls of the porch arc 
 obtained from the height AP, on the incerfedion, equal the height JT, 
 Fig. 2. P;« being drawn to the vanifhing point V, and m /i to X gives the 
 lines n 5, 53, and 3 2. 
 
 It mufl: be obferved that the inclined lines ^7/, le, kc, and vz, have a com- 
 mon vanifhing point, obtainable if required ; and which vanifliing point will 
 be in the fame vanifliing line with the point Q, and as much below the hori- 
 zontal vanifliing point X, as the point Q is above it j to which point, were it 
 obtained, thofe lines, already drawn, will be found exadly to tend. It is leldom 
 abfolutely neceffary to have both thofe points ; in the prefent inftance one of them 
 only, the point Q, is obtained, which would anfwer every end required of 
 both ; for fuppofing it were left to that vanifliing point for the finding the in- 
 clined lines,, the vifual lines being drawn, and the heights of the upright walls 
 being found, the line d k drawn in diredion to the vanilhing point O, determines 
 one fide of the gable-end at the vifual line in tlje middle ; the other is accom- 
 plilhcd by joining the points k and c together. So of the other gable, cl being 
 drawn, le is alfo had by joining the points 1 and e together. 
 
 To complete the whole, draw the line xy, on tlie tower, from the point 
 jc, to the angle of the tower, in diredion to the vanifliing point Qj thea 
 
M 
 
 V-*-^ 
 
 H 
 
 B P 
 
 E 
 
 F^ 
 
 . J 
 
 F/y.J 
 
 A 
 
 K 
 
 ^>V / 
 
 Fu;.7 
 
 O 
 
 M 
 
 ^ 
 
 yr 
 
 H 
 
 */ I? o m 
 
 1 
 
 •U 
 
 V 
 
 tl^TE X\II. 
 
 Fti]. 7 
 
 .i/t -r 
 
 A-. ' : X — L 
 
 F: 
 
 O 
 
 R 
 
 // 
 
 fl A' C 
 
 /•/./..; 
 
 G 
 
 SB. 1 
 
 P t 
 
 Inl'lilJullnJ.iLH.ill.m <'./'' 
 
PRACTICAL PERSPECTIVE. 65 
 
 draw die lines ah, and n/6 , to their proper vifual lines, and vaniHiing points f Plate 22.1 
 
 V and Q. The putting on of the Ipire is a work of fome confideration, and 
 
 muft be proceeded on with thought and care. The bafc of the fpire is intended 
 
 to be a regular o(5lagon. If the two external lines in the geometrical of the 
 
 fpire, be continued till they touch the fides of the tow€r, as is done at K and L, 
 
 (Fig. 2), and an odtagon be there conftruded , extending the fquare of the 
 
 tower, it will be the bafe of the fpire. Set up the height of the fpire B W, 
 
 Fig. 2, on the interfed:ion. Fig. 3, at B ; alfo the height of the bafe line KL, 
 
 at R ; and draw the lines B V and R V ; the firfl-, cutting the vifual line through 
 
 the centre of the tower in the point O, determines the height of the fpire j the 
 
 other, cutting the tower in the point u, determines its bafe. Through the 
 
 point u draw a line around the tower, and find the points of the o(9:agon in the 
 
 middle of each face of the tower, to w hich let lines be drawn from' the top O, 
 
 and the fpire and whole objed; will be completed, as is (hown in the Example. 
 
 I have now gone through the procefs of finding the above complicatecf 
 objed:. I had expedations of performing it with lefs confufion of lines than" 
 the refult has made neceffary ; but one thing fucceeding another, and each ne- 
 ceffitated to remain, for the obfervance of the ftudent, the whole together un- 
 avoidably becomes intricate. Nor is it now fo entirely performed, but that 
 fomething remains for the ftudent to complete, but which would take more 
 words to make clear, than the defcription of the whole has done. What I 
 allude to is, the interfedions that take place at the lodgment of the fpire on the 
 top of the tower, which, for clearer obfervance, is drawn to a larger fcale at 
 Fig. 4; the mere infpedion of that figure will ferve to convey a full, and I 
 hope fatisfador)'-, idea of what I allude to. The Student has alfo been left to 
 complete the bafe of the odagon, which, no doubt, he is well enabled to do,' 
 or he has gone through the work to little purpofe. As before obferved, it is 
 next to an impofi"ibility to give fuch thorough explanation in intricate matters 
 as to leave nothing for the Student to exercife his own judgment o\\ -, however 
 copious his infi:rudor may be, there will always fufiicient remain undone fo 
 keep alive the adive powers of his pupil, and give him opportunity of exerting' 
 his own ingenuity. That fcholar muft not fleep who would inftrud himfdf 
 in fcience from book alone. 
 
 Fig. 5 is a pidurefque reprefentation of the objed juft performed, which is 
 the form of a church very commonly met with in the country. 
 
 Having, by the exercife of the foregoing examples, advanced the Student to 
 fome tolerable knowledge of the pradice of perfpedive drawing, I will now 
 
66 PRACTICAL PEPvSPECTlVE. 
 
 enter into an inquiry of a very important confidcration. Methodically pro- 
 ceeding, it fliould have been antecedent to any pradice ; it is, however, fonie- 
 times expedient to do that firll, which in juil progrcffion ftiould follow ; as it 
 ie not until fome infight is had into a fubjedl that the neccHity of certain 
 inquiries becomes evident. 
 
 It has been matter of much difference of opinion, the adjufling what may 
 generally be confidered the befl angle of vifion, within w hich objeds fliould be 
 regarded to obtain the moft agreeable reprefentation of them. For, accordingly 
 as the angle of vifion is enlarged or leffened, by viewing the objects near or 
 remote, will their appearance vary, and their delineation in confequence be 
 affeded thereby. 
 £Plate 23.] ^y ^^^ angle of vifion, or angle of view, is to be underftood, the expanfion 
 of the lines, proceeding from the eye, by the two extreme vifual rays embracing 
 the whole extent of the view ; and this, whether it confift of one objed: or of 
 many. This can clearly be explained only by reference to fome figure. (Fig. i , 
 Plate 23.) Let A reprefent the plan of a manfion ; let B be the fituation of an 
 outhoufe contiguous to the manfion ; and let the places of trees be intimated by 
 the fpots C,C,C, and D,D,D. Let S be the flation or point of view whence 
 the whole is regarded. Confidering the manfion A, as a lone objedl, the extreme 
 vifual rays Sa, Sb, form at the eye, the angle aSb ; then is the angle aSb the 
 angle of view under which that objed: is feen, Sa and Sb being the two ex- 
 treme vifual rays embracing the whole extent of the objed. Again, if the out- 
 houie B be confidered as a lone objed, then will the extreme vifual rays, cS 
 and dS, form, at the eye, the angle cSd, being the magnitude of the angle- 
 Under which that objcd is feen. And fo of any objed, the vifual rays that: 
 embrace its whole extent, form the angle of view under which it is faid to be 
 feen. It mull be manifefl tlien, that this angle of view will be large or fmall, 
 as the eye is near to, or remote from the objed. 
 
 Let it be intended to take both objeds A, and B, into one view, with the ad- 
 dition of trees to the right, and to the left of them. Let vifual rays be drawn 
 from the extreme tree on either fide, to the ftation S: the angle CSD is the 
 angle of view under which the whole extent is feen ; and the rays CS and DS 
 are denominated the extreme vifual rays of the view. 
 
 Objeds may be placed too near the eye for fatisfadory obfervance of them s 
 they may be placed fo near as to pain the eye. The eye can contemplate only 
 a point at one time ; it is by its celerity and continual motion, that it becomes 
 perfedly fenfible of a whole, or many forms^ But when an objed, or many 
 
PRACTICAL PERSPECTIVE. 67 
 
 objeds, widely extended, are placed too near, the travcrfes of the eye in con- [P'^ie 23.] 
 templation of the whole become painful. It is not neceflary for nne to account 
 'trby it is fo, but that it is fo, every one muft have experienced ; and when that is 
 the cafe, t!ie caufe, or the eye, is removed to a more agreeable diftance, or the 
 head, as well as the eye, is turned from one fide to the other, the better to 
 comprehend the extent of the objedl or objefts in view. 
 
 The neceflity of turning the head fhould be avoided in taking a view : a view 
 fliould compnfe no greater extent than the eye can agreeably contemplate at one 
 coup d\til (or glance of fight), or than can be viewed by a pleafing and fatif- 
 faftory traverfe of the eye alone; which neceffarily confines the extent of 
 matter, and of courfe the angle of vifion, to fome certain limits. The eye refts 
 with compofure on what it can contemplate with little trouble; not only too 
 great an extent, but too many objedts, however they may intereft and delight 
 at firft, foon diftradt and tire the eye, a circumftance that may account why a 
 pidurefque bit gives more delight than an extenfive fcene comprifing many 
 
 parts. 
 
 Smallnefs of objed has nothing to do with angle of view ; a die, or the fmallefl 
 miniature, by being placed too near the eye, may form a large angle of view, 
 and caufe the eye pain in obferving it. A large extent of view, or a large 
 pifture, may be contemplated with as much eafe as a fmallone ; it is only placing 
 the larger at a greater diftance. If the place of the plane of delineation be at 
 FG (Fig. i). then will the angle FSG be the angle of view. If a fedion of 
 the fame vifual rays be taken at H I, then will HI be the extent of the pifture, 
 and the angle HSI be the angle of view; but the angles FSG and HSI are 
 one and the fame, of confequence the eye can contemplate either pidure with 
 equal fatisfadion-, but then one muft be placed at the diftance SO, the other 
 
 at the diftance SP. ^ 
 
 From whatever ftation an objedl be viewed, however diftant, or however 
 near, it never appears other wife than on refledlion we know or expedt it ftiould 
 do. ' Far different is the cafe with refped to perfpedtive delineation on planes, 
 according to certain pofitions. To find the reprefentation of a circle, viewed 
 horizontally, aft'ume the figure of un upright oval, as Fig. a : or the repre- 
 lentation of a fquare fo pofited, affume the form KM N L. Fig. 2 ; muft cer- 
 tainly exc.te doubt in the mind of the young ftudent, as to the truth of the 
 
 . In this view of tl-.e fubjeft of vifion, what is termed near, or fhort fightednefs, is not Uken into confidei*. 
 ■ Icoked UDon as a defeft in the organ itfelf. 
 
68 PRACTICAL PERSPECTIVE. 
 
 [Plate 23.] rules by which fuch deh'neations, fo repugnant ta belief, are afccrtaincd, and 
 given as the reprefentations of fuch well-known forms. Yet fuch may rever- 
 thclefs be true and juft reprtfentations, according to the point of view taken, 
 and ppfition chofen of the plane of delineation. 
 
 It is the fhortnefs of the diftance of the eye from the plane of delineation, 
 that caufes fuch unpleafant diftortion. This may clearly be feen by infpe<3ion 
 of Fig. 3, where, let the figure A BCD reprefent a fquare lying on the 
 ground plane; let the plane GHKL be the plane of delineation, and let E be 
 the point of view. It muft be evident by the vifual rays EA and EB, that the 
 figure DabC, on the plane of delineation, is to the eye at E, the reprefenta- 
 tion of the fquare ABCD, and that an oval defcribed therein would, of courfc, 
 be the reprefentation of a circle, and would be as much diftorted as the oval 
 within the fquare KMNL, Fig. 2. But let the eye be removed to a greater 
 diftance from the plane of delineation, fuppofe to the point E, then will the 
 reprefentation of the fquare, and circle within, come within more admiflible and 
 pleafing forms; as may be gathered by the vifual ray to the farther place of the 
 eye E in the diagram. Fig. 3, determining the figure DefC as the reprefenta- 
 tion of the fame fquare; and which feen direcflly before the eye, would be as the 
 lower fquare KOPL, and circle within, Fig. 2. 
 
 To fix upon an angle that fliould extend to every cafe, as being the i>r^ angle 
 of view, would be as vain, as it would be an abfurd endeavour. Different 
 fubjedls require diflFerent treatment ; infide fubjedts different from external 
 ones, and external ones from each other, as they happen to be fituated. 
 
 The angle of view, as was before obfervcd, is regulated by the diftance of 
 the eye from the plane of delineation. Thus, if GL, Fig. 4, be the extent of 
 the picfture, and A the diftance of the point of view, the angle GAL 
 will be the angle of view ; and fo on, every remove of diftance varying 
 the angle of view of the f^ime extent looked at. Some authors on perfpedlive 
 have cxpreftly advifed, that the greateft diftance of the eye from the pifture 
 fliould not exceed the width of the pidture laterally, which makes the angle of 
 view fifty-three degrees. Others would have tlie diftance lefs, requiring the 
 angle of view never to be fmaller than an angle of fixty degrees ; fuch is the ■ 
 angle GAL ; others are for having a ftill Icfs diftance to be the greateft ufed, 
 and, of confequence, would have a larger angle of view than fixty degrees. My 
 Father, who, I am perfuaded, fpeaks from more prad:ical experience than any 
 of his predeceflbrs, advifes the extent of the pidiure, laterally, to be the leaft 
 diftance ufed, its angle of view fifty-three degrees, or at the very moft, fixty 
 
PRACTICAL PERSPECTIVE. 69 
 
 degrees, to the largeft angle of view ; and recommends an angle of forty-five de- [Plate 23.3 
 grees as the befl angle of view, being, in his opinion, neither too large nor 
 too fmall; fuch is the angle GB L. It is his advice to keep between the one and 
 the other, that is, not to let the angle of view exceed fixty degrees, nor be Icfs 
 than forty-fiv« ; too large an angle of view fubjeding the objedls to diftortion, 
 and too fmall a one rendering them too tame. His advice I know, from my own 
 experience, to be ftridly good j I have, however, in fome inftances, in adlual 
 views, experienced the abfolute neceffity of iifing a larger angle of view than lixty 
 deo-rees, but fuch do not often occur. After all that can be faid, determination 
 in this particular muft ever be left to the difcretion of the artift, and the abfo- 
 lute neceffity his fubje<ft lays him under, as to the adoption of his angle of view. 
 The angle of view determined, as alio the extent of matter to be included in 
 the view fettled, it will then remain to place the plane of delineation in themoffc 
 judicious manner. In regarding a pidure, the obferver, in general, places 
 himfelf in the middle of it, between its lateral extremes, with his eye perpen- 
 dicularly oppoiite to where the horizon is concluded to be, as nearly as he can 
 determine it. Such being the flation whence a pidure is ufually regarded, from 
 fuch point of view it fliould be that the artifl Ihould calculate his effedls to be 
 the moft perfect, both as to linear and aerial perfpedive j and which, as fitr as 
 the influence of linear perfpedlivc extends, is very ealily effected. 
 
 T^he angle of view being determined^ how to place the plane oj delineation in 
 
 the mojl judicious ma?7ner, before the eye of the obferver. 
 Bifed: the angle of view, and place the plane of delineation ,at right angles 
 with the line of bifedion ; which alfo place nearer or farther from the point of 
 view, as the pidlure is required to be fmall or large. 
 
 The angle of view, FSG, Fig. i, Plate 23, is bifededby the line SP, and 
 the pidlures FG and HI are each placed at right angles^ or perpendicular to 
 the line of bifeclion, SP ; each of which pidlures ftands diredlly before the ob- 
 ferver, as required : others might be thus placed, at pleafure, agreeably to the 
 dimenfions of the pidlure defired. 
 
 From fuch pofition of the plane of delineation, the eye of the obferver, or, 
 what is the fame thing, the point of view, comes direcflly in the middle of the 
 pifture, laterally, with the eye level with the horizon ; and from the flation 
 generally chofen to regard a picture, a pidlure io proceeded on muft make its 
 mofl: perfed; appearance. In fome cafes, however, this abfolute pofition may, 
 and muft be deviated from ; but it is neceifary to know where perfed ion is, 
 that departure from it may be known, in order that fuch departure may be the 
 leift poihble, agreeably to the fubjed in hand. 
 
 s 
 
?« "PRACTICAL PERSPECTIVE. 
 
 [PJafe 23.] Let the boundary line around Fig. 5, be the dimenfions of a pidlure. Let 
 the line A B be the horizon, parallel to the bottom edge, or ground line of the 
 pidure ; then will the point C, in the middle, be the point that fliould be op- 
 pofite the point of fight, or point of view; which point C, late writers on 
 pcrfpedtve have termed the centre of the pidure, and which has been fo de- 
 fined in this work. If the horizon, which is quite arbitrary, be placed higher 
 on the plane of the piclure, as at the line DE, then would the point F, 
 agreeably to the principle laid down, be the moll: eligible place for the centre of 
 the pidure. If the horizon were taken ftill higher, as in fuch reprefentations as 
 Rre termed bird's-eye views, at G H for inftance, then would the point I be the 
 bell: fituation for the centre ; always placing it in the middle between the two 
 extreme ends ; as then the fpedtator being direftly before the pidlure to obfervc 
 it, places himfelf neareft its true and jull point of view, which would not be 
 the cafe, had the effeds of the linear reprefentation been calculated from the 
 point K, K, or 3{ ; lefs fo if it had been calculated from the point L, L, or J£> ; 
 and ftill kfs fo, if delineated agreeably to the point M, M, or .M, as the centre; 
 but vwhich, from want of knowing better, are often as erroneoufly, though un- 
 wittingly, delineated. 
 
 From what has now been advanced in this work, if thoroughly underftood, 
 it is poflible to perform any thing that linear perfpedive can efFedt; but it is 
 apprehended, few will feel themfelves competent to fuch a trial. There arc 
 perfons of fuch profound thinking, fo acutely penetrating, that from a clofely 
 i'ompaded theory can extradt a general pradice. To fuch, Brook Taylor's 
 condenfed Elements on this fubjedl, would be ample infight. But works like 
 his are not addrelled to the many : one compadled general obfervation ne^*ds 
 much elucidation to make it manifeft to the multitude : wherefore the necefiity 
 ■of works of a more open inquiry, of more familiar and minute inftrudlion, 
 and according to the different powers and intention by which authors work, 
 ilifterent roads are made to the fame fummit, and each who follows will 
 prefer that path which, moft agreeably to his humour, will condud; him to 
 the objed he wilhes to attain. 
 
 The endeavour to avoid trouble is continually inflanced in every occupation 
 in life : Lazy perfons give themfelves moil trouble, lays the proverb. Com- 
 plaint may be made of the extraordinary tedioufnefs of true perfpedive delinea- 
 tion, and impatience may fpurn at the apparent tedioufnefs of the procefs. 
 From my own experience I have ever found, when by lazinefs or impatience 
 I have been induced to flight or rejed the application of rule, that at laft I have 
 been forced to have recourfe to it, even for the advantage of that difpatch 
 
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 __^//rfi»^ .i^i*fA»/ft//^ ^rffK*. i/fi/A'^t . 4hfffAfr f-foi' 
 
PRACTICAL PERSPECTIVE. 71 
 
 I was endeavouring othcrwife in vain to obtain, and after confiderable time had [Plate 23.] 
 been loft, to wave the ncccflity of the appeal. Thus had the aid of method 
 been firH applied to, not only much time had been faved, but the delufive 
 effed: required been better accompliflicd. However ftrong the wifti to fliorten 
 the road leading to a defired objedl, that way is not always found the readieft, 
 that feemingly points the moft diredly to it. Sir Jofhua Reynolds, in his divine 
 Difcourfes on Painting, moft aptly fpeaks my fentiments j and fays, " The im- 
 petuofity of youth is difgufted at the flow approaches of a regular fiege, and de- 
 fires, from mere impatience of labour, to take the citadel by ftorm. They 
 wifli to find fome ftiorter path to excellence, and hope to obtain the reward of 
 eminence by other means than thofe which the indifpenfable rules of art have 
 prefcribed, — In this art, as in others, there are many teachers who profefs to 
 fliow the neareft way to excellence; and many expedients have been invented 
 by which the toil of ftudy might be faved. But let no man be feduced to 
 idlenefs by fpecious promifes. Excellence is never granted to man, but as the 
 reward of labour." 
 
 FINIS. 
 
 S. GosNtii, Printer, 
 Little Queen Street, Holborn. 
 
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