The Practice of Perspective: 
 
 Or, An Easy 
 
 method 
 
 Of Representing 
 
 NATURAL OBJECTS 
 
 According to the Rules of ART, 
 
 Applied and Exemplified in all the Variety of Cafes 5 as Landsk ips, 
 Gardens, Buildings, of divers Kinds their Appendages, 
 Farts, Furniture, &c. 
 
 With RULES for the Proportions, Pofitions, &c. FIGURES, 
 both in Draught and Relievo. 
 
 Alfo the Manner of conducing the S h a d o w s by divers Luminaries ; and Practical Me- 
 thods of Designing truly, without underftanding any Rules at all, 
 
 AWORK highly neceflary for 
 
 PAINTER S, 
 
 Engravers^ 
 Architects, 
 embro i derers, 
 
 s x a tuaries, 
 
 Jewellers, 
 
 Tapestry-Workers, 
 
 And others concerned in Designing. 
 
 The Whole illuftrated with One Hundred and Fifty Copper-Flatjes. 
 
 Written in French by a Jesuit of Paris fince tranllated into German ', by 
 Ch, RimbOld and into Englijh, by* Rob. Pricke. And now, a fecond 
 Time, into the fame Language, byE, Chambers, F. R. S. 
 
 The Third Edition. 
 
 To which is prefixed the Theory ofPerfpeclive, in which the Reafonsand Grounds of the feveral 
 Methods made ufe of in the Practice are mewed and demonstrated, by James Hodgfon, Fel- 
 low of the Royal Society, and Matter of the Royal Mathematical School in Cbriji Hofpital. 
 
 If you would proceed immediately to the Practice of Perfpeftive, without engaging in the Intricacies 
 of the Theory, the J E s U I T 's Perspective will anfwer your Purpofe. 
 
 Wolfi us in Element. Mathef. Tom. II. p. 1048. 
 
 L 0 N D 0 N: 
 
 Printed for Tho» .Bowles, Print and Map-Seller in St. Paul's Church-Tard ; 
 and John Bowles, Print and Map-Seller at the Bkck-Horfe in Cornhill, 
 
 MDCCXLIfT, 
 
The 
 
 P R E F A C E. 
 
 H E Principle or Foundation from which P erspec- 
 t i v e arifes, is the Eye ; an Organ which Nature has 
 endued with a greater Share of Vivacity and other 
 Perfections, than the reft of theSenfes; and which 
 even holds the fame Advantage over them, that the 
 Soul does over the Body. The like Advantage does the Art of 
 Perspective hold over the other Mathematical Arts ; being 
 confeffedly the mod elegant and agreeable, and affording more 
 Matter of Entertainment, than all the reft. 'Tis the very Soul 
 of all Painting; and that alone which can make the PA INT- 
 ER a Mafter. 'Tis this muft conduct him in the Difpofitions, 
 Heights and Proportions of his Figures, Buildings, Moveables, 
 and other Ornaments. 'Tis this muft mew him what Colours 
 are to be deep, or feint, or vivid, or dull ; where each is to 
 be applied ,• what to be finim'd up, and what only touched ; 
 where Light is to be beftowed, and where not: In a Word, 'tis 
 this begins and ends the Painting. Without the Affiftance of 
 Perspective, the beft Mafter muft make as many Faults as 
 
 A Strokes ; 
 
iv PRE FA C E. 
 
 Strokes : And efpecially in Buildings, and fome other Enrich- 
 ments; which are Things I find fome of our mod reputable 
 Painters fo horribly defective in, that this has been one great 
 Motive to my undertaking the following Work ; wherein their 
 Errors will be fliewn, without naming the Authors ; and No- 
 vices inftructed how to avoid the like. The moft confummate 
 Mafter is tied to the ftricr. Obfervation of every one of thefe 
 Rules, on Pain of pleafmg none but the Ignorant : And an 
 indifferent Painter may be told this to his Comfort, that if he 
 make himfelf a thorough Mafter of thefe Rules, he fhall be 
 able to do Wonders. 
 
 THEENGRAVERin Copper can no more do without 
 Perspective, than the Painter ; as having every Thing to 
 do with the Graver, that the other does with his Pencil. From 
 Perspective he muft learn where to lean heavily, and 
 where lightly ; what muft be funk deep, and what foftned. 
 Add, that his Occafion for this Art is more important, as his 
 Pieces multiply to a much greater Degree than thofe of the 
 Painter : So that if artfully performed, his Praife will be the 
 greater ; and if otherwife, his Failing the more notorious ; 
 each Piece being a Sort of Mouth to vilify its Author. 
 
 THE SCULPTOR and ST ATU ARYmuft here learn 
 the Heights both for the high, low, and middle Sight ; the 
 Slopes and Inclinations of Buildings, and other Bodies ; the 
 Angle for the Point of Sight ; and the Proportions and Di- 
 meniions of all Objects, near and remote. 
 
 BY the fame Art the ARCHITECT muft learn how to 
 make his Defigns intelligible in a little Compafs : He may like- 
 wife raife one Part, and leave the other in its Plan, to fliew the 
 whole Conduct and Effect of his Work. By the way, having 
 mentioned Architecture, we muft obferveof how much Con- 
 fequence it is, for fuch as practife Perspective, to be know- 
 ing therein; the fineft Pieces of Perspective being thofe 
 
PRE FA C E. v 
 
 of great and magnificent Buildings, raifed according to the 
 Order of Columns, all the Beauty whereof depends on their 
 Meafures and Proportions, which muft be obferved with the 
 laft Exactnefs, otherwife they mock and offend the Eye. Archi- 
 tecture, therefore, muft be ftudied heartily : Nor can it any 
 way be excufed, to be ignorant of the fame ; confiderkig 
 with how much eafe it may be learned in Vitruvius^ Vignola, 
 Scamozzi) and fome others. 
 
 TO know the Orders of Columns, and their Characters, is 
 not enough : He muft likewife underftand all theufual Dimen- 
 fionsof Buildings, and the feveral Parts thereof; as Doors, 
 Windows, Chimneys, & c. how to difpofe them to receive the 
 Lights to Advantage, that nothing may appear maim'd, or dark- 
 ly ; to take care that every Thing be well fupported ; that no- 
 thing be ufelefs; and that there be a Symmetry and Proportion 
 running throughout the whole. Without fuch Regulation, a 
 Piece of P e r s p e c t i v e, far from plealing the Eye, will 
 wound and offend it. 
 
 GOLDSMITHS, EMBROIDERERS, TAPES- 
 TRY-MAKERS, ENAMELLERS,andevenJOINERS 
 and others who have occafion to make Defigns, are under the 
 ftricteft Obligations to apply themfelves to Perspective, 
 if they would do any Thing to deferve Applaufe. 
 
 THE greateft Part of fuch as I have known well affe&ed to 
 this Art have aflured me, that they were difcouraged by the 
 great Number of Lines which moft Authors make ufe of to form, 
 and find the Places of their Objects, or Figures. Others have 
 been caftoff by the great Number of Obfcurities in the Rules 
 and Operations ; and particularly from the Inftructions not be- 
 ing immediately annexed to the Figures ; fo that in turning over 
 to find them, they were apt to forget what they wanted. Now 
 thefe Complaints have warned me to be more clear and me- 
 thodical in my Inftructions, which are plac'd immediately before 
 
 A 2 • each 
 
vi PRE FA C E. 
 
 each Figure, that the Reader may have both the Rule and the 
 Example in his Eye at once. Through the whole I have accom- 
 modated myfelf to the Capacity of Learners $ not perplexing 
 them with too many Demonftrations ; nor ufing any Words but 
 fuch as may be underftood, at leaft in the Definitions. With 
 the fame view I have followed the common Cuftom of attribut- 
 ing Qualities to certain Things which really have them not. 
 Thus, in considering Diflance, or Removal, I have been forc'd 
 to fay, contrary to my own Sentiment, that 'tis the Pupil which 
 receives the Rays from Objects, as if they terminated therein ; 
 whereas 'tis paft Difpute, that Virion is perform'd on the Retina 
 at the Bottom of the Eye ; and that the Rays only pafs thro' 
 the Pupil in the way thither: Which, to fome People, will ap- 
 pear a new Language, and not to be conceived. However, 
 being aflured that fuch a Piece of Knowledge imported but 
 little to the Practice of Perspective, I have attributed to the 
 Pupil what really belongs to the Fund of the Eye, the proper 
 Place of Vifion, where the Species of Objects are formed ; 
 tho' there are others who refer this to the Cryftalline. The 
 Reader who requires farther Satisfaction as to this Point, may 
 confult Aquillo Scheiner^ and Des Cartes. 
 
 THO' I have ftrained every Nerve to render the Science 
 eafy, I don't doubt but there are feveral will find fome Diffi- 
 culty at the Beginning. But whoever can furmount the firft 
 Difficulties may go on aflured, that there is nothing but he 
 will underftand, and practife ; provided he takes care to ma- 
 iler one Rule well before he turn over the Leaf to another. 
 The Truth is, they may be faid, in fome meafure, to hang and 
 depend on each other : And a little Trouble of this Kind, at 
 firft, will be abundantly recompenfed by the future Eafe ac- 
 cruing from it. 
 
 IT will appear from the following Table, that this Work a- 
 lone fuffices to carry you thro' all the Stages and Degrees of P e r- 
 
 4 SPECTIVE, 
 
PRE FA C E. vii 
 
 spective, and to perform all Kinds of Draughts; by only 
 having recourfe to the feveral Rules, which the Figures indicate, 
 and bringing and collating them together, to furnifh out the 
 Thing requir'd. This, no doubt, muft be agreeable enough to 
 a Perfon who defires to make a Draught, to find immediately 
 what may anfwer his Purpofe : The Satisfaction, affuredly, muft 
 far tranfcend that of copying a Piece already done by another. 
 Add, that in cafe he beoblig'd to copy any other, he will doit 
 with much more eafe, by means hereof; inafmuch as we fur- 
 nifli Instructions for every Thing that can occur. I confefs I 
 take infinite Pleafure in making new Defigns, and inventing 
 new Figures ; which I fhould have made publick, as my Prede- 
 ceffors have done, but that I was willing every Perfon fhould 
 participate in the Pleafure of compofing from his own Fancy ; 
 having furnifti'd him with all the Means requifice thereto. Such 
 as choofe to decline that Trouble, will meet with Defigns enough 
 ready to their Hand, in Marolois^ V redeman, Uriejfe y and others, 
 who have affected to fhew the Politenefs of their Genius in 
 this Way. 
 
 S O many fine Performances, I doubt, have help'd to render 
 many of our Painters too lazy to learn to do what they find rea- 
 dy done. All they afpire at, is, to copy them as well as they 
 can ; which were excufable, did they know how to ufe them 
 to the Purpofe: But their way is to copy without knowing. 
 And hence it is, that we have ufually as many different Points 
 in a Painting, as there are Objects, Lines, and Returns. Some 
 of them will let you fee the Bottom of a Thing that fliould on- 
 ly fhew the Top ; and others, rather than be fhort, will fhew 
 both. Others, again, having feveral Figures to fhew in a Paint- 
 ing, will make them all of the fame Height : Tho' fometimes 
 they vouchfafe todifpenfe with that Rule, and make thofe in 
 the Fore-part lefs than thofe behind, to give Room, as they tell 
 
 us > 
 
viii PRE FA C E. 
 
 us, for the hind Figures to be feen : Which is to overturn both 
 Art and Nature at once. 
 
 TO fatisfy the Curious, who are always inquifitive after the 
 Reafons of Things, and require Order and Meafure every 
 where \ I have divided this Work into five Parts. In the fir Jl 
 are delivered a few Definitions, Demonftrations, and Reafons, 
 which need no great Stock of Mathematicks, to be underftood, 
 and which yet give a deal of Light into the Subject in Hand. 
 Thence I proceed to mew the Nature of the Point of Sight, 
 Points of Diftance, Accidental Points, Front Point, and Side 
 Point, Vifual Rays, Diagonals, Parallels, Perpendiculars, and 
 Bafe Line ; the previous Knowledge of which Things is ex- 
 tremely neceffary, before you come to the Figures, and con- 
 tribute exceedingly to the eafy underftanding the Inftru&ions 
 that follow. In the fecond Part we give the Methods of fhort- 
 ning and diminifhing Plans divers Ways • with feveral Forms of 
 Pavements which ordinarily ferve for the Foundations of Per- 
 fpective Draughts. Having given funicient Inftructions for put- 
 ting all Sorts of Planes in P e r s p e c t i v e, we proceed, In the 
 third Part) to the Elevations of divers Obje&s, beginning with 
 the eafieft, which are Cubes, and other Bodies of feveral Sides, 
 or Faces : Thefe are follow'd by Walls, Doors, Windows, Ceil- 
 ings, Vaults, and Stair-cafes of divers Forms, all without Or- 
 naments, or Mouldings, that the Rules might be the lefs per- 
 plex'd with a Number of Lines which fuch Enrichments would 
 have render'd neceffary. After fhewing all the Buildings in 
 their Simplicity and Nakednefs, I go on to furnifh them with 
 Columns, Cornices, and other Ornaments, which add a Maje- 
 fty and Grace. The Houfes, all built to the Roof, I fhew how 
 that is to be manag'd, with variety of Coverings : Then ad- 
 vance to the Infides, and give Rules for the Furniture, Move- 
 ables, ft? c. Thefe are followed by Inftruclions relating to 
 Streets; Gardens, Trees, Walks ; which are Things that infpire 
 
 4 a Ga- 
 
PREFACE. ix 
 
 a Gaiety, and render the Draughts more entertaining. This 
 Part is clofed with two or three Contrivances for facilitating the 
 Bufinefs of Perspective, and even for making the fineft 
 Defigns, without knowing any Thing of the Rules of Art. 
 In the fourth Part we give the Meafures and Proportions of 
 Figures, both in Draughts and Paintings, their Poftu res, Situ- 
 ations, and Horizons, both for flat Paintings, and Relievo's. 
 The Jifth and ' laji Part confiders natural Shadows, both thole of 
 the Sun, Torch, Candle, and Lamp. 
 
 WHEN the Perspective of a Building, Garden, Range 
 of Trees, Pallifade, or the like, intermixed with Figures, is 
 intended, I would recommend it to you, to sketch out what 
 relates to the Perspective with a Pencil in the firft Place ; 
 which done, you will proceed with more Afliirance to fix the 
 Heights of Figures, and other Circumftances. 
 
 ONE Thing fome People will find to cenfure in this Work, 
 viz. That the Points of Diftance in all my Figures are too near 
 the Point of Sight. But if this be a Fault, 'tis a voluntary one : 
 For my Defign being to teach, it was neceflary every Thing 
 fhould be fliewn, and the Reader let to fee where fo many Lines 
 were to terminate ; otherwife he would have been left to his 
 own Conjectures. 'Tis fufEcient that I direcl; the Learner to 
 place them farther off ; and even fhew the Laws and Occafions 
 thereof. Nor can it be fuppos'd I mould have made any Diffi- 
 culty of making them more remote, had not other Considerati- 
 ons prevail'd with me: One of which was, to render the Book 
 as fmall, portable and cheap, aspoflible. Had I follow d the Ad- 
 vice of fome of my Friends, I mould only have given a {ingle In- 
 ftruction in each Leaf; which would havefwell d the Book to a- 
 bout thrice its Bulk, without rendering it a whit the more 
 intelligible. 
 
 SOME People affect, to conceal the Names of the Authors 
 they have follow'd; and, as has been well obferv'd of a certain 
 
 one, 
 
x PRE FA C E. 
 
 one, pilfer from private Perfons what they give to the Publick. 
 For my own fhare, I confefs, that having propos'd to write a 
 little Treatife of P e rs p e c t i v e, I was willing to fee as many 
 as I could on the fame Subject ; nor made any Scruple of bor- 
 rowing from any of them what 1 found to my Purpofe, with 
 an Intention of making an open Reftitution of all my private 
 Thefts to the Publick. The firft Writer of any account, is George 
 Reich, in Cap. X. of his Works. The next, Vi&or, a Canon of 
 7bul> who gives us a Number of good Figures, but is too fparing 
 in his Inftru&ions. After him comes Albert Durer, who has 
 left us fome Rules and Principles, in Lib. IV. of his Geometry. 
 Then J. Coujin^ who has an exprefs Treatife on the Art, where- 
 in are many valuable Things. After thefe come Dan Barbaro, 
 Pignola, Serlio, Du Cerceau, Sirigaty, Solomon de Caus, Maro- 
 lois, V redement) Uriejfe, Guidus Ubaldus, Pietro y Acolty, the 
 Sieur de Vaulizard, the Situx Def argues, and lately Father Ni- 
 cer on> a Minim: All whom I have read, one after another, 
 and not without admiring their great and happy Induftry in 
 the Service of the Publick ; efteeming it fufficient Honour for 
 me to imitate what they have done, and to be the unknown 
 Copift of their Works. Befide thofe already recited, there are 
 many others, whom I have never feen; which Multitude of 
 Authors mull be allowed an Argument of the great Efteem the 
 Art has always been in, as well as the fuperior Regard paid to 
 it by the prefent Age. On this Confideration, I cannot doubt 
 but the following Work will be favourably received ; efpecial- 
 ly, as it brings along with it feveralnew Rules, and Inftrudti- 
 ons for putting in Perspective any of the Objecls ordinari- 
 ly under our Senfes, and, by Confequence, of performing 
 whatever relates to that Art. 
 
 A 
 
TABLE 
 
 DIRECTING TO 
 
 The feveral Parts and Members whereof 
 any Perfpe&ive Draught is to confift. 
 
 PERSPECTIVE muft begin with Plans, and, 
 | of Courfe, wich fuch as are the moft fimple and 
 | eafy ; among which is the Square, or Cube : The 
 
 B$ffi« l Method of making the Plan whereof is found in jr , . m 
 rag. 19. and that of its Elevation in Pag. 44, 49. i« and 
 If an angular View be required its Plan is given in Pag. 2 o. J "£ /e -™f e - 
 and its Elevation in Pag. 50. 
 
 To raife the Walls of a Houfe, or the Palifades of a Gar-*f«'/'WiV- 
 den, &c. fee Pag. 51, 52. where you have both their Plans, l ^ ade> ' 
 and the Elevations. 
 
 Such as require the Infide of a Hall, or Chamber, in a¥^»/« 
 front View, muft take the fame Pag. 51, 52. for the Walls * oom ' 
 the following Page for the Doors; Pag. 54. for the Win- -En- 
 dows ; and Pag. 77. for the Chimney. The Cieling they 
 will find in Pag. 3 1, 32, 33, and 34. If a Door is to be open, Windvws ' 
 you have your Inftrudtions in Pag. 33. and the Page follow- cw ^'' 
 ing gives a Window or Cafement open. The fame Rules are C ' v/ ^'* 
 to be obferved when there are two or three Stories over each pimemnU ' 
 other, as in Tag. 76. To afcend to thofe Stories, we furnifh 
 Stair-cafes in Pag. 82, 83, and 84. 
 
 Houfes viewed on the Infide are ufually furnifhed with 
 Moveables 5 moft Kinds whereof are fhewn in Pag. uweabU*. 
 
 a 96—103. 
 
A 7 A B L E, See. 
 
 96— 103. The Proportions of Figures to be placed therein, 
 are found in Pag. 122, 123, 124, 125. 
 
 To (hew the Infide of a Church, a Plan muft be pitched on, 
 and put in Perfpective, according to the Inftructions in Pag. 
 37, or 41. The Walls to be raifed, from Pag. 51. The Win- 
 dows made like the Arches of Pag. 62, or 54. Pillars and Pi- 
 lafters to be taken from Pag. 4$- Columns from 87. A Vaulr, 
 
 or Vaults, from Pag. 68 72. And a Dome, or Cupola, from 
 
 Pag. 74, 75. To enrich it with Cornices, Mouldings, and 
 Comkes and other Ornaments, have Recourfe to Pag. 88— —5)2. For Al- 
 tars, to Pag, 31, 32, 33, 34. ■ 
 
 For Outfides of Buildings : The Doors, and Windows are 
 performed as in the Infides, fee Pag, 53, 54, and 106. When 
 raifed to the proper Height, the Method of roofing and cover- 
 ing them will be found in Pag. 107, 108. And if a Cor- 
 nice, or other Ornaments be required, you have them in Pag. 
 
 88 02. Arched Galleries, both within and without Side, 
 
 are (hewn in Pag. 63, 66, 67, and 106. 
 
 If a whole Street of Buildings be required, you muft mul- 
 tiply the Houfes on either Side, as in Pag. 109. When Houfes 
 Houjesfaroff. are made pretty deep within the Draught, fee Pag. no. In 
 large Squares, &c. frequent in Streets, in Perfpective, a Pyra- 
 pyramid. rnid may be erected, as in Pag. 80. Or fome other Statue, or 
 
 Figure, or a Pedeftal, as in Pag. 91, and 124. 
 Buildings When a Building is to be viewed by the Angle, you may 
 viewed h t he take its Plan from Pag. 19, 30, and m. and manage the Ele- 
 Angit ' vation as taught in Pag. 50, and 111. which give Rules for 
 Doors and Windows therein. 
 
 Gardens in Perfpective rejoice the Sight more than any Thing, 
 on Account of their Colour, the Variety of Objects, 
 Their Plans are to be made, as in Pag. 35, 38, or 113. and 
 Compartments contrived therein at Difcretion. If Arbours 
 be required, you are fupplied from Pag. 60, or 61. If you 
 rather choofe Palifades, look to Pag. 51, and 52. And if 
 Jihys 0/ Trees, you prefer a Grove, Thicket, or Walk planted with Trees, 
 to either of them, Pag. 112. furnifhes Variety of each. If 
 Fountains, or Jets d'Eau be wanted Tag. 29. gives a Bafon, 
 and its Elevation as in Pag. 73. For Squares, or Beds, fee 
 Pag. 99, or 44. For Polygons, 45, or 46. For Statues, or 
 Figures, which make a fine Ornament for Gardens, take the 
 Meafures from Pag. 122, or 125. For Grotto's, or Nitches, 
 
 4 fee 
 
 Xll 
 
 Infide of a 
 Church. 
 
 Windows. 
 Pilafiers. 
 Columns. 
 Vault. 
 Dome. 
 
 Mouldings 
 Altars. 
 Outfides of 
 Buildings. 
 
 Galleries. 
 
 Street. 
 
 Gardens. 
 
 Arbours. 
 
 Pali fades. 
 
 fountains. 
 
A TA B L E y &c. xiii 
 
 fee Pag. 74. For an Afcent out of one Garden into another, 
 you have divers Forms of Steps in Pag. 78, 75), 80, 81. In $ ttpt . 
 fine, you are at Liberty to choofe whatever pleafes your Fancy, 
 and may range them all in the fame Piece, provided you avoid 
 Confufion, and obferve the due Symmetry and Proportions. 
 
 If you would have open Shops, without any Thing in them Shop,. 
 but the Walls, you are furniftied in Pag. 55-. If you require 
 them fitted up with Drawers, Boxes, &c. look to Pag. g^Bo Xes . 
 and 105. 
 
 Amphitheatres were antiently of more ufe in Paintings than Mhithea- 
 at prefent, for which Reafon 1 have chofe to omit them : And tr "' 
 yet mift might be made, by taking the Plan in Pag. 29, and 
 adding more Circle^ according to the Number of Stories in- 
 tended. To raife the Stories, you are to ufe the Lines of Ele- 
 vation in Pag. 7 
 
 For Fortifications, you have the Method of diminiming&r/^//,*,. 
 their Plans in Pag. 39. and the Method of railing them in 
 Pag. 114. 
 
 To give the Shadows to Bodies of all Kinds, both thofe oc- shad**, 
 cafioned by the Sun, Candle and Torch, is (hewn from Pag. 
 129. to the End of the Book. 
 
 Particulars fee in the following Table of Contents. 
 
 a 2 
 
 THE 
 
THE 
 
 CONTENTS 
 
 DEfinitions, Names, and 'Terms of the 
 Points, Lines and Figures ufed in 
 the following Work Page i 
 
 Sequel of the 'Definitions , Names and 
 Terms. 2 
 Methods of defcribing the Lines and Figures 
 above defined 3 
 Methods of defcribing the Figures 4 
 Of circular Polygons, which are Figures of 
 feveral Angles infcribed in Circles ib. 
 Of the vifual Rays f 
 IVhy a Piece of Perfpeblive is feen better 
 with one Eye than with two ib. 
 Fir ft Definition 6 
 Second, third, and fourth Definitions 7 
 Why Objetls appear the nearer each other, 
 as they are more remote from the Eye 8 
 Why Objetls appear the fmaller as they are 
 at the greater Diftdnce 9 
 Of the Horizon 1 1 
 
 Of the terreftrial Line 1 2 
 
 Of the Point of Sight, Point of the Eye, 
 principal Point, or Point of PerfpeQive ib. 
 Of the Points of Diftance ib. 
 Of the accidental Points ib. 
 Of the Point of the Front 13 
 Of the Side Point ib. 
 Of the vifual Rays 14 
 
 Of the Diagonals or Diametrals of their 
 Sections Page 14 
 
 Of the Diftance, or Removal 1 5 
 
 Advert. I. Relating to the Side-Point 16 
 Advert. II. Of the Depths and Hollowings 
 
 ib, 
 
 Advert. III. Of the Meafures upon the 
 Bafe 17 
 
 Advert. IV. Of the Bafe Line, and afin- 
 gle Point of Diftance ib. 
 
 Advert. V. Not to deceive one's felf in the 
 Meafures ib. 
 
 Advert. VI. Of a/ Jingle Point of Diftance 
 
 18 
 
 Advert. VII. How to do without making 
 ufe of the Diagonal ib. 
 Advert. VIII. Of feveral Ways of fhort- 
 ning or diminijhing ib. 
 Of Plans viewed direclly, or in Front 19 
 Plans viewed obliquely, or fide-wife 20 
 Of a Triangle 21 
 Of the Pentagon^ or Five- Angle 22 
 Of the Hexagon, or Six-Angle 23 
 Of the Heptagon, or Sept- Angle 24 
 Of theOtlogon, or Eight- Angle 25 
 Another Method for the Otlogon 26 
 Of the Hexagon, or Six- Angle ib. 
 Of the double Oftogon 27 
 
 Of 
 
CONTENTS. 
 
 Of the double Hexagon Page 27 
 
 Of the Circle 28 
 Of the double Circle 29 
 A Plan of Squares viewed Angle-wife 
 
 30 
 
 A Pavement of Squares viewed by the An- 
 gle : 3 1 
 Of Squares encompaffed with a Lift, or 
 
 Fillet to- 
 
 Pavements viewed Angle- wife encompafs y d 
 with a Band, or Fillet 32 
 
 Pavements of Squares view'd in Front, en- 
 compaffed with Lifts, or Bands, whofe 
 Squares are divided by the Angle- ib. 
 
 Pavement of Squares viewed Angle-wife, 
 with Chains of Squares in Front 33 
 
 Pavement of Squares in Front, with Chains 
 of Squares Angle-wife ib. 
 
 Pavement of Qtlogons, intermixed with 
 Squares 34 
 
 Pavement of fmgle Squares view'd in Front 
 
 ib. 
 
 Plan of a Garden in Perfpetlive 35 
 Plan of a Building in Perfpetlive 36 
 Plan of a Church in Perfpetlive 3 7 
 
 Plan of a Houfe with a Garden 38 
 Plan of a Fortification in Perfpetlive 39 
 An irregular Plan and Figure in Perspec- 
 tive 4° 
 Another Plan of a Church in Perfpetlive 41 
 Preliminary Inftrutlions necejfary to the 
 following Methods 4 2 
 
 Of the Line of Elevation, ferving to give 
 the Heights of all Kinds of Objetls in all 
 Parts of the Plan 43 
 Elevation of a Cube in Perfpetlive 44 
 Elevation of a Triangle 45 
 A Pentagon, or Five- Angle in Perfpetlive 
 
 ib. 
 
 The Hexagon? or Six- Angle in Perfpetlive 
 
 ib. 
 
 The Heptagon, or Seven- Angle in Perfpec- 
 tive 46 
 
 c Ihe Otlogon, or Eight-Angle in Perfpec- 
 live ib. 
 
 A double Crofs in Perfpetlive 47 
 
 A Stone fluted, or channelled ft ar -wife, in 
 Perfpetlive Page 47 
 
 Of Pilafters in Perfpetlive 48 
 Of Pilafters viewed by the Angle ib. 
 Effect of the Difference of Horizons 49. 
 Elevation of Objetls viewed by the Angle- 
 
 50 
 
 To raife Objetls of any Heights, and remove 
 them to any Diftance at Pleafure 5 1 
 Of Walls viewed in Front 52 
 Another Wall viewed by the Angle ib. 
 To place a Door in any part of a Wall at 
 pleafure ' 53 
 To draw Windows in Perfpetlive 54 
 Of deling s 55 
 Another Difpofttion of Cielings in Perfpec- 
 tive 57 
 Circular Gates and Arches view'd diretlly 
 
 59 
 
 Round Arches over Pilafters view'd in 
 Front 60 
 Gothic Arch, or Arch in the third Point ib. 
 Sequel of the former Figure 61 
 To defcribe, and put in Perfpetlive, round 
 Arches and Doors 62 
 To defcribe and put in Perfpetlive, double 
 Arches and Gates, i. e. fetch as fhew their 
 Thickneffes 63 
 Another Method for circular Arches 64 
 Arches viewed obliquely in Perfpetlive ib. 
 Flat Arches 65 
 T 0 raife Arches upon Pilafters or Columns 67 
 Gothic Arches ib. 
 To find crofs Vaults in Perfpetlive 6 8 
 To draw the fame Vault more accurately 69 
 To form narrow Vaults jo 
 A Vault on the Foot of the preceding Rules 
 
 Arches and Gates with three Sides 72 
 An Arch with five Sides ib. 
 Elevation of round Objetls 73 
 Elevation of Pilafters ib. 
 A Vault in Form of a Shell in Perfpetlive 
 
 74 
 
 Open Domes, or Vaults in Perfpetlive 75 
 
 That 
 
CONTENTS. 
 
 That a Number of Objecls, and Plurality 
 of Stories, only admit of one Point of 
 Sight Page 76 
 
 To put Chimneys in Perfective 77 
 Stairs in Perfpective 78 
 Stairs open, or perforated underneath 79 
 Stairs viewed in Front ib. 
 Stairs that fhew four Sides 80 
 Another Manner ib. 
 Stairs view' d fide- wife in Perfpective 81 
 Stairs in a Wall in Perfpective ib. 
 A Stair-cafe with Landing-places in Per- 
 fpective 82 
 Winding or fpiral Stairs in Perfpective 83 
 Squares with Circles therein, in Perfpec~ 
 live 84 
 Round Stairs in Perfpective 85 
 Round Steps viewed fide-wife ib. 
 Winding Stairs 86 
 Columns in Perfpective 8 7 
 
 Cornices and Mouldings in Perfpective 8 8 
 A large Cornice above the Horizon in Per- 
 fpective 89 
 To find the Bottoms of large Projectures 90 
 Cornices and Mouldings below the Horizon 
 
 9* 
 
 Cornices with fever al Returns 92 
 The Apertures of Boors in Perfpective 
 
 93 
 
 Apertures of Cafements in Perfpective 
 
 94 
 
 Apertures of Cafements with Embrafures 
 
 ib. 
 
 Divers other Apertures 95 
 Plans and firft Elevations of Moveables 
 
 96 
 
 Elevations of Moveables 97 
 To make the upper Part of Tables, Stools, 
 
 &c. 98 
 Elevation of Buffets and Cup-boards 99 
 Elevations of Chairs 1 00 
 
 Another Method of gutting Moveables in 
 
 Perfpective 101 
 Moveables placed without any Order 102 
 Moveables laid or tumbled on the Ground 
 
 103 
 
 Altars in Perfpective Page 104 
 
 Shops in Perfpective 105 
 Buildings viewed on the Outfide 106 
 Roofs of Houfes in Perfpective 107 
 Sequel of the Roofs in Perfpective 108 
 To put a Street in Perfpective 109- 
 That remote Objects do not fhew theit 
 Thicknefs no 
 Buildings view'd by the Angle m 
 To put Walks, with Rows of Trees, in 
 Perfpective nz 
 To put Gardens in Perfpective 113 
 Beds with Borders ib. 
 To put Fortifications in Perfpective 114 
 To make Defigns in Perfpective 1 1 5. 
 
 Reduction of Perfpective Draughts out of 
 fmall into great, and out of great into 
 fmall 1 1 6 
 
 Apparatus to the univerfal Method of the 
 Sieur G. D. L. 1 ij 
 
 An univerfal Method of performing Per- 
 fpective, without having the Point of 
 Diftance out of the Painting, or Ground 
 of the Work, made publick by the Sieur 
 G. D. L. n8 
 To give anyprecife Diftance required, with- 
 out removing the Point of Sight out of 
 
 the Piece 
 
 119 
 
 A very curious Method of drawing all Per- 
 fpectives in the moft natural Manner, 
 without obferving the Rules 12a 
 
 Another elegant Manner of practifing Per- 
 fpective, without under/landing it 121 
 
 Figures in Perfpective 122 
 
 For Figures that have the Eye in the Hori- 
 zon ib. 
 
 For Figures that have a low Horizon ib. 
 
 For Figures that have a high Horizon 123 
 
 For Figures that have their Feet in the Ho- 
 rizon ib- 
 
 Figures raifed above the Plan 124 
 
 The Pofiures of Figures in Perfpective 1 25. 
 
 Beafls and Birds in Perfpective ib. 
 
 To find the Height of remote Figures, where- 
 of the firft is on a Mountain near the 
 Eye 126 
 
 To 
 
CONTENTS. 
 
 To give the natural, or any other Height, 
 to Figures much elevated Page 127 
 To find in what Proportion Figures grow 
 lefs to the Eye, when placed over one an- 
 other ib. 
 Meafures for elevated Figures 128 
 Origin of Shadows 129 
 Of the Difference of Shadows 130 
 To find the Form of the Shadows 131 
 Shadows from the Sun 132 
 The Shadows of the Sun are equal in Ob- 
 jecls of the fame Height, tho* at a Dif- 
 tance from each other 133 
 Of Shadows, when the Sun is directly op- 
 pofed to the Eye 134 
 For the Shadows of perforated Objects 
 
 135 
 
 Shadows affume the Form of the Planes 
 they are caft upon 136 
 
 To find the Shadows of Objects broader at 
 Top than at Bottom 137 
 
 To find the Shadows of Objects fufpended 
 from the G round 138 
 
 To find the S un's Shadow for human Figure 
 
 Page 139 
 
 An eafy Method of finding the Shadow of 
 the Sun 140 
 
 Shadows from a Torch, Flambeau, Can die \ 
 and Lamp 14! 
 
 Of the Foot of the Luminary 1 42 
 
 To find the Shadows of a Torch on all the 
 Sides of a Room 143 
 
 The Shadow of an erect and inverted Py- 
 ramid by Torch -light 144 
 
 The Shadow of a Crofs ib. 
 
 To find the Shadows of round Objects by 
 Torch -light 145 
 
 Shadows on feveral parallel Planes 146 
 
 Shadows of Cielings by Torch light i^y 
 
 To find the Shadow by the Foot of the Lu- 
 minary 14$ 
 
 The Shadow doubled ib. 
 
 The Shadows of human Figures by Torch- 
 light 149 
 
 The different Pofttions and Heights of Sha- 
 dows by Torch- light 150 
 
 SOME 
 
THE 
 
 THEORY 
 
 O F 
 
 PERSPECTIVE. 
 
 By James Hodgfon, F. R. S. 
 
 DEFINITIONS. 
 
 i. ERSPECTIVE is the Art of deferring on a plain Surface 
 
 the true Reprefentation or Appearance of any given Object, as feen 
 ■ from one determinate Point for any given Diftance and Height of 
 the Eye. 
 
 2. The Perfpective Table, or Plane, is that Surface whereon the Picture of the 
 Object is formed, according to the Rules of Perfpective as AB CF. See Fig. i. 
 
 3. The geometrical or ground Plane is that Surface whereon the Perfpective 
 Table is fuppofed to {land, as G I K L. 
 
 4. The Height of the Eye is equal to the Length of a Perpendicular let fall 
 from it to the ground Plane, as EH. 
 
 5. The Diftance of the Eye from the Picture is equal to the Length of a Per- 
 pendicular drawn from the Eye to the Perfpective Table, as E D. 
 
 6. The common Section of the Perfpective Table with the ground Plane is 
 called the Ground Line or Section, as A B. 
 
 7. The horizontal Line is a Line in the Perfpective Table or Picture, parallel 
 to the Section or ground Line, and of the Height of the Eye above it, as M D N. 
 
 8. The principal Ray is the Line drawn from the Eye perpendicular to the 
 Table, and is therefore equal to the Diftance of the Eye from the 1 able, as E D. 
 
 A 9. 
 
2 
 
 The THEORY 
 
 9. The Diftance of any Point in the ground Plane from the Table is a Per- 
 pendicular drawn from that Point to the Ground Line or Section, as QJT. 
 
 10. Direct parallel Lines are fuch as cut the Ground Line or Section at right 
 Angles, as Q T and S O. 
 
 1 1 . Oblique parallel Lines are fuch as cut the Ground Line or Section at 
 oblique Angles, as X T and Y Z. 
 
 12. Tranfverfe parallel Lines are thofe Lines which cut the direct parallel 
 Lines at right Angles, as P R and QJ>. 
 
 13. Radial Lines, or Vifual Rays, are fuch as run up from Points on the ground 
 Line, and unite in fome certain Point in the horizontal Line, namely, either in the 
 Point of Sight or in an accidental Point, as D T, D Z, DO. 
 
 14. The Point of Sight is that Point in the Picture, which is found by draw- 
 ing a Perpendicular from the Eye to the Perfpective Table or Picture, in which all 
 the direct Rays concur as the Point D. 
 
 15. The accidental Point is that Point in the Picture, where Lines that fall 
 obliquely on the ground Line or Section, but parallel amongft themfelves, unite 
 or concur as the direct Rays do in the vifual Point, as the Point E. See Fig. 2. 
 
 1 6. The Point of Diftance E is a Point in the horizontal Line of the Tabic 
 or Picture removed as far diftant from the vifual Point D in the 2d Figure, as the 
 Eye at E in the firft Figure is diftant from the Table or Picture A B C F, namely, 
 JDE. 
 
 17. The Point of Incidence is a Point in the Ground Line or Section, where 
 a Perpendicular let fall from any Point in the geometrical Plane interfects it, as the 
 Point T or Z. See Fig. 1. 
 
 1 8. The Perfpective of any Point is that Point in the Picture, where the 
 vifual Ray drawn from the Eye at E to any Point, as P, in the geometrical or 
 ground Plane, interfects the Picture or Table as the Point p. 
 
 19. The Perfpective of a Line is the common Section of the Table or Picture, 
 and the imaginary Plane formed by an infinite Number of Rays flowing from the 
 Eye at E, and falling upon every Point of the Line R S to be reprefented, as the 
 Line r s. 
 
 20. The Perfpective of any Plane Figure is the Section of the Cone or Pyra- 
 mid of Rays, whofe Vertex is the Eye, and Bafis the Figure propofed, made by the 
 Plane of the Table or Picture. 
 
 21. The Perfpective of any Solid upon the Table or Picture is the aggregate 
 of the Perfpectives of all the Planes whereof the Solid is compofed. 
 
 22. The optick Angle, under which any Object appears, is formed by two 
 Lines drawn from the Center of the Eye, to the two Extremities of the Object, 
 and here it is to be noted, that the moft convenient Diftance of the Eye, from the 
 Extremities of the Object mould be nearly equal to the longeft Dimenfion of the 
 Object, whether Breadth or Height. 
 
 For as the Beauty of Perfpective depends upon the Point of Diftance, fo the 
 Eye ought never to be placed too near the Object, nor too far from it, but at a 
 convenient Diftance ; and never nearer to the Object than one half of the largeft 
 Dimenfion, for in this Situation the vifual Angle will be a right Angle or 90 Degrees ; 
 and as this is the largeft Angle that the Eye can well difcover at one caft, fo if it 
 
 3 *> c 
 
o/" PERSPECTIVE. 3 
 
 be made lefs than 45 Degrees, the Object will be too much contracted, and the 
 Vifual Angle will be fo fmall that the Returns in Buildings would not be diftin- 
 guifhed, and the Whole would appear confufed, and therefore when the Vifual 
 An^le is about 60 Degrees, which agrees with the above-mentioned Limitation, then 
 the Objecl; is feen with the moft Advantage, and confequently in all Perfpective 
 Defigns they ought to come as near this Situation as poffible. 
 
 23. When the Projection of any Object is made on a Plane parallel to the 
 Horizon by Rays parallel and perpendicular to the fame Plane, the Reprefentation 
 of the Object in this Cafe is called the Ichnography of the Figure propofed, whence 
 the Bafe, Bottom or Platform, whereon a Body or Building is erected, is called the 
 Ichnography of that Building, fothat to project the Ichnographick Reprefentation 
 of any Building is to draw the exact Ground Plot of the fame Building thus the 
 Geometrick Ichnography of a Column is a Circle, of a Pedeftal is a Square, 65V. 
 
 24. When the Projection is made on a Plane perpendicular to the Horizon 
 by Rays parallel and perpendicular to the Plane upon which the Object is repre- 
 fented, the Reprefentation in this Cafe is called the Orthography of the Figure 
 propofed ; thus the upright Front of any Building or Object is called the Ortho- 
 graphy of that Object or Building, fo that to draw the Orthographick Reprefen- 
 tation of any Object or Building is to draw the exact Front of the Objector 
 Building as it really is and appears to be. 
 
 25. But when the Reprefentation or Projection of any Object is made by Rays 
 flowing from the feveral Parts of the Object, as the Front, Top or Bottom, Side or 
 Sides, and uniting in one Point where the Eye is fuppofed to be placed, the Re- 
 prefentation of this Object (upon a Plane placed before the Eye itanding at Right 
 Angles to the Line drawn from the Eye perpendicular to the Object, and) formed 
 by the Interferon of the feveral Rays with this Plane, is called the Schenography 
 of that Object, fo that to draw the Schenographick Projection or Reprefentation 
 of any Object is to draw the Projection or Reprefentation of the feveral Parts of 
 that Object, as they will appear to the Eye fituated at a convenient Diftance from 
 the Object upon a Plane placed perpendicular to the Horizon, and in a proper 
 Situation to receive the Object ; and how this is to be done, is the proper Bufinefs 
 of Perfpective. 
 
 AXIOMS. 
 
 1 . The common Interferon of two Planes is a Right Line. 
 
 2. If two Right Lines meet in a Point, a Plane may pafs through them both. 
 
 3. If two or more Right Lines are parallel to each other, they will all be in 
 the fame Plane ; that is, if a Plane pafs through any two of thefe, it will pafs 
 through all the reft. 
 
 4. If two or more parallel Right Lines are cut by another Right Line, there 
 may be a Plane that will pafs through them all. 
 
 5. If two parallel Planes are interfered by another Plane, the common Inter- 
 ferons will be parallel to each other. 
 
 A 2 6. Lines 
 
+ The THEORY 
 
 6. Lines parallel to the fame Right Line, or to parallel Lines, are parallel one 
 to another ; conceive the fame of parallel Planes. 
 
 7. Every Point in any Right Line is in any Plane that Line is in. 
 
 8. A Space feen under a lefs Angle appears lefs, and the fame Space feen un- 
 der a bigger Angle appears bigger, and confequently Spaces feen under equal 
 Angles are equal amongft themfelves. 
 
 N. B. In this Axiom we fuppofe the Spaces viewed ftand at Right Angles to 
 the Axis or principal Ray ifluing directly from the Eye, or which is the fame 
 Thing, that they are parallel to the Perfpective Table, for in other Cafes, where 
 the Diameter of the Object is inclined to the Table, it will not hold good. 
 
 THEOREM I. 
 
 If the Eye be placed any where between two parallel Right Lines, the farthet 
 theie Lines are produced from the Sight, the nearer they will feem to approach 
 each other. See Fig. 3. 
 
 Let S reprefent the Seat of the Eye, E M and Q^N the two given parallel 
 Lines, and S V the Axis or principal Ray, through the Points A C and M draw 
 the Lines A B, C D and M N perpendicular to the principal Ray S V, and thefe 
 Lines will be parallel and equal to each other. Alfo from S, the Point of Sight, let 
 the Rays S A, SB, S C, S D, S M, S N be drawn. 
 
 Demon. Becaufe the right angled Triangles S QJ5, S QJD, have the Perpendi- 
 cular S common to them both, but have the Bafe QJD of the Triangle S QJD, 
 greater than the Bafe Q^B of the Triangle S Q^B, therefore the Angle S D Q^, 
 of the Triangle S QJ3, will be lefs than the Angle S B Qof the Triangle S QJB * 
 confequently the Angle PSD, which is equal to S D Q^ will be lefs than the 
 Angle O S B, which is equal to S B Q^, and confequently the double of the Angle 
 P S D, or the Angle C S D, will be leffer than the double of the Angle O S B, 
 of the Angle A S B, wherefore the Line C D will appear lefs than A B by the 8th 
 Axiom, and confequently the Points C and D of the Parallels E M and Q^N will 
 appear to the Eye placed at S nearer than the Points A and B of the fame Parallels 
 E M and Q^N. After the fame manner it may be proved that the Line M N,which 
 is placed farther off from the Eye at S than the Line C D, will appear lefs 
 than C D, and confequently the Points M and N will feem to approach nearer to 
 each other than the Points C and D which are nearer, and that the fame Line 
 M N being placed at a greater Diftance than S V from the Point of Sight will ap- 
 pear leiTer, and confequently the Points M and N in the laft Situation will feem to 
 approach nearer to each other than in the prefent Situation, and thus fucceflively, 
 till at laft the Line M N will appear indefinitely fmall, and the Points. M and N will 
 feem to come together. 
 
 Let us now fuppofe the Eye, fee Figure the 4th, placed above the Plane pafling 
 through the given Parallels, and let E M and QJM be the Parallels themfelves. 
 
 From H, the middle Point of the Line E Q^, erect the Perpendicular H S equal 
 to the Height of the Eye above the Plane, then will S be the Place of the Eye - 9 
 
 3 £tom 
 
of PERSPECTIVE 5 
 
 from the Point S draw the Rays S E, S Q_, S A, SB, &c . now becaufe the 
 Angles SEA and S QJ3 are right Angles, the Hypothenufes or Rays S A and 
 S B will be longer than the Perpendiculars S E and S Q^, and inafmuch as both 
 Triangles have the Sides S E and S Q^equal to each other, it follows that the 
 Angle QJS E will be greater than the Angle B S A, and confequently the Line A B 
 will appear lefs than the Line E Q^by Axiom the 8th, and the Points A and B 
 will feem to be nearer to each other than the Points E and Q^, and by the fame 
 way of Reafoning it will follow, that the Angle DSC will be lefs than the Angle 
 B S A, confequently the Line C D will appear lefs than the Line A B, and the 
 Points C and D will feem to come nearer to each other than the Points A and B, 
 &c. which was to be demonstrated ; and the fame Ccnfequences will follow if we 
 fuppofe the Point S placed below the given Plane of Parallels. - 
 
 Let us now imagine a Plane, as E M N Qj to pafs through the Parallels E M 
 and QJS", it ismanifeft that to the Eye placed in the Plane itfelf or above or 
 below it, as in Figure the 4th, the two Extremities M and N which are farther! 
 from the Eye will appear the neareft, to each other, and the farther they are pro- 
 duced the nearer they will approach, till at laft being indefinitely produced, 
 they will feem to meet in a Point, and the Diftance will vanifh. 
 
 And the fame Confequence will follow in whatfoever Situation the Plane is placed, 
 whether it be perpendicular to the Horizon,or parallel to it, or inclined to it at any 
 given Angle. 
 
 Hence we fee why Rows of Trees,, of Columns, of Pilafters, why Walls and 
 the Sides of Buildings contract themfelves and feem to grow narrower and nar- 
 rower the farther they are extended from the Eye. 
 
 Hence we fee the Reafon why Floors and Pavements of Buildings feem to rife 
 upwards towards the Eye of the Spectator, as is very vifible in long Rooms or 
 Galleries, and why the Cielings feem to fink gradually downwards towards the Eye, 
 whilft the Sides of the fame Building feem to come clofer and clofer, that the 
 Right-fide feems to approach towards the Left, and at the fame Time the Left- 
 fide feems to approach toward the Right-fide, each Dimenfion growing lefler and , 
 lefier, and approaching nearer and nearer, the longer the Room is, till at laft if 
 the Length be indefinite, they will all vanifh into the Vifual Point. 
 
 Hence we fee the Reafon why the Horizon appears higher than really it is, and 
 that the convex Surface of the Sea to an Eye placed upon it appears curved and 
 protuberant, and different from what it really is in itfelf. And, 
 
 Hence we fee alfo the Reafon why Statues and Pictures placed at a confiderable 
 Height above the Eye, alfo why Ornaments placed upon the Tops of Churches 
 or other publick Buildings appear fo much fmaller than really they are, as well in 
 Breadth as in Height, and hence are drawn Rules for giving them their due Pro- 
 portion of Magnitude according to the feveral Stations allotted them, alfo for Por- 
 traits drawn upon Cielings or fet up at any confiderable Height, and for a great 
 Variety of Appearances too many here to enumerate. 
 
 Now inafmuch as the vifible Magnitude of the Lines A O, C P, M V, fee Fi-, 
 gure the 3d, or their Doubles, namely the Lines A B, CD, M N, are as the 
 Tangents of the optick Angles, A S Q, C S P, M S V, to the feveral Radii' S O, 
 
6 Ihe THEORY 
 
 S P, S V, or to their feveral Diftances from the Eye, it follows that the vifible 
 Magnitude of any Object increafes or decreafes in its various Approaches to or Re- 
 moves from the Eye in a reciprocal Proportion to its feveral Diftances from it : 
 And hence, . 
 
 The vifible Magnitude of any Body being given, and its Pittance from the 
 Spectator, the true Magnitude of the fame Body may be found, and on the con- 
 trary, the "true or real Magnitude of the Object being given, its vifible Magnitude 
 at any given Diftance may be determined ; and hence we are taught to find of 
 what Magnitude any Object ought to be made to appear of a given Bignefs at a 
 given Diftance. 
 
 Thefe Laws extend to Objects that are placed above or below the Eye, as well 
 as to Objects that are placed upon the fame horizontal Plane with the Eye, provi- 
 ded they be placed at the fame Diftance from the Eye ; but if they are erected 
 perpendicularly over the Plane, their Altitudes muft be increafed in the Propor- 
 tion of the Difference of the Tangent of the Angle of Elevation, and the Tan- 
 gent of the fame Angle of Elevation increafed by the optick Angle of the Figure 
 when viewed upon the horizontal Surface, and confequently the higher any Ob- 
 ject is placed above the Eye, the greater will be the Difference between the Tanr 
 gents of the feveral Angles of Elevation, and the Tangents of the fame Angles of 
 Elevation increafed by the horizontal optic Angle of the Figure, and confequently 
 the greater muft the real Magnitude of the Object be made to appear of the fame 
 Bignefs as if it was placed upon the fame horizontal Plane with the Eye. 
 
 THEOREM II. 
 
 If any Line in the Object be parallel to the Ground-line, its Perfpective in the 
 Picture will be parallel to the Ground-line alfo. 
 
 Let M N O P, fee Figure the 5th, be the Picture or Perfpe&ive Table, S the 
 Place of the Eye, and A B parallel to the Ground-line O P, the Line to be drawn 
 in Perfpective. 
 
 From S, the Place of the Eye, to the Extremities A and B of the Line A B let 
 the Vifual Rays S A, S B be drawn to cut the Perfpective Table in the Points a 
 and b. If thefe Points a and b be joined together by the right Line a b, I fay 
 this Line a b in the Table, which is the Perfpective of the Line A B the given 
 Object, will be parallel to the Ground-line OP. 
 
 Imagine a Plane as K AB L to pafs through the Line A B, and to ftand at Right 
 Angles to the Plain CDRQj now becaufe the Lines a b and A B are the common 
 Interferons of the parallel Planes M N O P, and A B K L, by the Vifual Plane 
 SAB, they will be parallel by the 5th Axiom, but A B is parallel to the Ground- 
 line O P by Hypothecs, therefore its Perfpective a b in the Table will be parallel 
 to the Ground-line alfo, by the 6th Axiom which was to be proved and inafmuch 
 as the fame Confequence will follow in whatfoever Place of the Plane CDQR, 
 the Line A B is feated, provided it be parallel to the Ground Line A B, or 
 at whatfoever Diftance from the Eye the Plane C D R QJs fixed, it follows 
 that all Lines, that are parallel to the Ground-line of any Picture will, when drawn 
 
of PERSPECTIVE. 7 
 
 in Pefpective, be parallel to each other and to the Ground-line alfo. Again, becaufe 
 the Triangles Sab and S A B are fimilar, S X will be to S x as A 8 to a b but S X is 
 to S x as S Z to S E, therefore, by a Similitude of Ratios, a b will be to A B as 
 S E is to S Z, that is, the Length of the Perfpective Line in any Picture is to the 
 Length of its Original Line, as the Pittance of the Eye from the Picture or Per- 
 fpective Table to the Diftance of the Eye from the Plane of the original Object. 
 
 THEOREM III. 
 
 The Perfpective of any Line, that is perpendicular to the Ground-line in the 
 Original Plane, will, when drawn on the Perfpective Table, run up into the Point 
 of Sight. 
 
 Let S, fee Figure the 6th, be the Place of the Eye, M N O P the Perfpective 
 Table, M N the horizontal Line, E the Vifual Point, O P the Ground-line, and 
 P R the given right Line cutting the Ground-line O P at right Angles in the 
 Point of Incidence P, I fay,if from P, the Point of Incidence, to E, the Vifual Point, 
 the Line E P be drawn in the Picture, the Perfpective of every Point R in the 
 given Line P R will be found fomewhere in the Line E P, in the Picture. 
 
 Produce the Lines S E and R P to G and and draw the Line S 
 
 Becaufe S G and Q^_R are parallel, and the Line E P interfects them both in the 
 Points E and P, they will all be in the fame Plane S QJR G by the 4th Axiom ; 
 and becaufe the Point of Sight S, and the Point R will be always found in this 
 Plane, the Perfpective of the Point R will always be found in the common Inter- 
 feron of this Plane S QR G, and the Plane of the Perfpective Table MNO P, 
 that is in the Line E P, and confequently in the Point r, where the Ray S R drawn 
 from the Eye at S to the given Point R in the Line P R interfects the Line E P 
 drawn from the Point of Sight E, to the Point of Incidence P, and confequently 
 if the Point R were placed in the Point P, the Point P will be the Perfpective at 
 the Point R, and the farther the Point R is removed from the Point P, the higher 
 will its Perfpective r be in the Table, and the nearer will it approach to the Vifual 
 Point E, till at laft, being removed at an indefinite Diftance from the Point of Inci- 
 cidence P, it will be projected in the Vifual Point E, and confequently the Line 
 E P in the Picture will be the Perfpective of the Right Line P R, drawn perpen- 
 dicular to the Ground-line O P in the original Plane, and indefinitely produced, 
 which was to be proved. 
 
 After the fame manner it may be proved that any other Right Line, as O D, 
 indefinitely produced, that cuts the Ground-line at Right Angles, will be reprefent- 
 ed in the Perfpective Table by the Line E O, drawn from the Point of Sight E in 
 the Table to O, the Point of Incidence or Point where the Line O D cuts the 
 Ground-line. 
 
 Whence it follows, that all itraight Lines in the original Plane, that cut the 
 Ground-line at Right Angles, will when drawn upon the Perfpective Table meet or 
 interfect each other in the Point of Sight. 
 
 THEOREM 
 
8 
 
 the THEORY 
 
 THEOREM IV. 
 
 The«Perfpective of any Line in the original Plane, that cuts the Ground-line at 
 oblique or unequal Angles, will be found in that Right Line that is drawn from 
 the Point of Incidence P, to the Point A in the horizontal Line of the Table, 
 which is found by drawing a Line, as S A from the Eye at S, parallel to the origi- 
 nal Line P R, till it interfecl the horizontal Line of the Table M N. See Fig. 7. 
 
 Becaufe the Lines S A and P R are parallel by Hypothefis, and AP interfects them 
 in the Points A and P, they will all be found in the fame Plane S A P R by the 4th 
 Axiom, and confequently the Perfpective of the Point R will be found in the 
 Table in the Point r, where the Ray S R mail interfecl: the Line A P, the com- 
 mon Interferon of the Plane S A PR , and the Perfpective Table M N OP, 
 and if the Line P R be indefinitely produced from the Point of Incidence P, that 
 is, if the Point R be removed at an indefinite Diftance from the Point P, its Per- 
 fpective will be in the Point of the Table at A, that is, the Line A P will be the 
 Perfpective Appearance upon the Table of the Line P R produced indefinitely. 
 
 After the fame manner it may be proved, that any other ftraight Line,_ as O D, 
 indefinitely produced will be projected on the Perfpeclive Table into the Right Line 
 A O, drawn from the Point of Incidence O to the Point found A, whence it 
 follows, that all ftraight Lines that fall obliquely on the Ground-line, yet if they 
 be parallel amongft themfelves, they will all unite or interfecl: each other in fome 
 Point in the horizontal Line, and that Point is called the accidental Point ; and 
 to find it, 
 
 From the Eye Point S draw a Line parallel to the original Line upon the ho- 
 rizontal Table, and where this Line cuts the horizontal Line it will give the ac- 
 cidental Point. 
 
 Hence it follows, that if the Eye be placed any where in the Line AS, pro- 
 duced from A towards S as far as you pleafe, the fame converging Lines on the 
 Table will be the Perfpectives of the fame Parallels in the Ground- plane, and 
 hence innumerable Points of Sight may be afllgned for viewing the fame Picture, 
 and hence we have a Solution of that Perfpeclive Paradox, that the fame Repre- 
 fentation of any ^original Object will be projected on the Table in the fame Lines, 
 though the Eye mould change its Place and Diftance. 
 
 This Propofition is of very great Ufe, and therefore ought to be throughly un- 
 derftood, it' being the main and principal Foundation of all the Practice in Per- 
 fpeclive, and indeed the preceding or third Theorem is nothing but a particular 
 Cafe of this general Propofition. Though I have given it a Place by its felf for 
 Order's Sake, fince when the Lines on the original Plane fall at right Angles upon 
 the Ground-line, the Point of Concourfe of thefe Rays will be found by drawing 
 a Line from the Eye perpendicular to the Picture, and this will neceflarily give the 
 Point of Sight to which all the Lines,that fall perpendicularly upon the Ground-line 
 on the original Plane, muft neceflarily tend, as has been proved in the third 
 Theorem. 
 
 ^ And 
 
of PERSPECTIVE. 9 
 
 And in as much as the Line drawn from the Eye to the Point of Diftance upon 
 the Perfpective Table, muft neceflarily form an Angle of 45 Degrees, with the 
 Principle Ray or the horizontal Line, the containing Sides of the Right Angle being 
 equal, it follows that the Diagonals of all Squares, one of whofe Sides is parallel 
 to the Picture, and all other Lines that form an Angle of 45 Degrees with the 
 Ground-line, will have the Point of Diftance upon the Table for their Point of 
 Concourfe ; and where, if produced upon the Table, they will all center. 
 
 THEOREM V. 
 
 The Projection or Perfpective of any Line, that is perpendicular to the horizontal 
 or Ground-plane, will on the Picture or Perfpective Table be perpendicular to the 
 Ground-line. 
 
 Let NMOP, in Fig. 8. reprefent the Perfpective Table, C D K the ho- 
 rizontal or Ground-plane, S the Place of the Eye, and A B the Line to be pro- 
 jected, which in the prefent Cafe is fuppofed to be perpendicular to the horizontal 
 Plane CDKQ^ imagine the Plane RTZX to pafs through the Line A B, and 
 to be parallel to the Picture MNOPj now becaufe S B A is another Plane inter- 
 fering the two former Planes, their common Sections, or the Lines A B, a b, will 
 be parallel to each other by the 5th Axiom, but A B is perpendicular to the hori- 
 zontal Line X Z, therefore a b, if produced to G, will be perpendicular to the 
 Ground-line O P, which is parallel to the Line X Z, the Ground-line of the 
 Plane RTZX. w. w. d. 
 
 And fince the fame Confequence will follow if the Line A B be fet upon any 
 other Point of the horizontal Table, it follows that the Perfpective Reprefentation 
 of all Lines, that on the Ground-plane are erected perpendicularly, will when pro- 
 jected on the Perfpective Table be perpendicular to the Ground-line and parallel to 
 each other. And in as much as the Line a b is to the Line A B, as s b is to S B, 
 that is, as S E is to S L, it follows that a b, the Perfpective of A B, is to its Original 
 AB, as SE, the Diftance of the Eye from the Perfpective Table,, to S L, the 
 Diftance of the Eye from the Plane of the original Object. 
 
 Again, through the Point a in the Picture, the Perfpective of the Point A in 
 the Ground-plane, draw x z parallel to the Ground-line O P, to cut the Rays S X, 
 S Z, in the Points x and z, then will x z in the Picture be the Perfpective of the 
 LineXZ on the Ground-plane, and becaufe, by the Similitude of the Triangles 
 sax and SAX, it will be as A X is to a x, fb is S A to s a, and fo is S E to S L, 
 and fo is a E to a S, and fo is a b to A B j whence it follows that x a is toXA> as 
 a bis to A B, that is, any perpendicular on the Ground-plane is to its Perfpective 
 in the Picture, as any Parallel on the Ground-plane is to its Perfpective in the fame 
 Picture, fuppofing the perpendicular and Parallel at the fame Diftance from 
 the Picture whence it follows, that if the perpendicular and the parallel are both of 
 the fame Length, their Perfpectives in the Picture will be of the fame Length alfo k 
 And this is a Property of no fmall Ufe in the Practice of Perfpective s for the 
 
 B Length 
 
io Ihe THEORY 
 
 Length of any original Parallel or Perpendicular being known, it will be eafy by 
 the Help of a Sector to give any part of a Senographick Projection its Due Dimen- 
 sions in any Situation upon the Table. 
 
 Again, if from any Point S, in the Line S F confidered as the Place of the 
 Eye, Rays, as SpB, S q A be drawn to the Extremities of the perpen- 
 dicular A B, becaufe A B is to p q, as S B is to S p, that is, as S B is to S b, 
 that is, as A B is to a b, it follows that p q, and a b are equal : Wherefore the 
 Diftance of the Object and the Eye from the Table, continuing the fame the 
 Perfpectives of the lame Perpendiculars, are equal to each other, whether the Eye 
 be placed at a greater or lefs Height above the Horizon. 
 
 PROBLEM 1. 
 
 To find the Seat in the Perfpective Table of any given Point in the Original or 
 Ground-plane, the Height of the Eye, its Diftance from the Picture, and the 
 Diftance of the original Point from the Table being given. 
 
 Let N M O P, See Fig. 9. reprefent the Table, S the Place of the Eye, S F, 
 its Height above the Ground-plane CDKR, S E its Diftance- from the Picture, 
 Q^the original Point in the horizontal Plane CDKR, and A its Diftance 
 from the Perfpective Table. 
 
 From S draw the Line S E, parallel to the Horizon or perpendicular to the Ta- 
 ble to cut the Table in the Point E, the Vifual Point in the Table, and from Q^, 
 draw the Line Q^A perpendicular to the Picture M N O P, to cut the Ground-line 
 in the Point A, the Point of Incidence. Now if a Plane as T S F Q^, be ima- 
 
 fined to pafs through the Lines, S T, F Q^, it will cut the Pefpectire Table in the 
 ine E A their common Interferon i and in this Line of the Table will the Per- 
 fpective of the Point QJbe found, and confequently in the Point q the Interfer- 
 on of the Diagonal S Q drawn from S, the Point of Sight, to O, the given Point 
 on the Ground-plane. Let us now imagine the Plane of the Perfpective Table to 
 revolve about the Line E A, the common Interferon of the two Planes till it 
 coincide with the Plane S TQJF, as in Fig. 10. then will the Point QJn the 
 horizontal Table coincide with the Point in the Ground-line, the Point S 
 or Seat of the Eye in the Plane S F QT will coincide with the Point S in the hori- 
 zontal Line of the Perfpective Table, and at the fame Diftance from the Vifual 
 Point E,as it was from the Perfpective Table : In Fig. 9. in the like Manner, the 
 Diftance of the Point Q, in the Ground-line O P will be as far diftant from its 
 Point of Incidence A, as it was in the horizontal Plane from the fame Point A, 
 for by this Revolution of the Plane of the Perfpective Table, the Points S and 
 revolve about the Centers E and A, and confequently always keep the fame 
 Diftance from them, but the Line E A, the common Interferon of the two 
 Planes MNOP, and S T QJF becoming now the Axis about which the Plane 
 of the Table revolves remains the fame and immoveable, and confequently the 
 Seat of the Point QJn the Perfpective Table, remains in the fame Place as at firft 
 before the Plane was fuppofed to revolve, and is therefore the true Perrpefti ve 
 Place upon the Table, which being allowed, we fhall have this general Rule. 
 
 2 For 
 
©/"PERSPECTIVE. ii 
 
 Tor finding the Seat in the Perfpective Table of any Point In the horizontal 
 Table. See Fig. 10. Namely, 
 
 1 . From Q the given Point in the horizontal Table draw the Line Q^A perpen- 
 dicular to the Ground-line to cut it in the Point of Incidence A. 
 
 2. Set off the Diftance A of the Point Qjn the horizontal Line from the 
 Ground- line O P, from its Point of Incidence A in the fame Ground-line to 
 
 3. From E, the Point of Sight, to A, the Point of Incidence, draw the Ray E A, 
 and from S, the Point of Diftance, to the Point Qjn the Ground- line laft found 
 draw the Diagonal S Q^, and where this interfects the Ray E A laft drawn as in 
 the Point q, it will give the Perfpective in the Table of the given Point Qjn the 
 Ground-plane. 
 
 Now as every Line is bounded by Points, and every Surface by Lines, and 
 every folid by Surfaces hence we are taught how to draw the Reprefentation of 
 any given Object upon the Perfpective Table. And indeed the Laws here laid 
 down and demonftrated are fo general, that whofoever underftands them readily 
 •will fee the Reafon of every Step taken in drawing the Scenographick Reprefenta- 
 tion of any original Object upon any Vertical Perfpective Table. 
 
 THEOREM VI. 
 
 If the Perfpective Table be inclined to the Plane of the Horizon at any given 
 Angle, the Perfpective of any original Line, that is parallel to the Ground-line,, 
 will in the Perfpective Table be parallel to the Ground-line alfo. 
 
 Let M N O P, in Fig. 1 1 . reprefent the Perfpective Table inclined to the hori- 
 zontal Plane C AB Q^ at an Angle equal toMOA; let S be the Place of the Eye, 
 and A B the Ground-line, whofe Perfpective is to be drawn, from S the Eye, let the 
 Vifual Rays S A, S B, be drawn to the Extremities A and B of the given Line 
 A B,to cut the Perfpective Table, in the Points a and b ; now ifthefe Points a and b 
 are connected together by a Right Line a b, I fay, this Right Line a b, which is 
 the Perfpective of the original Line A B, will be parallel to the Ground-line O P. 
 
 Imagine a Plane as R A B T to pais throught he given Line A B, and to be pa- 
 rallel to the Plane of the Table M N O P. 
 
 Now becaufe the Lines a b and A B are the common Interactions of the 
 parallel Planes M N OP, and R A BT by the Vifual Plane SAB, they wilt 
 be parallel to each other by the 5th Axiom ; but the original Line A B is parallel- 
 to the Ground-line O P by Hypothecs, therefore a b its Perfpective in the Table 
 will be parallel to the fame Ground-line O P alfo, by the 6th Axiom, w. w. d . 
 
 Hence it follows that all Lines whatfoever, that upon the Ground-plane are 
 parallel to the Ground-line, their Perfpectives upon the Picture will be Parallel to- 
 the' Ground-line and to each other alfo. 
 
 THE- 
 
12 
 
 The THEORY 
 
 THEOREM VII. 
 
 In any inclined Plane, the Perfpective of any Line in the original Plane, that, 
 being produced, will cut the Ground-line at oblique Angles, will be found in that 
 Right Line that is drawn from the Point of Incidence P. See Fig : 12. to the Point 
 A in the horizontal Line of the Table, which is found by drawing a Line as S A 
 from the Seat of the Eye at S parallel to the original Line P R, till it interfect the 
 horizontal Line of the Table M N. 
 
 Becaufe the Lines S A and P R are parallel by Hypothecs, and A P a right 
 Line interfering them both, therefore a Plane as S PR A will pais through 
 them all, and therefore the Perfpective of the Point R will be found in the 
 Table in the Point r, the Interaction of the Diagonal S R, with the Line 
 A P, the common Interferon of the Plane of the Table M N O P, and the 
 Plane A S P R, confequently wherefoever the Point R be taken in the right 
 Line PR, its Perfpective will be found fomewhere in the Line AP, and 
 confequently the Line A P in the Table will be the Perfpective of the Line P R in- 
 definitely produced, fo that in whatfoever Part of the horizontal Plane the Line 
 P R be taken, provided it always forms the fame Angle with the Ground-line, 
 its Perfpective upon the Table will be always found in that Right Line which con- 
 nects its Point of Incidence P on the Ground-line with its accidental Point A in 
 the horizontal Line. 
 
 If the Line P R cuts the Ground-line at right Angles, its parallel S A will in- 
 terfect the Table in the Point of Sight E upon the Table ; wherefore in inclined 
 Planes as well as vertical Planes, as all Lines, that are perpendicular to the Ground- 
 line in the horizontal Plane, when drawn on the Perfpective Table, do run up and 
 unite in the Point of Sight, fo all other Lines in the Ground- plane that cut the 
 Ground-line when produced at unequal Angles, will if they are parallel to each 
 other when projected on the Perfpective Table run up and unite in one common 
 Point ; whence it follows that the Height of the Eye and its Diftance from the 
 inclined Table being known or given, the Perfpective Reprefentation of any ori- 
 ginal Ground-plane is drawn on the inclined Table by the fame Method, and after 
 the fame manner as it is done upon Vertical Tables. Let it therefore be required in, 
 
 PROBLEM II. 
 
 To find the Length of the principal Ray intercepted between the Point of Sight 
 and the Ground-line, or which is the fame Thing, the Height of the Eye in the in- 
 clined Table and its Diftance from the Table, the perpendicular Height of the Eye 
 above the Horizon, and the Inclination of the Perfpective Table being given. 
 
 Let O P, fee Fig. 13. reprefent the Ground-line, F QC a Line drawn at right 
 Angles to it, S the Seat of the Eye, S F its perpendicular Height above the 
 Ground-plane, and QJI the inclined Plane forming an Angle with the horizontal 
 Plane equal to the Angle E Q^C 
 
 2 From 
 
of PERSPECTIVE 13 
 
 From Qjhe Point of Incidence of the Li;ne E Qjn the Ground-line, draw A 
 perpendicular to the Ground-plane, and through S the Seat of the Eye draw S A E 
 parallel to the Line F C to interfect the Line QE in E, then will E be the Point of 
 Sight in the inclined Plane, Q^E the Height of the Eye, and S E the Space 
 between the Vifual Point E and the Point of Diftance S, whence the Perfpective 
 of any Ground Plot may be drawn on that Plane. 
 
 THEOREM VIII. 
 
 In any inclined Plane, as M N O P, Sets Fig. 14. if from E the Point of Sight 
 through the Point b,where the Bafe F B of the Eye's perpendicular Height S F cuts 
 the Ground-line of the Table, a Line as E lb be drawn and produced till it cut S F, 
 the Line drawn from the Eye at S perpendicular to the horizontal Plane C QO P 
 produced downwards in the Point D, I fay the Perfpective of every Line perpendi- 
 cular to the horizontal Plane, will be found in that right Line in the Table that is 
 drawn from the Point D through the Point: of Incidence made by a perpendicular 
 drawn from the Bafe of the elevated Line on the horizontal Plane to the Ground-line 
 of the inclined Table. 
 
 Let M N O P be the inclined Perfpective Table, O P its Ground-line, where 
 it interfects the Ground-plane CRTQ^S the Seat of the Eye, S F its perpen- 
 dicular Height, E the Point of Sight in the Table, AB a Line perpendicular 
 to the Ground-plane, whofe Point of Incidence b is coincident with the Foot 
 b of the principal Ray E b drawn on the Table ; now if the Lines S F and E b 
 are produced till they interfecl: each other im the Point D, I fay, that if from this 
 Point D through any other Point of Incidence as x in the Ground-line, a right Line 
 as D x z be drawn the Perfpective of the JLine Z X erected perpendicularly over 
 the horizontal Plane, which Point of Incidence in the Ground-line is x, mail be 
 found in this Line z x in the Table. 
 
 Becaufe the Lines S F D and A B W, are parallel by Hypothefis, a Plane as 
 S A BWDF will pafs through them, and becaufe the Eye is feated in this 
 Plane in the Point S, the Perfpective of the Line A B will be found upon 
 the Table in the Line E D, the common Interfe&ion of the two Planes, which 
 Line produced muft neceflarily cut the perpendicular S F, produced downwards 
 in the Point D, fince they all lye in the fam e Plane. S YWD. 
 
 Now if from this Point D a Line as Dx be drawn through x, the Point of Inci- 
 dence of the Line Z X erected perpendicular over the horizontal Plane C R T Q, I 
 fay the Perfpective of this Line Z X will be found in the Line D z x. 
 
 For becaufe the Lines S D and Z X are parallel by Hypothefls,a Plane as S Z XD 
 will pafs through them both ; and becaufe the Eye is feated in this Plane at S, the 
 Perfpective of the Line Z X will be found on the Table in the Line x z, the com- 
 mon Interfection of the two Planes, which being produced muft neceflarily cut 
 the Line S D in the Point D, the Interfection of the fame Line S D with the Plane 
 of the inclined Table produced, whence the Perfpectives of the Lines AB and ZX 
 on the Table will be the Lines a w and z q, intercepted between the Rays S A, S Z, 
 S X, and S B flowing from the Eye to the Top and Bottom of the eiven Perpen- 
 diculars AB, andZX. , 
 
 And 
 
14 'The THEORY 
 
 And after the fame manner may the Perfective of any other Line elevated per- 
 pendicularly over the horizontal Plane be drawn on the Table. 
 
 For if xve imagine a Plane to pafs through the Line S D perpendicular to the ho- 
 rizontal Plane indefinitely extended, and at the fame Time conceive this Plane to 
 revolve about the Line S D as an Axis, it will during the Courfe of this Revolu- 
 tion pais through every Line that ftands perpendicular to the horizontal Plane, and 
 the fucceffive Interferons of this Plane with the Plane of the Table will be the 
 fucceflive Perfpectives of the feveral Perpendiculars it fhall happen to pafs through, 
 and as all thefe Lines muft neceflarily center in the immoveable Point D, as being 
 common to every Situation of the revolving Plane, it muft neceflary follow, the 
 Eye remaining alfo immoveable, that the Perfpective of every Line, that is per- 
 pendicular to the Ground-plane, will be found in that Line in the Table which is 
 produced by drawing a Line from this Point D, through the Point of Incidence 
 in the Ground-line made by a Perpendicular drawn from the Bafe of the given elevat- 
 ed Line to the GrOund-line of the inclined Table ; which was to be demonftrated. 
 
 Hence and from the Rules demonftrated in 'Theorem 6, and 7. the Practice of 
 drawing the Perfpective of Objects of any kind upon inclined Tables is eafily 
 deduced. 
 
 By viewing the Figure, it is evident that the greater the Inclination of the Plane, 
 the lefler will be the Angle S D E, and the farther will the Point D be removed 
 from the horizontal Plane CRT Q^, till at laft when the Plane becomes Vertical 
 the Point of Interferon D vanifhes, and the Lines E b D and SFD become pa- 
 rallel, whence, as has been proved in the 5th Theorem, it follows that all Lines that 
 are perpendicular to the horizontal Plane will, when projected on theTable, be per- 
 pendicular to the Ground-line alfo. 
 
 Again, the farther the Point of Sight S is removed from the Table, the greater 
 will be the Diftance of the Point of Interfection D from the horizontal Plane 
 CRT till at laft the Eye being fuppofed at an infinite Diftance the Line 
 SFD will be removed at an infinite Diftance from the Picture, alfo the Point 
 Of Interfection D will vanifh, and the Elevation of all Lines perpendicular to the 
 horizontal Plane will become Perpendiculars to the horizontal Plane in the Table, 
 Which is the Foundation upon which the Military or Birds Perspective is founded. 
 
 Again, the lelTer the Inclination of the Table M N O P, the nearer does the 
 Point of Interfection D approach to the Point F in the horizontal Table, the Foot 
 of the Eyes perpendicular, till at laft when the inclined Plane M N O P coincides 
 with the horizontal Table CRT the Angle of Incidence vanilhes, and the 
 Point of Concourfe D coincides with the Point F •, whence it follows, 
 
 That in all horizontal or optical Projections, the Perfpective of" every Line, that 
 is erected perpendicularly over the horizontal Table, will be found in that Line of 
 the Table which is produced by drawing a Line from the Foot of the Eye perpen- 
 dicular through the Bafe of the elevated Line ; whence it follows that the Perspec- 
 tive of all Lines, that ftand perpendicular upon the horizontal Plane, will if pro- 
 duced unite or center in one common Point, namely the Point where a Line let fall 
 perpendicularly fhall interfect the horizontal Table. 
 
 THEOREM 
 
O/PERSPECTTIVE. 
 
 THEOREM IX. 
 
 If the Plane of any original Figure be parallel to the Table, its Perfpective will 
 ;be fimilar to its Original, alike, and a^ike fituated. 
 
 Let S, fee Fig. 1 5. be the Seat of the Eye, M N O P the Table, H I K L the 
 Plane of the original Figure A B C D. 
 
 I fay, if the Planes M N O P and H I K L are parallel, the Perfpective Ap- 
 *pearance abed upon the Table Ihall be flmilar to its original A B C D. 
 
 For from S the Point of Sight draw the Rays S a A, S b B. S c C, and S dD. 
 
 Becaufe the Planes M N OP and H I KLare parallel, SAB is a Vifual Plane 
 Interfering them, therefore the common Interferons ab and A B will be parallel, 
 therefore A B will be to a b as S B is to S b : And again, becaufe SB C is aVifual Plane 
 terfecting the fame parallel Planes, therefore their common Interferons, namely 
 the Lines B C and b c will be parallel, therefore B C will be to b c, as the fame 
 Ray ,S B is to the Ray S b, wherefore by Equality of Ratios a b will be to b c, as 
 A B is to B C ; after the fame manner it may be proved that b c is to c d, as B C is 
 to C D, and c d is to d a, as C D is to D A, whence the Perfpective Figure abed 
 is flmilar to its original ABCD which was to be proved ; whence it follows, that 
 the optical or horizontal Perfpective of all Plane Figures that are parallel to the 
 Table, will be fimilar to their Originals ; that is, that the Perfpective of fquare 
 Figures parallel to the horizontal or perfpective Table, will on the Table be fquare, 
 alfo the Perfpectives of Circles, will be Circles, of Hexagons, will be Hexagons, cjfr. 
 
 Whence and from the laft Corollary of the preceding Theorem, the Reafons of 
 all the Appearances in horizontal Perfpective are manifeft, and as all Shadows are 
 nothing elfe but horizontal Projections of the feveral Objects, the Candle or lumi- 
 nous Body fupplying the Place of the Eye ; hence it follows that every horizontal 
 Projection of any Object elevated above the Plane is the Projection of the Shadow 
 of the fame Object, and confequently the Rules given for forming of one will 
 ferve for forming the other. And inafmuch as the immenfe Diftance of the Sun 
 is infinite with regard to any terreftrial Object, hence it is that the Rays that flow 
 from the Sun to form the folar Shadow are fuppofed to be parallel and hence it 
 is that every Orthographick Perfpective of any Object elevated above the Plane of 
 the Horizon, is the Projection of the Shadow of the fame Body, and confequently 
 in drawing of one, you draw the other alfo ; and thefe feveral Shadows, when 
 drawn upon the Scenographick Table according to the Rules of Scenographick 
 Projection, will exhibit upon the fame Table the Shadows of all Objects drawn upon 
 the Picture. r 
 
 Again, inafmuch as the Practice of horizontal Perfpective proceeds after the 
 fame manner as does the Practice of Scenographick Projections, fo in Problem the 
 firft, Page the 10th. 
 
 If we fuppofe the Eye in Figure 2, in S, the Point of Diftance in that Cafe, 
 and E A to be the Diftance of the Eye from the given Object, the Demonftration 
 for one will hold good for the other, and confequently in proving the Operation 
 in one, you prove the Operation in the/ other alfo. 
 
 Though 
 
16 The T HEORY.^f, 
 
 Though my principal View in this Tract has been to render the Demonftrations 
 plain and concife, and the Number of theorems as few as poflible, yet at the fame 
 Time I have endeavoured to make them fo general, that I may venture to fay there 
 is fcarce any Operation made ufe of in the Practice of the feveral Kinds of Perfpeffive 
 but what may be accounted for by fome one or other of the preceding Laws ; this 
 together with the following Treatife, which I look upon as one of the beft practical 
 Books of its Size that has appeared in the Engli/h Language, will I hope make the 
 Whole as compleat and ufeful a Piece as the narrow Bounds will admit of. 
 
u Fig. the 8 ! k 
 
 i .„ 1 — JV"— 1 
 
 i , — I — — a *^- 
 
 M it 
 
 Fig. the 
 
 Fig. the n*> 
 
 N 
 
 B 
 
 K 
 
 . the IR^ 
 
 H 
 
SOME 
 
 DEFINITIONS 
 
 AND 
 
 PRINCIPLES 
 
 0 F 
 
 PERSPECTIVE. 
 
 A 
 
I 
 
 PERSPECTIVE 
 
 Definitions, Names and Terms of the Points, Lines and Figures ufed m 
 
 the following Work. 
 
 APo i nt is that which is conceived to have no Parts ; fuch as A, Fig. r. 
 There are three Kinds of Points ufed in Perfpective, called Points of Sight 
 or View, Points of Di/lance, and Contingent or Accidental Points. 
 
 A L i n e is a Length without Breadth ; fuch is A B, Fig. z. There are five 
 principal Lines ufed in Perfpective, viz. i. The Line of the Bafe, called alfo the 
 Line of the Plane, or the terrejl rial Line, as C D, Fig. 3. % The perpendicular or 
 plumb Line, which, falling on another, makes the Angles on either Side equal : 
 Such Angles are faid to be Right ones, and the Line fo falling on the other 
 called a Perpendicular thereto. Thus, in Pig. 3. A BandEF, falling no CD, 
 and making Right Angles in B and G, is a Perpendicular thereto. 3. The pa- 
 rallel Lines, which, being continued on the fame Plane to Infinity, never meet ; 
 as the Lines N and.O, Fig. 6. The horizontal Line is no more than-a Line drawn 
 parallel to the terreftrial Line ; as we (hall fhew more amply rn its Place. 4. The 
 Diagonal Line, which is that drawn acrofs a Figure, from one Angle to another ; 
 fuch is K L, Fig. 10. 5. The occult Line, which is either drawn in Dots, or dry, 
 and isfuppofed not to appear when the Work is finifhed ; fuch is O N, Fig. 2. 
 
 A Right. Angle we have already faid to be that formed by a Perpendi- 
 cular. 'Tis here reprefented a-part, by E F G, Fig. 4. to fhew what it is the more 
 diftinctly. There are two other kinds of Angles, which cocnprife all thofe that 
 are not Right ones: The firft, called ohtufe, are fuch as are greater than a Right 
 Angle ; as HL M, Fig. 5. The other, 'acute, are lefs than a Right Angle ; fuch 
 is H I K in the fame Figure. 
 
 A T e r m is the Extreme of any Thing: Thus the Points A and B, Fig. 2. 
 are the Terms of the Line A B. 
 
 A F 1 g u r e is comprehended under one or more Terms: Thus 7, 8, 9, 13, 
 &c. are Figures. 
 
 A S qjj are has its four Sides equal, and its four Angles Right ; fuch is 
 A BCD, Fig. 7. 
 
 AParallelogram, or long Square, has its four Angles Right, but 
 not its Sides equal ; fuch is C D E F, Fig. 8. » 
 
 An Equilateral Triangle confifts of three equal Sides •, as GHI, Fig. 9. 
 
 The Section* or Intersection of two Lines is when they run acrofs, or 
 cut each other in a Point, as in Fig. 11. where AB and CD cut or interfetl in E. 
 
 ACurveLineIs that which goes indirectly, or about, from one Point to 
 another-, fuch is LM, Fig. 12. 
 
 A Circle is a plain Figure, comprehended under one fingle Line, called the 
 Circumference, to which all the Lines drawn from the Center are equal ; fuch is 
 B C D, in Fig. 1 3. And the Point A in the Middle thereof is called the Center. 
 
 The Diameter of a Circle is a Right Line B C, paffing through the Cen- 
 ter A, and dividing the Circle into two Parts. 
 
 An Oval, or E l l y p s i s, is an oblong Figure, comprehended under one 
 crooked, regular, but not circular, Line ; fuch is E, Fig. 14. 
 
 ASpiral, or Volute, is a Line found by a Revolution about one or 
 two Centers ; fuch is F, Fig. 15. 3 
 
f 
 
2 
 
 PERSPECTIVE 
 
 Sequel^/ the Definitions, Names and Terms. 
 
 ATANGENTisa Line, which being produc'd only touches or razes 
 an Object, Figure, or Line, wichout cutting it: Thus the Lines 
 AB are Tangents to the Circle C, in the Points D D. We here add 
 two kinds of Lines, which have the fame Denominations as the former, 
 and yet have different Effects, on account of the Point of View : For 
 the Angle E A B is to be efteem'd a right Angle, and all the Lines 
 CCC, &c. to be efteem'd as Perpendiculars to the Plane, as DF is ; 
 and the Lines A B, G I, and H K, as Perpendiculars to the terreftrial 
 Line. All the Lines drawn to the Point of Sight, whether from above, 
 or below, or from either fide, are called Rays, or Visual Rays. 
 
 APlan, Ichnography, or Ground- Plat, is a firft Draught 
 or Defign of a Thing, reprefenting the Traces or Paths of its Foundati- 
 on on the Ground, fo as to exhibit the Correfpondence, Situation, Di- 
 ftance, and Magnitude of the Parts, refpe&ively, at one View. This is 
 what we have reprefented in L and M. 
 
 A Polygon is a Figure containing feveral Angles ; as L. 
 A D e gr e e is a little Arch or Portion of a Circle, whereof it con- 
 tains 360. Each Degree the Aftronomers fubdivide into 60 Minutes, and 
 each Minute into 60 Seconds, &c. But fuch Subdivifion has no place here. 
 'Tis enough we know that Degrees are thofe little Divifions in the Circle 
 NOP Qj^ whereby Angles are eftimated. From them we derive an eafy 
 Method of making all forts of Polygons, viz. by dividing 360 by the 
 Number of Angles the Figures areto confift of. Thus, for Inftance, if I 
 would make a Square, I divide 360 by 4, the Quotient is 90, which 
 gives the right Angle NMO: And fo for the reft. Such as are unac- 
 quainted with Arithmetic, will find geometrical Methods of doing the 
 fame in Plate IV. 
 
3 
 
 PERSPECTIVE 
 
 Methods of Defcribing the Lines and Figures above defined, 
 
 i.*T"0 raife Perpendiculars i If it be in the Middle of a Line that a Perpendicu- 
 1 lar is required, open the Compafles to more than half the Length of the 
 Line, and fetting one Foot in the Point A, Fig. i. with the other ftrike little 
 Arches both above and below, as F and F: The like do for the Point E, and the 
 two Interferons of thofe Arches will give a Perpendicular to the Line A E. 
 
 2. If the Line be at the Top or Bottom of a Draught or Paper , fo that Arches can- 
 not be (truck both above and underneath, divide the Line into two, to get the 
 Point G, Fig. 2. and, from the two Extremes of the Line, make Arches in- 
 terfering each other in H ; then draw a Line from H to G. 
 
 3. To raife a Perpendicular at the End of a Line, as at the Point I, of the Line 
 I K, Fig. 3. there are divers Methods : The firft is that already delivered. But 
 where room is wanting, one Leg of the Compafles is to be fet in the Point I, 
 and with the other a large Portion of a Circle L M is to be ftruck, and the Com- 
 pafles* thus open, to be fet on the Point M, and with the other Leg the Circle to 
 be cut in the Point N, half the Arch M N being fet off from M towards O, 
 gives the Right Angle OIK: Or, without feeking for half the Arch M N, 
 from the Point N, defcribe an Arch P Qj then, laying a Ruler over the Points 
 M and N, draw a Line, cutting the Arch P QJn the Point P, and raife a Line 
 from I to P ; which is the Perpendicular required. 
 
 4. Or thus: If you would raife a Perpendicular from the Point P, Fig. 4. take 
 a Point, at Pleafure, over the Line PS, as the Point and from this Point 
 defcribe a Circle pafling thro' the Point P, and cutting the Line P S in fome 
 Place, as S ; then from S draw a Line thro' Qjo the Circumference of the Cir- 
 cle T, and the Point T gives the Extreme of the Perpendicular TP. A juft 
 Square fhortens all thefe Operations. 
 
 5. To let fall a Perpendicular from a given Point : From the Point, as A, Fig. 5. 
 defcribe the Arch B C, cutting the given Line E F in the Points G H, from 
 which Points defcribe two little Arches above or below, cutting each other in 
 the Point I ; then, from the Point A let fall a Line thro' I to the Line E F, 
 and it will be the Perpendicular of the given Point. 
 
 6. From a Point given at the End of a Line to let fall a Perpendicular: Suppofe the 
 given Point K, and the Line L M, Fig. 6. from K draw a traverfe Line at 
 Pleafure, cutting the Line L M in fome Point, as N ; divide the Line KN into 
 two equal Parts, and, from the middle Point O, draw an Arch thro' K ; and 
 from the Point M, where it interfects the Line L M, draw the Perpendicular K P. 
 
 7. A Parallel Line, if truly drawn, will be a Tangent to Semi-circles drawn 
 from Points affumed in the other Line : Thus F G, Fig. 7. is parallel to H I, 
 becaufe it only touches or razes the Semi-circles L and K. 
 
 8. To divide a Line into equal Parts : Suppofe the Line be A B, draw another 
 Parallel thereto, either above or below it, as C D ; and on this laft, which is ei- 
 ther to be greater or lefs than that to be divided, fet off as many Parts as A B 
 is to be divided into, ex. gr. into feven ; from the firft and laft of thefe Divisions 
 draw Lines thro' the Extremes of A B, interfering each other in fome Point, 
 as E ; from which Point drawing Lines to all the Divifions of the Line C D> the 
 Line A B will be divided into feven equal Parts. 
 
4 
 
 PERSPECTIVE 
 
 METHODS of Defcribing tbi Figures] 
 
 I. \ Lfoe&$ AB, Fig. I, being given to form a Square on, fet one Foot of the Companies in the 
 Jt\_ Point A, and extending the other the Length A B, defcribe the Arch B C ; then from the Point 
 B defcribe another Arch A D, interfe&ing the former in E, and from E fet off half the Arch E A, or 
 E B outwardly, to D and C ; to which Points drawing Lines from A, B, &c the Square is form'd. 
 
 Or thus. Upon the given Line A B erett a Perpendicular A C equal to A B ; then, taking the Length 
 A B in your Compaffes, fet one Foot in B, and with the other defcribe an Arch :* The like being done 
 from the Point C, the Interferon of the two Arches will be the Point D, which gives the Square ABCD. 
 
 2. To defcribe a Parallelogram, or long Square, on the Term E, of the given Line E F, ereft a Perpen- 
 dicular either greater or lefs than the fame, as E G ; then taking E G in your Compaffes, fet one Foot 
 in F, and with the other defcribe an Arch ; take alfo E F in your Compaffes, and fetting one Foot in G, 
 defcribe a fecond Arch, cutting the former in H : This will give you the Parallelogram requir'd. 
 
 Of Circular Polygons, which are Figures of fever al Angles infcribed in Circles. 
 
 3. To defcribe an equilateral Triangle : The Compaffes being open to the Radius of the Circle, fet one 
 Foot in the Point A, defcribe the Arch D E, and draw a right Line D E, which will be the Side of 
 the Triangle DEF. 
 
 4. For a Square, draw two Diameters at right Angles, and join their Extremes; thus you will have 
 the Square ABCD. 
 
 5. For a Pentagon, or Five Angle, draw two Diameters, and take D G, half the Semi-diameter D I, 
 and from the Point G, with the Interval G A, defcribe the Arch AH; the Chord of which is the 
 Side of the Pentagon. 
 
 6. For the Hexagon, or Six- Angle, the Semi-diameter is the Side of the Hexagon. 
 
 7. For the Heptagon, or Sept Angle, take half a Side of the equilateral Triangle. 
 
 8. For the Oclogon, or Bight- Angle, take half a Quadrant of the Circle 
 
 9. For the Enneagon, or Nine-Angle, take two thirds of the Semi-diameter for the Side ; as E B. 
 
 10. For the Decagon, or Ten- Angle, divide the Semi-diameter into two in the Point G, and from G. 
 with the Interval G A, defcribe an Arch A B ; the Part of the Diameter B C will be the Side of the 
 Decagon. 
 
 11. For the Undecagon, or Eleven- Angle, draw two Diameters at right Angles, and from the Point A, 
 with the Interval of a Semi-diameter, defcribe an Arch B C ; then from the Point of Interferon C, 
 draw a Line to E ; the Portion C D will be the Side of the Undecagon. 
 
 12. Dodecagon, or Iwuelve- Angle, divide the Arch of a Hexagon, A B, into two equal Parts ; the 
 Chord of the Moiety will be the Side. 
 
 13. An Oval is formed divers ways ; in all which the Figure is either a compound of feveral Portions 
 of Circles, or it is one Line drawn from two Centres. .The moil ufual Methods arethefe: Having de- 
 scribed a Circle, and drawn two Diameters therein, as A B C D, from the Points A B we draw two 
 other Circles equal with the'firft ; then from the Point D we draw a Line through the Center of the 
 laft Circle to the Circumference E : This done, fetting one Foot of the Compaffes in D, and with the 
 other taking the Interval E, we defcribe an Arch E F. The like being done on the other Side, the Oval 
 is formed. 
 
 14. For a rounder Oval, draw a fingle Line, and from A, as a Center, defcribe a Circle, the Inter- 
 feron whereof with the right Line in the Point B, will be the Center of another Circle. Now, to form 
 the Oval, take in your Compaffes the whole Diameter of one of the Circles, as from A to F, andinone 
 of the Interferons of the Circles, as D, fetting one Foot of the Compaffes, with the other draw the 
 Arch G H : The like do from the Point E. 
 
 15. Otberivife we have an eafier and more ufeful manner of defcribing Ovals than any of the preced- 
 ing ones; the lame Rule ferving for all Form?, long, narrow, broad, fhort, &c. Thus: Set two Nails 
 or Pins in a right Line A B y to ferve as a Center, and about thefe tie a Thread of the Length and Width 
 of- the Oval required, as ABC; hold the Thread tight with a Pen or Pencil, and turn it about till you 
 arrive where you began. If you require it a long one, fet the Centers the farther apart ; and oblem- the 
 contrary for a fhort one : For if the Nails ftand clofe together, the Figure will be a Circle. 
 
 16. For a Spiral, or Volute, take two Points in a Line A B ; the Points to ferve, one after another, as 
 Centers. For inftance, having drawn the Semi-circle A B, fet one Foot of the Compaffes in B, anu open 
 the other to the Length B A, and defcribe a Semi-circle A C; then fetting one Foot in A, take the In- 
 terval A C, and draw the Semi-circle CD; and this continuing as long as youpleafe,. ftill fhifting Centers. 
 Yignola gives us another Method- 
 
 3 
 
5 
 
 PERSPECTIVE 
 
 Of the Visual RAYS. 
 
 IF an Object be a Jingle Point, it fends only one vifual Ray to the Center 
 of the Eye ; and that Ray is called the Axis, or Central Ray, as being the 
 moft vivid of all Rays : Such is A B. 
 
 If the ObjeSl be a right Line, the vifual Rays form a Triangle, as C A D, 
 whofe Bafe is the Line C D, and Sides the two extreme Rays A D and A C j 
 A B is the central Ray. If the Line were feen end-wife, it would appear as 
 a Point. 
 
 If the Object be a Surface, whether plane or fpherical, the vifual Rays 
 will make a Pyramid, whofe Bafis is the Object CDEF, and its Vertex 
 the Eye A. The reft of the Pyramid confifts of vifual Rays ; in which 
 Number the Central A B is the ftrongeft, the others being all weaker, as 
 they are farther therefrom, though they (till retain a competent Strength, 
 till they make a right-angled Triangle. Such as go beyond this, become 
 fo feeble, that they appear very confufedly. So that to have diftinct Vi- 
 lion, the extreme Rays under which the Object is comprehended, muft, 
 at moft, fubtend a right Angle in the Eye. If the Pyramid were viewed 
 fide-wife, it would appear no more than a Line. 
 
 Why a Piece of Perfpective is feen better with one Eye than with two. 
 
 Some hold that all Objects appear better with one than both Eyes; al- 
 ledging, that the Sight is render'd more penetrating by the vifual Rays of 
 the ftiut Eye being determined to the other; inafmuch as all Powers be- 
 come more vigorous when united, than when difperfed. Accordingly, fay 
 they, one of the Eyes being clofed, the whole vifive Virtue before diffus'd 
 thro' both, is now fuppos'd to be collected into one; a Re-inforcement, 
 muft neceflarily render it ftronger, more piercing, &c. than both. 
 
 Be this as it will, 'tis certain, we fee a Piece of perfpective with one 
 Eye better than with both. The reafon is, that the central Ray, in the 
 Cafe, is directed to the Point of Sight where all the Radials of the Piece 
 do meet; which is what {hews a Picture in its laft Perfection. 'Tis for 
 this reafon that we don't fay, the Points of the Eyes, but, the Point of the 
 Eye, as infinuating, that Perfpective is moft pleafing, when viewed by a 
 fingle Eye. a 
 
6 
 
 PERSPECTIVE 
 
 Firjl Definition. 
 
 PERSPECTIVE is the Art of reprefenting Objeds fcen through 
 fome tranfparenc Medium, which the vifual Rays penetrate in paf- 
 fing from the feveral Points of the Object to the Eye. Accordingly, 
 whatever is feen through any Thing, as through Air, Water, Clouds, Glafs, 
 and the like, may be faid to be feen in Perfpedive. And fince we fee no- 
 thing but through thofe Mediums, 'tis certain all we fee is in Perfpedive. 
 
 The End of Perfpedive is to exhibit Objects upon a Plane, fituate be- 
 tween the Eye and them, ex. gr. on the Plane E F G H, to reprefent the 
 Objeds A B C D, in the Points IKLM. 
 
 The better to conceive this, fuppofe an Objed A BCD on the Ground, 
 and a Spedator's Eye in O ; if a tranfparent Body EFGH be placed be- 
 tween the two, the Interferons of the vifual Rays, with the Perpendicu- 
 lars OR S T, will give the Figure IKLM, fuch as the Objed appears on 
 that Plane. Perfpedive, therefore, confifts altogether in the Interfer- 
 ons of Lines: Whence it is, that Marolou always calls any Thing put in 
 Perfpedive the Appearance of the Section-, fmce the Plane EFGH 
 cuts the vifual Pyramid A C B D and O, and gives IKLM for its 
 Sedion. 
 
 The Reafon of thefe Sedions is, that one fingle Line determines no- 
 thing; but there are two required to cut one another, to give a Point. Now, 
 as 'tis evident, that between our Eye and an Objed, there is always a right 
 Line, or Ray, that can never be wanting : But to get the other, which is 
 to cut it, 'tis neceffary we conceive, that from our Foot as a Center, there 
 are a Number of Lines, or Rays, continually flowing to the Angles of the 
 Objedswefee ; as from P to the Angles A B C D: All which Rays being 
 cut by fome tranfparent Plane, as EF G H, the Rays P B, P A, P C, P D, 
 which before were horizontal, are now ereded and become perpendicular: 
 EB, forlnftance, becoming Q^M, PD becoming. RL, &c. For if they 
 continued horizontal, the vifual Rays would never interfed them, till they 
 both met in the Objed itfelf. 'Tis for this Reafon we always fuppofe a 
 Plane, which, refleding the Rays, gives them an Occafion of interfeding, 
 and fo of finding the Points to form the Appearances of Objeds, 
 
7 
 
 PERSPECTIVE 
 
 Second Definition. 
 
 IChnography is the Figure of the Platform, or the Plan 
 any thing is to be rais'd upon : Thus AB CD is the Ichno- 
 graphy^ or Plan, of a fquare Body. 
 
 'Third Definition. 
 
 Orthography is the Figure of the Front or Fore- fide 
 of an Object, as an Houfe, Sf c. Or it is the Figure of an Ob- 
 je6t, as a Houfe, &c. directly oppofite to the Eye : Thus 
 EFGH is the Orthography, or Fore-part, of a Cube, or 
 Houfe. As the Ichnography reprefents the Plan, the Ortho~ 
 graphy reprefents the Side oppofite to the Eye. 
 
 Fourth Definition. 
 
 Scenography is what exhibits the Object quite rais'd, 
 and perfect, with all its Diminutions and Shadows, both in 
 Front, the Sides which may be feen, and the Top : Thus 
 IKLMNOPisa Scenography, or perfect Cube. This is the 
 whole, and comprehends all the others as Parts. 
 
 To render the Terms more familiar, we fhall, for the future, 
 call the Ichnography Plan, the Orthography Front, and the 
 Scenography Elevation. 
 
8 
 
 PERSPECTIVE 
 
 Why Obje&s appear the nearer each other, as they are more 
 
 remote from the Eye. 
 
 THIS Figure may help to folve a Queftion of fome Difficulty : Snppofe 
 a Spectator's Eye in the Middle of a Line at 'tis evident, that if 
 it would fee the two Extremes thereof, A and B, it muft take in a Semi- 
 circle V X, whofe Center is in the Eye itfelf, and whofe central Ray is 
 the Line -\- T. By taking in this Semi-circle, it will perceive the Ob- 
 jects on either Side, and in fuch manner, as that thofe fartheft off from 
 the Side A appear to approach towards the Center T, and thofe on the 
 Side B feem to approach likewife. 
 
 Now 'tis afked, How Things fo wide afunder mould come to approach 
 and join each other, and that whether fituate fide-wife or over one an- 
 other ? 
 
 The Anfwer in few Words is this : All Objects appear under the vi- 
 fual Angle they fubtend at the Eye. Now, be they Columns, Trees, 
 Animals, or any other Things, placed on the Side of A, the remoteft will 
 feem to border on the Center T, by reafon they are feen under an Angle, 
 or Ray, that is near thereto. The Ray K, for Inftance, being much 
 nearer the central Ray T, than is the Ray -f- C and + E, anQV of Con- 
 fequence muft appear to be there: Add, that if the Objects were pro- 
 longed to Infinity, they would ftill approach nearer the central Ray T, 
 till fuch Time as they feemed contiguous therewith, and only to form 
 one Point together. 
 
 Now, in Perfpeclive, the Sides A K and B S don't continue parallel, 
 but degenerate into vifual Rays, interfering each other in the Point of 
 Sight, and by that Means giving the Diminutions of Objects. Thus, for 
 Inftance, in the fecond Figure, the Eye being at a Diftance capable of 
 feeing the Line A B, from the two Angles A B arife two Rays, which 
 proceed to the Point of Sight T, which Rays AT and B T receive the 
 Interferons the Point of Diftance makes with the Objects, which all the 
 while contract themfelves proportionably ; as will be {hewn in its Place. 
 By fuch Means the whole Parallelogram A K B S, and all the Obje&s on 
 either Side become reduced into the narrow Compafs A V, B X : An'd if 
 the Eye were more remote, that Space would be ftill fmaller, fince the 
 farther an Objeft is off, the fmaller it appears, as we mall make appear 
 in the following Page. 
 2 
 
9 
 
 PERSPECTIVE 
 
 Why Objeds appear the /matter as they are at the greater Diftance. 
 
 w 
 
 E have already obferved, that Things appear according to the Angle 
 wherein they are feen, and that this Angle is taken at the Eye, where 
 the Lines terminating the Objeft, meet. The Eye A, for Inftance, viewing the 
 Objeft B C, will draw the Rays A B and A C, which give the Angle B A C •, fo 
 that an Objeft viewed under a greater Angle will appear large, and another under 
 a letter Angle little. Now 'tis certain, that among equal Objects, thofe at the 
 greateft Diftance will appear under the fmalleft Angle \ confequently in all Per- 
 fpeftives the remoteft Objefts muft be made the fmalleft : For Example, if the 
 Eye be in A, the Objeft B C, which is the neareft, will appear the biggeft, be- 
 caufe feen under the greateft Angle; and the fecond, third, fourth, and fifth 
 Objefts will all appear fmaller and fmaller, tho' really all equal, inafmuch as 
 the Angles diminifh in Proportion as the Objefts recede. If the Eye were re- 
 moved fntoM, KL would appear the largeft ; and B C, in this latter Cafe, no 
 bigger than NO. 
 
 The fecond Figure is a Sequel of what we have advanced : For, fuppofing the 
 Objefts to appear fuch as is the Angle they are feen in, it follows, that if fe- 
 veral Lines be drawn between the Sides of the fame Triangle, they will all appear 
 equal - Thus, all the Lines com prifed between the Sides ON, OP, of the Tri- 
 angle NOP, will appear equal to each other; and, as Objects comprehended 
 under the fame Angle feem equal, fo all comprehended under a greater Angle, 
 feem greater, and all under a fmaller, fmaller. 
 
 Thus much fuppofed : If there be a Number of Columns, or Pilafters, to be 
 ranged in Perfpeftive on each Side of a Hall or Church, they muft of Neceffity 
 be all made under the fame Angle, and all tend towards one common Point in 
 the Horizon O : For Inftance, the Eye being placed in A, viewing the firft Ob- 
 ieft DE; if from the Points DE you draw the vifua] Rays D O, EO, they 
 will make the Triangle DOE, which will include the Columns DE, F G, HI, 
 KL, MN, fo as they will all appear equal. 
 
 What we have faid of the Sides, is likewife to be underftood of the Cielings 
 and Pavements ; the Diminutions of the Angles of remote Objefts, placed either 
 above or below, following the fame Rule as thofe placed laterally. We need not 
 therefore add any Thing farther unlefs, that Care be taken there be as many 
 Squares or Divifions between the remoteft Objefts as between the neareft: For m 
 that Cafe tho' diftant Objefts be the clofer as they are farther from us, they will 
 appear in fome Meafure to preferve their Diftance; thus, in BCDE, the In- 
 terval between the lour neareft Columns, there are fixteen Squares, and no fewer 
 thanfixteen between the four remoteft KLMN. 
 
IO PERSPECTIVE 
 
 &&&&&&&&&&& * jy & 
 
 IT follows from what we have faid, that if you join two 
 Triangles, as in the laft Figure but one, for the Sides, and 
 two others, of the laft, for the Tops and Bottoms of an Ob- 
 ject, all four will terminate in one fingle Point A, which is the 
 Point of Sight, wherein all the vifual Rays meet. And this 
 will give a Proof of what we have advanced, viz. That 
 Objeds diminifli as they remove, the lower rifing, the upper 
 falling, and the lateral clofing or approaching: An Example of 
 all which we give in Fig. L which exhibits, as it were, Depths 
 and Diftances falling back, and receding from us, though all 
 equally near the Eye. 
 
 The Trees being ranged by the fame Law, have the lame 
 Effed as the Columns, &c. For being all comprehended in 
 the fame Angle, and the two Rows having each its own Angle, 
 and the Angles all meeting in a Point A, they form a third, 
 which is the Earth, and a fourth, which, if you pleafe, is 
 the Air ; and thus afford an elegant Objefl, highly entertain- 
 ing the Eye. 
 
 We come now to fliew how you are to proceed in putting 
 any plane Body, or other Figure, in Perfpedive. 
 
II 
 
 PERSPECTIVE 
 
 Of the Horizon. 
 
 WHAT we call the Hor i zon, in Perfpective, is only a Line given us by 
 the Height of our Eye : Thus, if we be raifed on an Eminence, as is 
 the firft Man, our Horizon will be high; if we be only our own Height, as is 
 the fecond Man, the Horizon will be our own Pitch ; and if we be feated or laid 
 along, as is the third, the Horizon will be low : So that 'tis the Horizon fhews 
 how high the Eye is above the Ground. 
 
 This, in Effect, is the principal Article in a Picture, and that which directs and 
 gives Law to all the reft ; both as to the Slope and Inclination of Buildings, 
 and to the Meafures and Heights of the Figures. This has occafioned a little 
 Difpute among our beft Painters ; fome of them holding that all Paintings mould 
 have their Horizon in the Work itfelf, and that Perfpective allows, where the 
 Painting is raifed very high above the Eye, that it have its particular Horizon : 
 The reft do not allow of fuch a fecond Horizon, but always ufe the natural one, 
 where-ever the Painting be placed ; as imagining that the whole H ight and 
 Breadth before them is, as it were, one large Painting, from which that which 
 is raifed above ought to take its Meafures. The Refpect we bear to the Pa- 
 trons of each Opinion will not allow us to determine between them •, efpecially, 
 as feveral good Authors have tolerated both. But, if my own Sentiments were 
 asked, I mould make no Scruple to profefs myfclf of the Opinion of thefe 
 latter ; by Reafon every Thing in the Painting will thereby appear the more 
 natural. 
 
 In this Line are always found the Points of Sight and Diftance, and fome- 
 times the contingent or accidental Point. 'Tis this Line, in fine, that feparates 
 Heaven from Earth, and that terminates the View ; and it is always parallel 
 to the Bottom of the Piece, or the Plan the Object is placed upon: Whence it 
 appears that nothing ought to be placed above the Horizon, but what furpafles 
 the Height of the Eye ; and if an Object be fo high as that it furpafles this Hori- 
 zon, the Plan of the fame Object muft be placed below it: Thus, a Tree-or 
 Mountain may have its Top above the Horizon, but its Bottom muft be a good 
 deal below it. 
 
 Whatever is below the Horizon fhews its Top ; but in Objects ever fo little 
 above it, the Top is invifible : Thus, the two Blocks A B, placed on the Ground 
 of the firft Figure, mew their Tops, by Reafon the Horizon is over them ; but 
 inthofeof the fecond Figure CD, the Top does not appear; and much lefs in 
 thofe of the third Figure : Yet, in Reality, they are all of the fame Height, fo 
 that 'tis the Horizon makes all the Difference. 
 
12 
 
 PERSPECTIVE 
 
 Of the Terreftrial Line. 
 
 THE Terrestrial Lin e,Bas e Line, orLiNEof the Plan, 
 is the Line an Object is placed or (lands upon, whereof each Object has its 
 particular one, and the whole Draught a general one. This is always parallel to 
 the Horizon, as is feen in A B of the firft Figure, F G of the fecond, and N O 
 of the third ; and fometimes ferves to determine the Lengths and Breadths, par- 
 ticularly that at the Bottom of the Piece, whereto all the Meafures are to be ac- 
 commodated, as will be fhewn hereafter. 
 
 Of the Point of Sight, Point of the Eye, principal Point, or Point 
 
 of Perfpective. 
 
 THE P o i n T of Sight, of the E y e, Perspective, or Prin- 
 cipal Point, is a Point in the Axis of the Eye, or in the central 
 Ray, where the fame is interfered by the Horizon. Thus the Point E in the 
 firft Figure is the Point of Sight in the Horizon C D, wherein all the vifual Rays 
 meet. It is called the Point of the Eye, or ocular Point, becaufe directly oppofed 
 to the Eye of the Perfon who is to view the Piece. 
 
 Of the Points of Diftance. 
 
 POint of Distance, or Points of Distance, is a Point, or 
 Points (for there are fometimes two of them) placed at equal Diftance from 
 the Point of Sight. They are thus denominated, by reafon the Spectator ought to 
 be fo far remov'd from the Figure, or Painting, and the terreftrial Line, as thefe 
 Points are from the Point of the Eye, and are always to be in the horizontal Line. 
 Thus H I being the Horizon, and K the Point of Sight, L and M are Points of 
 Diftance, ferving to give all the Shortnings. Thus, ex. gr. if from the Extremes 
 of the Line F G you draw two Lines to the Point K, and from the fame Points 
 draw two Lines to the Points of Diftance M and L, where thefe two Lines G L and 
 FM cut the Lines FK and G K, in the Points X and Y, will be the Line of 
 Depth, and the Shortning of the Square, whereof F G is the Side and Bafe. The 
 Lines drawn to the Point of Sight are all vifual Rays, and thofe drawn to the 
 Points of Diftance, all Diagonals. 
 
 Of the Accidental Points. 
 
 Contingent, or AccidentalPoints, are certain Points wherein 
 fuch Objects as may be thrown negligently, and without Order, under the 
 Plan, do tend to terminate. For this Reafon they are not drawn to the Point of 
 Sight, nor the Points of Diftance, but meet accidentally, and at random, in the 
 Horizon. Thus, for Inftance, the two Pieces of Wood X and Y terminate in 
 the Points WW in the Horizon PQ, not in the Point of View, which is R, 
 nor in the Points of Diftance S and T. Indeed fometimes the Obje&s'are fo ill 
 difpofed, that thefe Points muft be made out of the Horizon, as we (hall have 
 Occafion to mew hereafter. They ferve particularly in the Apertures of Doors, 
 Windows, Stair-cafes, and the like. 4 
 
PERSPECTIVE 
 
 Of the Point of the Front. 
 
 THE Point of Direct View, or of the Front, is 
 when we have the Object directly before us, and not 
 more on one Side than the other ; in which Cafe it only fhews 
 the Fore-fide, and, if it be below the Horizon, a little of the 
 Top too, but nothing, of the Sides, unlefs the Objecl: be poly- 
 gonous. Thus the Plan A B C D is all in Front, and, if it were 
 rais'd, we fhould not fee any Thing of the Sides AB, or C D, 
 but only the Front A D : The reafon is, that the Point of 
 View E, being directly oppofite thereto, caufes a Diminution 
 on each Side ; which, however, is only to be understood where 
 an Elevation is the Objecl: ; for, if it be a Plan, it fhews the 
 whole, asABCD. 
 
 Of the S i d e Point. 
 
 TH E Point of Oblique View, or of the Side, is 
 when we fee the Objecl: afide of us, and only, as it 
 were a-flant, or with a Corner of the Eye ; the Eye, how- 
 ever, being all the while oppofite to the Point of Sight : In 
 which Cafe we view the Objecl: laterally, and it prefents us two 
 Faces, or Sides. For Inftance, if the Point of Sight be in F, 
 the Object GHIK will appear a-th wart, and mew two Faces, 
 G K and GH; in which Cafe it will be a Side Point. The 
 Practice is the fame in the Side Points as in the Front Points ; 
 a Point of Sight, Points of Diftance, &c. being laid down 
 in the one as well as the other. 
 
H "PERSPECTIVE 
 
 Of the Visual Rays. 
 
 "Tp I San univerfal Rule, That all the Lines which, in a geometrical Plan, are 
 A perpendicular to the terreftrial Line, be always drawn to the Point of Sight, 
 when the faid Plan is to be put in Perfpective : Thus, in the little Plan AO, OB, 
 Fig. i. A B is the terreftrial Line, to which all the Lines Z, Z, &c. are perpen- 
 dicular. But if the Plan be to be thrown into Perfpective, and either a greater 
 or a lefs Line than that of the Plan be pitched on, ex. gr. the Line A B, which 
 has the fame Number of Divifions as the fmall one, from the feveral DivifionsZ, 
 the Lines are to be drawn directly to the Point of Sight E. Such Lines are pro- 
 perly denominated Radials and vifaal Rays; and the laft of them, the Extremes, 
 as being drawn from the Extremities of the terreftrial Line AB. 
 
 Of the Diagonals^ or Diametral their Sections. 
 
 'Tis likewife a Rule, That all the Diagonals of Squares in the Plan be drawn, 
 in Perfpedive, to the Point of Diftance: Thus, in the little Plan of Fig. i. the 
 Diagonals GO and FOare drawn to the Points of Diftance; when the fame 
 Plan comes to be put in Perfpe&ive, and by fuch Means the Shortnings or Dimi- 
 nutions of the Objects are got : So, if from the Extremes of the Bafe Line FG, 
 Lines be drawn to the Points of Diftance L M, they will be Diagonals ; and 
 where thofe Lines cut the extreme Rays FK and GK in the Points O, will be 
 marked out the Diminution of the Square, whereof FG is the Side j and where 
 the fame Lines cut the Lines Z, Z, &c. in the Points Q, Q, &V. Parallels to 
 the Bafe Line are to be drawn, which will give the Diminution of all the Squares, 
 and the fame Number of Sides as in the little Plan. And ftill, the more remote 
 the Points of Diftance are from the Points of Sight, the more the Objects are di- 
 minifhed. Hence all the Beauty of a Perfpective depends on the nice Adjuftment 
 of the Interval between the Points of Diftance and that of Sight: On which Ac- 
 count we have added a third Figure, with a Diverfity of Intervals, to evince the 
 Truth of what is juft now obferved. Suppofe then R to be the Point of Sight, 
 and S S the Extreme Rays ; if the Point of Diftance be at T, it will cut the Ray 
 S R in the Point V, which will give the Diminution of the Square, whereof S S 
 is a Side: But it would be ridiculous to fee a Square fo extravagantly deep from 
 the Point of Diftance T, being fo much too near the Point of Sight R. In Effect, 
 the leaft, that is any-wife allowable, is for the Point of Diftance to be removed from 
 that of Sight, half the Breadth of the whole Draught or Perfpective; (fuch as 
 is the Diftance of X from R ;) by reafon fuch Removals always give a Right An- 
 gle at the Spectator's Eye. It would, however, be ftill more agreeable at i, the 
 Line in that Cafe cutting the Square at 2 ; and it would be better yet at 3, cut- 
 ting at 4 ; and beft of all at 5 ; being then remote enough, and making the Square 
 fhorterat6: The Reafon whereof will be afiign'd under the following Figure. 
 
 It may be demanded, Why, throughout the Courfe of this Work, I have put 
 the Points of Diftance fo near, when they have fo much better Effect at a greater 
 Diftance? The Anfwer is, That the Book not being intended to be view'd 
 merely out of Curiofity, but to inftruct, it was neceflary every Circumftance 
 mould be feen, that the Methods might be the better conceiv'd : For this Rea- 
 son we have included as much of the feveral Operations aspoffibly we might. 
 
PERSPECTIVE 
 
 OQQQQQQQQ SOQQQg QQQ Q QSQQGQQQQQQQQQGQQQQqqqq 
 
 Of the Distance, or Removal. 
 
 WE-have already faid, in fpeaking of the vifual Rays, that the Eye cannot 
 commodioufly take in more than is included in a right Angle ; that is, 
 that the Sight does not receive Objects fully and diftinctly, when the vifual Rays 
 exceed a right Angle. The Reafon is, that the Pupil being nearly in the Center 
 of the Eye, does not well admit above a Quadrant of a Circle j fo that all the 
 Rays exceeding that, have only a dim confufed Effect, On this Account it is bet- 
 ter to have the Angle lefs than greater for Inftance, two thirds of a right Angle, 
 or fixty Degrees, but not lefs, ;by Reafon the Rays, in fuch Cafe, being fo ftrait- 
 ned, do not fatisfy the Eye, the Angle being little more than a Point in the Pu- 
 pil. To fliew this Difference in Figures : Suppofe the Plans and Squares the fame 
 as in thelaft Figure, the Diftance of the Point T from R will give the Diftance 
 of T from the terreftrial Line; where it would be neceffhry the Angle mould 
 open much farther, to fee the Extremes Y Y. If ir only opened to a right Angle, 
 the^ Eye could not fee all as T, for Inftance, could not fee beyond the Points' 
 YVr Whence would arife a very faulty Perfpective, inafmuch as what fhould 
 exhibit a Square, will now only form a Parallelogram. The neareft one can put 
 it is in the Point X, which, as we have already obferved, is the juft Meafure of 
 a right Angle, comprehending the whole Piece Y Y. If it be carried ftill farther 
 back from the Point of Sight, it will be ftill the more agreeable, as in I, where 
 the Angle will only be 72 Degrees : If it be brought back as far as Z, it will 
 be in Perfection, inafmuch as the Rays being now the lefs dilated, have the 
 more Force, and exhibit Objects with the greater Vivacity. But I would never 
 choofe to go beyond five, for the Reafon already infinuated, that the Angle then 
 dwindles to a mere Point. Too much Care, then, cannot be taken in the Difpo- 
 fal of Points of fo much Importance \ with Regard to which it muft be efteemed 
 a certain Rule, that the Diftance be equal to the Space between the direct Ray 
 and the Corner of the Perfpective. -4- R> f° r Inftance, is the direct Ray and 
 X -f- the leaft Diftance, which is equal to -\- Y. This Meafure being taken, 
 muft be fet off each Way from the Point of Sight, as here from R to S S ; or only 
 one Way, as in the following Page. 
 
 Thus much we learn from Reafons that regard the Eye : But Experience fur- 
 nifties another noble Rule, which may be general too, provided it be ufed with 
 Difcretion, viz. That having chofe the Place where the Perfpective is to be 
 made, you are to determine from what Quarter it is to be feen to the beft Ad- 
 vantage •, then taking the Diftance from this Place to the firft, fet off* this Inter, 
 val, by a little Scale, from the Point of Sight to the Point of Diftance, provided 
 it be not too remote : Which is a Circumftance that will require fome Difcretion, 
 to avoid the Inconveniences either of placing it too near, or too far off*. 
 
r6 PERSPECTIVE 
 
 Advert. I. Relating to the Side-Point. 
 
 TH E Rules for the Front Points, are never chang'd for the Points of the 
 Sides, as being both founded on the fame Caufe, which always produces 
 the like Effects : We mall fpare therefore to fpeak particularly thereof, the 
 Praftice for Side Points being the fame as for thofe of the Front ; as is fhewn 
 in Fig. i. where the terreftrial Line A B has the very fame Divifions as the pre- 
 ceding ones : And if the Point of Sight be iuppofed in C, and the Point of Di- 
 ftance in D, drawing the Line AD, you will have the Interferons Q, fcrV. 
 which give the Diminutions of the Squares in the fame Number as the former. 
 The reft will be learnt from the fucceeding Rules. 
 
 Advert. II. Of the Depths or Hollowings. 
 
 APerspective may be funk as deep as one pleafes, by means of the ter- 
 reftrial Line, drawing Lines from that Line, as E F, to the Points of Diftance 
 H I : for where they interfect the vifual Rays E G and F G, in the Points K, K, 
 we have already obferv'd, the Diminutions of the firft. Square will be. Now, if 
 we take this Line K L for the terreftrial Line, and from its Extremes K K draw 
 Lines to the Points of Diftance ; where thefe cut the fame Lines E G and F G, 
 viz. in the Points L L, will be the Diminution of the fecond Square, which will 
 have as many Divifions and Squares as the firft. Again, if we take this Line 
 L L, and repeat the fame Operation, we fhall have the Diminution of the third 
 Square in the Point M : And if we begin again with this, we (hall have a fourth ; 
 and fo on, till we arrive at a Point, which will be a Length that will appear in- 
 finite. By fuch Means, then, it is eafy finking and ihortning Perfpe&ives : 
 Thus, if you would have it twice its Width, proceed as already directed } and if 
 you would only have it half thereof, draw a Line where thofe from the Points 
 of Diftance interfecl each other, and you will have your Requeft. 
 
 Since this is infallible, that as many vifual Rays as cut the Diagonal Line, 
 drawn from the Points of Diftance to the terreftrial Line, fo many Squares of 
 Depths you have ; it follows, as has been already hinted, that you may give the 
 Perfpeftive what Depth you pleafe. For if, inftead of drawing the Diagonal from 
 the Ray F to the Point of Diftance O, you draw it from Q, you will want two 
 Squares of theother diminifh'd Square R; and if you would have two Squares 
 more than the Square R, draw a Line from the fame Point O, cutting two Rays, 
 to V: If you defire four, take X; if fix, Y; and if the entire Square, Z; 
 Which is a wondrous Eafmefs, when well underftood. 
 
17 
 
 P E R S P E C T I V E 
 
 Advert. III. Of the Meafures upon the Bafe. 
 
 BY the Bafe Line alone one may give any Depth, and in any Place, at Pleafure, 
 without the ufe of Squares •, which is a very expeditious Way, tho' fome- 
 what difficult to learn. We (hall, however, endeavour to make it underftood, 
 by Reafon we fhall make frequent ufe thereof. For an Example ; Suppofe the 
 Bafe Line, BS ; the Point of View A and the Points of Diftance DE; if now 
 you would make a Plan of a Cube BC, draw two occult, or dotted Lines, from 
 the Extremes B C, to the Points of Sight: Then, to give the Breadth, take the 
 fame Meafure B C, and fet it off on the terreftrial Line C F ; and from F draw a 
 Line to the Point of Diftance D •, and where this Line interfefts the firft Ray C, 
 in the Point G, will be the Diminution of the Plan of the Cube B H G C. 
 - If you would have an Object farther towards the Middle, take the Breadth and 
 the Diftance of the Bafe Line, as I K ; and to have the Depth, fet it as you 
 would have it on the fame Bafe, as LM, and its Width both onLM; then from 
 L and M draw occult Lines to the Point of Diftance D, and from the Points N O, 
 where thofe Lines interfed the Ray K, draw Parallels to the terreftrial Line, and 
 you will have the Square Q_P O N. 
 
 After the fame Manner may you fet off the other Side of the Square, which 
 fhould be on the Bafe ; as B H G C is here transferred to V. The Points M and 
 T, which are only two Feet from the Point S, afford a very narrow Figure in X, 
 as being very near. 
 
 Advert. IV. Of the Bafe Line, and a [ingle Point of Diftance, 
 Since the Depths and Widths may be had by Means of this Bafe Line, we 
 need not give our felves any further Trouble in the making of Squares •, as fhall 
 be fhewn in this Example. Suppofe a Row of Trees, or Columns, is to be made 
 on each Side ; on the Bafe Line lay down the Place, and the Diftance between 
 them, with their Breadth or Diameters, asABCDEFG, then laying a Ruler 
 from the Point of Diftance O, to each of the Points ABCDEFG, the Inter- 
 jections it makes on the vifual Ray A H, will be the Bounds of the Objects de- 
 fired. To fet them off on the other Side, upon the Ray GH; fet one Foot of 
 your Compaffes on the Point of the Eye H, and with the other ftrike an Arch : 
 The Point wherein this cuts the Ray G H, will be the correfponding Bound. 
 Thus M will be the fame with N, andfoof the reft; thro' which drawing Paral- 
 lels, you will have the Breadths. And as for the Length, make it at Pleafure ; 
 fetting it off from A, for Inftance, to P, and then from P drawing a Line to 
 Hs and where this cuts the other Parallels, will be formed the Plan required: 
 Which you may make either round or fquare. 
 
 Advert. V. Not to deceive one's felf in the Meafures, 
 Never put any Objects that are intended to be within the Plan, on the Side 
 of the Point of Diftance, where you are to draw Lines for managing the Depth. 
 Thus, fuppofe AB the vifual Ray whereon the Meafures are to be marked ; if 
 you would produce the Points C and D thro' the fame, don't draw the Lines, 
 from the Point of Diftance E, but from that oppofite thereto, F : Or if C and 
 D were on the In fide, as G and H are, you fhould not draw from the Point F, 
 but from E ; by Reafon the Line of Interferon is found between the two. Con- 
 fequently, the two will cut each other in the fame Points I, K. 3 
 
18 PERSPECTIVE 
 
 Advert. VI. Of a Jingle Point of Dijlance. 
 
 A PERSON is fometimes fo ftreightned for want of Room, either on s 
 XjL Wall, a Cloth, Paper, or the like, that it is impoffible to make above one 
 Point of Diftance: On which Occafion, fuch as have been always accuftomed to 
 two, find themfelves at a Lofs. This we are now to recover them from, and to 
 give them to underftand how a fingle Point fuffices for the Bufinefs. Suppofe, 
 then* we have a Pavement to make of fquare Stones, and that we have already 
 di wn all the vifual Rays to the Point A ; to get the Diminutions of which, we 
 have Lines to draw to the Points of Diftance, the Interfections whereof are to 
 give us Points for Parallels to be drawn through : But here being only one, viz. 
 B, draw the fingle diagonal Stroke CB, to cut all the vifual Rays. And, to 
 mark the fame Interfections on the oppofite Rays, for the drawing of Parallels; 
 fet, as already directed, one Foot of your Compaffes in the Point A, and fweep 
 the other through all the Interferons, as I P. This however is only advifeable 
 for what is to be viewed in Front ; another Method is to be given for what is to 
 be feen Side-wife ; thus: Set one Foot of your Compaffes on the Bafe Line, and 
 with the other take the Interferon you want to transfer, as D, and fet it upon the 
 Perpendicular O E, marking the Extent thereof, as F ; then draw a Line from 
 D to F, and you will have the fame as if there had been two Points of Diftance. 
 And fo of all the other Interfections. 
 
 Advert. VII. How to do without making Vfe of the Diagonal. 
 
 If one would ufe the extreme Ray GH for the Line of Interferon, the Ob- 
 jects KLM NO muft be fet on the Bafe Line, and from them Lines are to be 
 drawn to the Point of Diftance I ; which is here to be removed as far as pofiible, 
 that the Diminution of the Perfpective may have the better Effect : (For if that 
 Point were too near the Point of Sight G, the Objects would be too flat ; I mean, 
 for Example, that a Square would appear a Parallelogram.) Then from the 
 Point I draw Lines to the feveral Objects K L M NO, and mark the Interfections 
 thereof on the Ray GH, and through thefe Interfections draw Parallels to the 
 terreftrial Line, as here PQ^ This Method is not much in ufe, tho' fome 
 fet a Value on it. 
 
 Advert. VIII. Of feveral Ways of Shortning or Diminifhing. 
 
 If you chance to be ftreightned, and cannot remove the Point of Diftance 
 far enough ; from the Foot of the Ray RS erect a Perpendicular TS, which will 
 receive the Interfections, and give a greater Diminution : And if you would have 
 the Diminutions ftill more, draw a flope Line, as X, which, by Means of its In- 
 clination, will give the Interfections ftill clofer : Then, to draw the Parallels, you 
 have nothing to do but fet off the Line X or T on the Foot of the Ray, as in V ; 
 and from thofe Points draw Parallels to the terreftrial Line. 
 
 3 
 
METHODS 
 
 OF PUTTING 
 
 P LANES 
 
 I N 
 
 PERSPECTIVE. 
 
x 9 PERSPECTIVE 
 
 Of Planes view'd direfily, or in Front. 
 
 FROM Advert. III. and IV. as well as from the Elevations that follow ; it 
 will appear that our Intention is not to ufe geometrical Plans, in order to the 
 drawing of Perfpe&ives : That being a double Labour ; and there being fcarce 
 any PaTnter would give himfelf the Trouble, feeing 1 teach him to do the fame 
 Thing, by the ufe of the terreftrial Line. But, as there is no Rule fo general, 
 but has its Exception ; fo there are certain Figures which cannot be put in Per- 
 fpeaive without the ufe of fuch Plans: Befide, the Confufion a Man would be 
 under, mould a Plane be given him to put in Perfpe&ive, if he had not been in- 
 ftru&ed how to proceed. On fuch Confiderations, I have been induc'd to give 
 the following Rules ; which may fuffice to (hew how any Plane that can be re- 
 quir'd, or even imagin'd, may be put in Perfpective. 
 
 f, Tojhorten, or diminijh a Square ; as A B C D : From A and B, to the Point 
 of Sic*ht E, draw the Lines A E, BE; and from the fame Angles A and B, 
 draw two Diagonals F B, A G ; and the Points H and I, where they interfecl 
 the Rays A E and BE, will give the Square ABCD, diminiQYd in A HI B. 
 To do it without the geometrical Plan ; draw a Line from B to F, or from A 
 to G ; or fee off the Line A B on the terreftrial Line •, as in B K : and from K 
 draw another Line to F ; which will give the fame Interferon I, on the Ray BE. 
 
 2. To dimini/h a Square view* d by the Angle D: Having defcrib'd the Plan A B 
 C D, draw a Line to touch or rafe the Angle B, and falling perpendicularly on 
 B D. This being continued as a Bafe-Line, lay your Ruler on the Sides of the 
 Square A D and D C ; and where the Ruler cuts the terreftrial Line, make Points, 
 H I. Then from H and B draw Lines to the Points of Diftance P ; and from 
 I draw a Line to the other Point of Diftance G ; and in the Interfe&ions of 
 thofe Lines make Points, which will give you the Square K L M B. To do 
 without the Plan : Set off the Diameter each way from the middle Point B ; as, 
 to H and I. But in either Cafe no Line is to be drawn to the Point of Sight, O. 
 
 3. To diminijh a Circle : Draw a Square ABCD about it •, and from the An- 
 gles A D and C B draw Diagonals, dividing the Circle into eight Parts ; and thro' 
 the Points where they cut it, O O, draw Lines from the Bafe-Line, perpendi- 
 cular to D E F. Then draw two Diagonals QR S P, interfering each other at 
 right Angles in the Centre G. The Plan thus difpos'd ; from all the Perpendi- 
 culars draw Lines to the Point of Sight H ; and where they are interfefted by the 
 Diagonals A K, and BI, make Points; the two laft of which, M N, give the 
 Square, which is to be divided into four by Diagonals, interfering each other in 
 the Point P. Laftly, from the Extremes of this Crofs, draw curve Lines thro 
 the faid Points, which will give the Form of the Circle in Perfpeftive. This Me- 
 thod may ferve for fmall Circles; but for large ones we mall give another Me- 
 thod, more exacl. . . 
 
 4. This Figure is a Compound of the two firft ; which is all we need to lay 
 
 about it, _ , . , 
 
 c This too depends on the two firft ; only here is a Lift, or Border, going round, 
 which the others have not. To put the Lift in Perfpeftive : From the four Rays 
 ABCD draw Lines from the Point of Sight G ; and where the inner Rays 
 BC interfea the Diagonals D F and D E, draw Parallels to the Bafe-Line ; and 
 you will have your Defire. . ■ 
 
 The fixth is the fame as the fecond ; except that it is (unrounded with two Borders. 
 
F 
 
20 
 
 PERSPECTIVE 
 
 Plans viewd obliquely, orjide-wife. 
 
 THESE Plans being much the fame with 
 thofe already difpatch'd, are to be manag'd 
 after the fame manner. In Effe&, it would be 
 lofing Time to repeat how they are to be dimi- 
 nifh'd in Perfpe&ive ; a bare Infpedtion of the 
 Figure fufficing to ftiew, that all the Difference 
 between thefe and the former confifts in the Si- 
 tuation of the Objects, which are here fliewn la- 
 terally, and there in front. 
 
 All the A A A's are Points of Sight, and the 
 B B B's Points of Diftance. 
 
21 
 
 PERSPECTIVE 
 
 jkx£&f&<X. xiM^ X^&Sa& X^&SjX X^^U. & 
 
 0/ ^Triangle. 
 
 TRIANGLE S, according to the Order of Numbers, ought to 
 precede Squares ; but, according to Reafon, they are to come after 
 them in this Work, as being more difficult to put in Perfpe&ive : Not 
 on account of the Plan, which is eafy enough, as only confiding of 
 three Lines join'd together, but on account of the Obliquity of its Sides. 
 
 We now come to apply fome of the Advertifements, relating to the 
 Meafures on the Bafe-Line AB: For, to put this Triangle in Perfpec- 
 tive, from all the Angles thereof, i, 2 and 3 Perpendiculars are to be 
 drawn to AB. Then fetting one Foot of your Compaffes in the Inter- 
 ferons, with the other fet off the Diftances of the Parts of the Object 
 from the terreftrial Line, along the fame Line, by (hiking Arches, as 
 from 2 to 2, from 3 to 3, &c. This done, having drawn another Bafe- 
 Line in another Place, as hereunder E F, transfer the Meafures from 
 A B to E F, and to the Point of Sight C draw Lines from the Points 
 T, 2, 3, &c. Laftly, having pitch'd one Point of Diftance D, draw 
 Lines thereto from the other Points of Depth, 1, 2, 3, &c. And be- 
 tween the Interferons made by thefe with the vifual Rays, Lines being 
 drawn, will give the Triangle requir'd. 
 
 If you would give it the Lift or Breadth, repeat the fame over again 
 for the feveral Points thereof , only ufing other Figures to prevent Con- 
 fufion ; as, next to 1, 4; next 2, 5 ; 3, 6, &c. Then drawing Perpen- 
 diculars to the Point C, and between the Points, where they interfect the 
 others, draw Lines as you fee in the Scheme. 
 
 The Equilateral Triangle, fuch as that here defcribed, is infcribed in 
 a Circle, i. e.. a Circle may be drawn upon it, every Side fubtending 12a 
 Degrees.. 3 
 
22 
 
 PERSPECTIVE 
 
 Of /^Pentagon, #r Five-Angle. 
 
 TP H E way to conftrucl: a Pentagon is to defcribe a Circle, 
 -V and divide it into five equal Parts, of feventy-two De- 
 grees each ; then, for putting it in Perfpe&ive, the Method is 
 the fame as for the Triangle, as appears from the Figure : 
 Where, however, it is obfervable, that there is a Lift or Breadth, 
 whereas it is only laid down, on the Bafe Line, {ingle ; the 
 Reader being fuppos'd fufliciently inftructed in what relates to 
 the Lift, from the Triangle. The Point of Sight, both of the 
 Front and the Side, is A ; the Point of Diftance B 3 the vifual 
 Rays, which are the Perpendiculars drawn from the Angles of 
 the Plan to the Bafe Line, are drawn to the Point of Sight A ; 
 and the other Rays that give the Diminution, and the Place of 
 the Angles, to the Point of Diftance B. As 2 cuts the Ray 
 mark'd 2, which gives the Angle 2, 4 gives the Angle 4 ; 
 and fo of the reft. All the reft is clear enough ; regard, 
 however, is to be had to one Thing, that all the Angles tend 
 towards the Center 6: For this Reafon the Centre is to be 
 mark'd in the Plans in Perfpedive, as well as in the geome- 
 trical Plans. 3 
 
23 
 
 PERSPECTIVE 
 
 Of the Hexagon, or Six- Angle. 
 
 THE Hexagon is a Plane with fix Angles, and as many Sides; 
 'tis the eafieft to defcribe of all the Polygons, by reafon the fame 
 Aperture of the Compaffes, that is, the Radius wherewith its Circle is 
 defcribed, gives its Sides of 60 Degrees apiece. As to the putting it in 
 Perfpedive, the Method does not at all differ from that of the Triangle, 
 or Pentagon ; either when fingle, or with the Lift or Thicknefs, A is the 
 Point of Sight, and B that of Diftance. 
 
 Since we have a good deal of room in this Page, we think it not 
 amifs to give a little Method of putting the Lifts or Thickneffes of all 
 Polygons, regular or irregular, in Perfpedive: And the prefent Hexa- 
 gon mall ferve for an Example of our Propofition. Suppofe the Front 
 Plan of Fig. 3. to be only a fingle Stroke, and it were requir'd to give 
 it a Lift or Thicknefs all around : To do this in Perfpedive, lay your 
 Ruler along the fingle Sides, and make Points in the Horizon where 
 it cuts the fame ; thus laying it along the Side A B, it will cut the Ho- 
 rizon in C 5 then laying it along B D, it will give the Point E ; and 
 the like of the other Sides. Before you proceed any farther, draw occult 
 Lines from the feveral Angles through the Center F, which Lines are 
 to receive the Interfedions that give the Diminutions. Such Difpofitions 
 made, fet the Breadth of the Band or Lift on the Bafe-Line, as A H, and 
 -draw'the firft Breadth to the Point of Diftance G, and where the Line 
 G H cuts I, will be the Bound of the Thicknefs of the firft Side, which 
 is to determine for all the reft : For from this Point a Line is to be 
 drawn to the Point correfponding to this Side C, and the Interfedion of 
 this Line with K will give the Diminution ; from the Point whereof draw- 
 ing a Line to the Point E, correfponding to the Line BD, you will have 
 the Diminution for the Point L, which ferves for the laft Side L M : 
 Then transferring all the fame Meafures to the other Side, you will have 
 die Figure complete. 
 
 Hereafter we (hall have occafion to give another Method. 
 
24 
 
 PERSPECTIVE 
 
 Of the Heptagon, or Sept-Angle. 
 
 TH E Heptagon is formed within a Circle, as the other Poly- 
 gons are j in order to which the Circle is divided into feven Parts, 
 each Side fubtending 5 1 Deg. 25 Min and fometimes more. The Me- 
 thod of putting it in Perfpedive is the fame with that of the preceding 
 ones, as to the Perpendiculars falling from the Angles to the Bafe-Line, 
 which are all drawn to the Point of View A ; but as to the Diminu- 
 tion, and the Lines that give the Points of the Angles, it is different, 
 and rather according to the feventh Advertifement though we donotab- 
 folutely approve that, as thinking the eighth Advertifement the better. 
 But to condefcend to fuch as do ufe it, and fhew them that it does not 
 diminilh enough. 
 
 Having drawn Perpendiculars from the Angles of the Plan to the ter- 
 reftrial Line, as in the preceding Cafes, a Perpendicular is to be made on 
 one Side, as A B, to receive the Interfedions of the Parallels drawn 
 through all the Angles. Thus, the firft Angle being plac'd on the ter- 
 reftrial Line of 2 and 7, I draw a Parallel through both, cutting the Per- 
 pendicular in C. After the fame manner, the Angles 3 and 6 give the In- 
 terfedion D, and 4 5 the Interfedion E. This Line A B, thus divided, 
 muft be fet off on the Bafe-Line of the Plan to be diminifh'd, begin- 
 ning to put the Point B in F, as in the Figure. Then making the other 
 DivifionsCDE, and from thefe drawing Lines to the Point of Diftance 
 O, from the Interferons of the extreme Ray draw Parallels to the ter- 
 reftrial Line, and where thefe cut the Rays that bear the Numbers of the 
 Angles, Points are to be made, which, being join'd by Right Lines, 
 will give the Figure denYd. As to the Thicknefs, or Lift, 'tis to be 
 made after one of the preceding Manners. 4 
 
PRACTICAL. 
 
 % 
 
 G 2 
 
25 
 
 PERSPECTIVE 
 
 Of the Octogon, or Eight-Angle* 
 
 TH E O&ogon is form'd of a Circle, divided 
 into eight Parts, of forty five Degrees each, 
 the Divifions whereof, Lines * being drawn, will 
 form an O&ogon, that is, a Figure of eight An- 
 gles, and as many Sides. The Rules already de- 
 livered, fhew abundantly how it is to be put in Per- 
 fpe&ive, whether for a Front or a Side View. I 
 ftiall only obferve here, that the Front-Plan is to 
 be diminished according to Advert. VIII. and the 
 Side-Plan according to the Vllth. The Point of 
 View is A, and that of Diftance B. The reft is 
 too obvious to need an Explanation. 
 
 4 
 
26 
 
 PERSPECTIVE 
 
 Another Method for the O c T o G o N. 
 
 THIS Method of conducing the Octogon was invented by Serlio. 
 The Pradice is thus ; having found a Square A B C D the ordinary 
 Way, divide the Bafe-Line C D into ten Parts, and, leaving three on each 
 Hand', from the third of either Side E and F, draw Lines to the Points of 
 Sight, G, and through the Interfedions of thofe Lines with the Diagonals 
 O O, draw Parallels to the terreftrial Line, cutting the Sides of the 
 Square in the Points H I K L : Then joining the Points E H, I E, F K, 
 L F, by Lines, you will have an Octogon, as in the preceding Figure. 
 
 Of the Hexagon, or Six- Angle. 
 
 TH E fame Serlio has contriv'd a like Way of managing the Hex- 
 agon. Suppofe, as above, a Square A B C D, and the Bafe-Line 
 AD divided into four Part?, from one of which, on either Side E andF, 
 draw Lines to the Point of Sight H; then through the Interferon of the 
 Diagonals, which is the Middle of the Square G, draw a Parallel to the 
 Bafe-Line, cutting the Sides of the Square in I K ; laftly, drawing Lines 
 through thefe Points E I E, and F K F, there will be found a Hexagon. 
 
 I (hall fay nothing of the Oftogon view'd fide-wife 5 fince, as has been 
 fo often repeated, the Method is the fame as for that view'd in front. 
 
27 
 
 PERSPECTIVE 
 
 (y /A* Double Octogon. 
 
 SUPPOSING a fmgle Odogon already made, if 'tis re- 
 quired to have it double, or to give it a Thicknefs, or Lift, 
 proceed thus : Set the Breadth or Thicknefs you are willing to 
 give it, within the Square comprehending the O&ogon, as here 
 A B ; and from thefe Points draw Lines to the Point of Sight 
 C and where thefe Lines cut the Diagonals, as in O O, draw 
 Parallels DD, which will form a bort of Band round the 
 Square; laftly, draw occult Lines from Angle to Angle, inter- 
 fering each other in N; and where they cut the Lines of the 
 inner Square, vm in the Points EFGHIKLM, will be the 
 Bounds of the inner Odtogon. 
 
 Of the Double Hexagon, 
 
 TH E fame may be done with a Hexagon drawn in a 
 Square! It would be needlefs to repeat Particulars, lince 
 the Figure will clear any Doubts that may arife. 
 
 The Oc~togon view'd Side-wife, is managed precifely as that 
 viewed in Front; the Point of Sight is A, and that of Dif- 
 tance B. 
 
28 
 
 PERSPECTIVE 
 
 Of the Circle. 
 
 TH E more Sides a Polygon has, the fooner and the- 
 eafier is it converted into a Circle. For thisreafon Serlio 
 directs a Semi-circle to be drawn, and the Circumference there- 
 of to be divided into any number of equal Parts at Pleafure; 
 for the more Divifions, the more perfed the Rotundity: Thus 
 the Semi-circle A Z B is here divided into eight Parts, which 
 give fixteen for the whole Circle ; then from the feveral Divi- 
 fions Z Z, &c Perpendiculars are raisd to the Bafe Line in 
 the Points E E, &c. this done, the two Diagonals are to be 
 drawn to the Points of Diftance, which are here remov'd be- 
 yond the Compafs of the Plate, but which are to be fuppos'd,. 
 as ufual, in the Horizon : Thus you get a Square A H I B. And 
 this Square thus form'd, draw Lines from all the Points E to- 
 wards the Point of Sight, as far as the Line H I, and thro' the 
 Interfedions of thofe Lines draw Parallels ; then, beginning 
 in the Middle of one of the Sides of the Square to make a 
 Point, as a> and another Point b in the oppofite Angle, as if 
 you were about to draw a Diagonal; and proceeding thus to 
 make Points from Angle to Angle, according to the Diredion 
 of Diagonals, zsabcdefghikltnnopq, thefe Points will 
 form a perfect Rotundity ; fo that conneding them together 
 by crooked or circular Lines drawn by the Hand, you will 
 have your Circle in Perfpedive. ? Tis neceffary People who 
 deal in Perfpedive have this Rule of diminiming Circles very 
 familiar to them, by reafon of the frequent Ufe thereof in 
 Columns, Vaults, Arches, Apertures of Doors, Windows, & c % 
 
2# 
 
 H a 
 
PERSPECTIVE 
 
 Of the Double Circl e. 
 
 THE firft Circle is fuppofed the fame that we have juft 
 now been defcribing; and 'tis requir cl to give it a Thick- 
 nefs,or Lift, by making another within-fi.de thereof ; Thus, give 
 it any Breadth atPleafure, as A C, and from the Center of the 
 outer Semi-circle G, defcribe the inner Semi-circle C D, which 
 you are farther to divide, like the great one, by drawing occult 
 Lines from the Divifions of the great one to the Center thereof: 
 and from the Interfedions of thofe Lines with the inner Circle,, 
 draw Perpendiculars II, II, (§fV. to the Bafe-Line ; and, to 
 prevent Confufion, let thefe laft Lines be dotted. This done, 
 from the Points I of the Bafe-Line draw dotted Lines towards 
 the Point of Sight F, as far as the Line HK, and through their 
 Interfedions, with the Diagonals draw other dotted Lines MN, 
 which will give the Thicknefs (G QJ the Circle is to have. 
 Laftly, draw Lines from all the Angles of the great Circle to- 
 wards the Center, and the Points wherein they interfed the 
 dotted Lines abcdefghiklmnopq will be the Points,, 
 which, connected with curve Lines, will form the inner Cir- 
 cle's Circumference. 
 
 A Perfon who mould defire a Plan of three, four, five, or 
 fix Circles in Perfpedive, muft lay them all down in the geo- 
 metrical Plan after the fame manner as the fecond is done in 
 this Example. 3 
 
I f — ■ 
 
 ■z 9 
 
30 PERSPECTIVE 
 
 AY l an of a Square viewed Angle-wife. 
 
 IF it fliould be required to draw a Square view'd by an Angle 
 dire&ly oppofite to the Eye, there is nothing more required 
 than to follow the Rule already laid down; which is, to 
 double the Diameter A B upon the Bafe Line, as here in A C, 
 and from the Points A and C to draw two Lines to the Point 
 of Diftance D, then to fet off the Meafures of the Line A Con 
 the Bafe Line towards A E, and from E A to draw Lines to 
 the Point of Diftance F, then will the three Interfe&ions of the 
 Lines H 1 K be the Bounds of the Square defired, A I H K. 
 
 When fuch a Plan is to be divided into feveral Parts, lay down 
 the Number of Divifions required between the Points C and A, 
 and the fame Number on the other fide A E ; and from all 
 thefe Points draw Lines to the Points of Diftance: As in the 
 prefent Figure, which has eight Squares on each Side, and 
 fixty-four in all. 
 
 T f in the fame Plan, thus view'd by the Angle, it were only 
 required to have four little Plans in the four Corners, as four 
 Lodges, Columns, Trees, or the like Objects, fet the Width 
 thereof on the Bafe Line, within the Side of the Square A B or 
 A C, D and E being between AB, and F G between AC; from 
 which Points drawing Lines to the Points of Diftance H I, 
 their Interfedions will give the four Plans KLMN required. 
 
PERSPECTIVE 
 
 A Pavement of Squares viewed by the Angles. 
 
 NOW we are about Places viewed angle-wife, it may not be amifs to (hew 
 how a Pavement of a Hall, Church, or other Place is to be conduced. 
 Having drawn the Horizon parallel to the terreftrial Line A B, the Point of Sight 
 C, and the Points of Diftance D and E, divide the Bafe into as many Parts as 
 you would have Squares j then draw Lines from the Extremities thereof A and B, 
 to the Point of SightC, and from the fame Points A and B draw two Diagonals 
 to the Points of Diftance D E, the Points of Interferon F G will give the Square 
 of the Hall, and through them the Line of Depth HI is to be drawn ; then 
 draw Lines from all the Divifions of the Bafe Line to the Point of Diftance D 
 UndE, and between the Rays A B you will have your Defire as appears from 
 the Figure. But here arifes a Difficulty, viz. how to fill the vacant Space BB 
 and G°I, A A and H F, with the fame Squares for 'tis fuppos'd the Bafe Line 
 cannot be prolonged any farther. On fuch Occafion, take the Meafure of one of 
 Che Squares, as GK, on the Line FG, and fet it off on the fame Line H I as 
 often as 'twill go, and you will have the Points LMNOPQjind R, through 
 which drawing Lines to the Point of Diftance, you will have the fame Squares as 
 before •, fuch are thofe here marked with Dots. The fame Method of fetting 
 off the Meafures on the Line of Depth, will be exemplified in other Pavements 
 thereafter. 
 
 O/SqV ares encompajfed with a Lift, or Fillet. 
 
 THE Method of managing this fecond Pavement with a Band around ir, is 
 the fame with that of fingle Squares viewed in Front i we (hall therefore 
 'decline to wafteany Time in teaching it, fince we have already given fo many Fi- 
 gures thereof. It may be proper, however, to add, that the Bafe Line is to be 
 divided into unequal Parts fas A, B and C, and Lines to be drawn from all thefe 
 Divifions to the Point of Sight D, and through the Points where thefe are inter- 
 feded by the Diagonals AE, and G F, Parallels to the Bafe Line are to be 
 drawn ; as in the Figure. 
 
32 
 
 PERSPECTIVE 
 
 Pavements viewed Angle-wife, encompafs'd with a 
 
 Band or Fillet. 
 
 FOR fuch kind of Pavement, the Bafe Line A Bis to 
 be divided into unequal Parts, the largeft whereof are 
 to be for the Squares, and the fmaller for the Band or Fillet ; 
 and from all thefe Divifions, Lines are to be drawn to the Points 
 of Diftance E F : As has been already dire&ed in Angle Squares. 
 
 M. $k j& #• 4> 
 
 5i .St $t SO- .35- S& 
 
 Pavements of Squares viewed in Front, encom- 
 pafs'd with Lifts, or Bands, whofe Squares are 
 divided by the Angle. 
 
 FOR this fifth kind of Pavement the fame Method is to be 
 taken as in the fecond, by dividing the Bafe Line into 
 unequal Parts ; but to make the Square that is feen Angle-wife 
 in the Middle, the largeft is to be divided into two, as A B C 
 D E F G ; from the feveral Points whereof, Lines are to be 
 drawn to the Points of Diftance* the Interferons whereof 
 \vill give the Square* orLozange, in the Middle. 
 
 3 
 
33 PERSPECTIVE 
 
 Pavement of Squares viewed jingle -wife, with 
 Chains of Squares in Front. 
 
 WE fuppofe the Perfpedtive, or Diminution of the 
 Square, by drawing the Line of Depth, to be already 
 done, that we may fave the Trouble of too frequent Repetiti- 
 ons in the enfuing Pavements. 
 
 To manage this fixth Sort of Pavement, divide the Bafe 
 Line into equal Parts, and from fome of them, as AB C, draw 
 Lines directly to the Point of Sight, and from all the reft draw 
 Lines to the Point of Diftance, but without marking them 
 thro 7 the Chains. After all fuch as are thus viewed by the An- 
 gle are thus drawn, Parallels muft be drawn for the reft> 
 meeting the Angles of the former; ex. gr. From the Angle D 
 and E the Line F to be drawn, and of all the reft, as is fhewn 
 by the Figure : Care ftill to be taken, that there be always the 
 fame Number of Squares between the Chains ; as here we 
 have three between AB. 
 
 Pavement of Squares in Fronts with Chains of 
 
 Squares Angle-wife. 
 
 THIS feventh Sort of Pavement is perform'd much after 
 the Manner of the preceding, by dividing the Bafe Line 
 into equal Parts, and from the Divifions drawing Lines to the 
 Point of Sight, to form the Bands or Chains G H I ; yet there is 
 fomewhat more in it, Care being required to make the crofs 
 Chains of the fame Breadth as the others that tend to the Point 
 of Sight O, and that there be the fame Number of Squares be- 
 tween the Vacuities, The reft is obvious enough. 3, 
 
34 
 
 PERSPECTIVE 
 
 Pavement of O&ogons intermixed with Squares. 
 
 Ji... .. -.; • ... «v ■ r*-i - ■ <i-.\,, ^ji , . ...... ' 
 
 E ftiould never have done, were we to give all the Va- 
 rieties of Pavements ; a Perfon of Fancy that Way 
 would eafily invent an Infinity. This feventh Way is obvious 
 enough; all we add it for, is, to open the Mind, and furnifh 
 Occafion for the contriving of others. All that is required is 
 to divide the Bafe Line into a Number of Parts, whereof the 
 Squares are to be formed, as already dire&ed : Of which Squares 
 a certain Number is to be taken, as here nine, five whereof 
 are full, and the reft only Halves $ the full ones give the Infide 
 of the Figure 12345, and the Diagonals of the reft, 
 6789, give the Sides : The reft is evident. 
 
 Pavement of {ingle Squares viewed in Front. 
 
 THIS Form I have put the laft, not as being the mod dif- 
 ficult, for in Reality it is the eafieft of all, and the very 
 Beginning of Perfpe&ive, but to intimate that it is the moft 
 ufeful and neceflary, the reft being feldom added but by Way 
 of Ornament, and this ferving as the Foundation whereon any 
 Thing is to be rais'd, to be made appear : As will be fhe wn here- 
 after. 
 
35 
 
 PERSPECTIVE 
 
 Plan of a Garden Perfpe&ive. 
 
 "TUT HAT we have been obferving, is confirmed by this 
 W Plan : For, drawing Lines from all the Divifions on 
 the BafeLineto the Point of Sight, the Diagonals will give the 
 Depth of the whole Plan, and the Diminution of all the little 
 Squares. Laftly, fettingoff the Alleys, Figures, &c. from the 
 correfpondent Quantities in the geometrical Plan, the whole 
 Parterre will be found in Perfpe&ive ; as is fhewn inthe Figure. 
 
 Let the Plan given you to diminifh, and put in Perfpeftive, 
 be of what Sort foever, the readieft Way will ftill be, to draw 
 a Square about it, and divide that into feveral leffer Squares. 
 For putting the grand Square, with all the leffer ones, in Per- 
 fpe&ive, by the ordinary Rules, you have nothing farther to 
 do, but take Care that every Thing take up the fame Number 
 of little Squares in the diminifh'd Plan as in the geometrical 
 one, and the Figure of the one will be found in the other. 
 
PRACTICAL. 
 
 K 
 
36 
 
 PERSPECTIVE 
 
 PLAN of ^Building in Perfpe&ive. 
 
 SERLIO, in his Treatife of Pe r s p e c t i v e, fets a 
 great value on this Method of putting Plans in Perfpe&ive, 
 as a Thing of lingular Ufe in Architecture, whereby a Perfon 
 is enabled to fhew one Part of a Building rais'd, and the 
 reft in Platform ; but his Method for Buildings being the fame 
 with that we have already laid down for a Garden, we need 
 not fay any Thing farther thereof : The Figure is fufficient for 
 the reft. And from this one Figure Meafures are eafily taken 
 for any other, either more eafy or difficult ones. 
 
 In the fecond Part of this Treatife you fhall have a Me- 
 thod of reprefenting a whole Houfe in Perfpe&ive, with ail 
 the Members and Apartments thereof, from the Roof to the 
 Cellar. 2 
 
PRACTICAL. 
 
 36 
 
 K a 
 
37 
 
 PERSPECTIVE 
 
 Plan ^ ^Church, Perfpe&ive. 
 
 TP HIS Plan is condu&ed according to Advert. VII. 
 
 That is, all the Sides perpendicular to the Bafe Line, as 
 are here the Places of the Walls and Pilafters, are drawn to the 
 Bafe Line, and from that Line to the Point of Sight ; and all 
 the other Sides parallel to the Bafe Line, as are here the 
 Breadths, & c. drawn to a Line on one Side, O P, which thus 
 {hews the Points a bcdefgbi kL Thefe Points transferred 
 hence upon the Bafe Line asab, 8cc. and -Lines drawn from 
 them to the Points of Diftance, their Interferons with the 
 extreme Ray, give Points for drawing Parallels through, ex- 
 hibiting the Diminution of every Thing : As fhewn by 
 a, 6, c y &c. 
 
 This Method of diminifhing on the extreme Ray is pra&is'd 
 by many ; and yet fuch as would take my Advice, fliould let 
 it alone, and rather follow the Method directed in Advert. VIII. 
 where a Perpendicular is rais'd on the End of the Bafe to re- 
 ceive the Interfe&ions, and to obviate the Defect of the pre- 
 fent Method, which does not diminifh enough, unlefs where 
 the Points of Diftance are very remote: For in that Cafe, the 
 Effect is the fame as in the other Methods. 
 
38 
 
 PERSPECTIVE 
 
 9 ^W* *W* *W # K W X *W X *W X ^ 
 
 P l a n of ^ Houfe w/V^ Garden. 
 
 TH E Method of putting this Plan in Per- 
 fpe£tive, is the fame with that of the Gar- 
 den alone ; fo that what is there faid may fuffice 
 for both. Our Defign in putting it here, is, to 
 (hew, that one may diminifli all Sorts of Plans, 
 whether confifting of equal or unequal Parts. 
 
39 
 
 PERSPECTIVE 
 
 Plan of # Fortification, in Perfpective. 
 
 TO put a Fortification, or other Thing of the like 
 Kind in Perfpedive, the Vlth and Vlllth Advert, are 
 tobeus'd. The fame in Effect is the Method already laid 
 down for the C h u r c h and House, viz. by drawing Perpen- 
 diculars from all the Angles to the Bafe Line, and Rays from 
 the Bafe Line to the Point of Sight, and from the fame Angles 
 drawing Parallels to the terreftrial Line, and marking the Di- 
 vifions on a Side-line, AB. Thefe Divifions being transferred 
 thence to the Bafe Line, and Lines drawn from them to the 
 Point of Diftance, we fhall have the Line of Interferons C D. 
 But by Reafon we have not Room here to put it on the Bafe 
 Line we have added it underneath the Figure, as in A B. Laft- 
 ly, having fix'd the Point of Diftance in E ; draw Lines thence 
 to all the Divifions of AB, cutting the Line of Interferon 
 CD info many Parts; which Line, CD, with its Divifions, 
 is to be transferr'd to the Bottom of the extreme Ray, or at leaft 
 fet on each Side, as DD ; and from all the Points of the Line 
 DC, draw Parallels, or only Mock-points, on the Ray pro- 
 ceeding from the Angle of the Plan belonging thereto. Which 
 Points, connected by Lines, give the Figure required. 
 
 4 
 
PERSPECTIVE 
 
 An Irregular Plan Figure z/zPer- 
 
 fpe&ive. 
 
 A Man who can perform what is directed un- 
 der the laft Article, will find no Difficulty 
 in any Thing elfe j that being the molt intricate 
 of all Kinds of Plans in Perfpe&ive. It was 
 judg'd, however, proper to add fome irregular 
 Thing, that might appear at firft Sight to be Dif- 
 ficult, in order to (hew that there is nothing but 
 what may be diminilh'd, in what View or Afpe& 
 foever it be. 4 
 
PRACTICAL. 
 
 40 
 
4* 
 
 PERSPECTIVE 
 
 Another Plan of a Church, in Perfpe&ive. 
 
 THE Manner of this Perfpe&ive fhould feem very dif- 
 ferent from what we have hitherto delivered, by Reafon 
 of the different Difpofition ; but that we own it a Thing done 
 defignedly, to fhew that there are divers Ways and Manners,, 
 tho' all reducible to one. For this, in EfTecT:, is the fame 
 with what we- have already prefcribed for Fortifications, irregu- 
 lar Figures, and other Plans , with this Difference, that the 
 Parallels to the Bafe Line are there mark'd on a Side Line, and 
 Jiere, on a Line in the Middle of the Plan : But the fame Ef- 
 fect is had from eacli Method; for drawing Lines from all the 
 Divifions of the middle Line to the Eye A, you will have the 
 Line of Interferon B C, which is upon what may be called 
 the Bafe Line DE. 
 
 To put it in Perfpe&ive, transfer the whole Length of the 
 terreftrial Line DE to any Place at Pleafure, asDE, andfetoff 
 the Height of the Eye AF; then, putting the Line of Inter- 
 feron BC either in the Middle, or one Side, draw Parallels 
 to the Bafe Line thro' all the Divifions to the extreme Rays 
 DA, E A, and fet the Breadth of the Pilafters D K on the Bafe 
 Line ; then drawing a Line from K to the Point of Sight 
 A, the Points wherein it interfects the parallel Lines will be the 
 Widths of the Pilafters. 
 
R U L E S 
 
 FOR 
 
 ELEVATIONS. 
 
4^ 
 
 PERSPECTIVE 
 
 Preliminary I nftruftions necejjarjy to the following Methods 
 
 WE fancy the Reader is by this Time fufficiently instructed in what 
 relates to Ichnography and Planigraphy, eonfidered as the Found a-« 
 tions of Orthography and Scenography, 
 
 Orthography, we have already defined, the Elevation of the Face or 
 Front, &c. and Scenography the Elevation of the Whole, See the D e f j-r 
 *T I t i ons at the Beginning of the Work. 
 
 To makemyfelf more intelligibly to fuch as are not verfed in the Ufe 
 of thofe Words, we purpofe for the future to call Ichnography, the Plan\ 
 the Orthography, the Upright, or Elevation of the Front ; and Scenogra- 
 phy, the Elevation of the Whole. 
 
 Before we proceed any farther^ it is to be obferved, that Elevations ne* 
 ver give the Eye ail the Angles of the Plan, and that the Quantity of Sides, 
 or Angles, depends on the Afpect or View the Object is taken in ? Thus, if 
 it be viewed in Front, as the Figure A, it will only (hew one Side, tho* 
 the Plan have fours if it be viewed by the Angle, it will (hew two, as 
 but never more s in. whatever View it be taken; We fpeak of Squares 5 
 for as to Objects of many Sides, they may fhew three, four, five, and more, 
 Now Objects declining ever fo little from the Point of View, are feen 
 by the Angle, and! of Confequence muft fhew two Sides ; And ftill the 
 farther they are removed from the Point of Sight, the more of themfelves 
 they fhew 5 thus K E fhews more of itfelf than CL, tho* their Thicknefg 
 be equal. 
 
 Another Thing to be obferved farther is, that what is parallel to the 
 Horizon when the Object is viewed in Front, as C D E F of the Door in 
 Fig, 1 « becomes a vifual Ray when the fame Object is view'da little ob-» 
 liquely ; Thus CDEF, which in the upper Figure ftands in Front, becomes 
 a vifual Ray in that underneath. And, on the contrary, what is a Ray in 
 the upper, becomes parallel to the Bafe in the under* As to Perpendicu- 
 Jars, they are always perpendicular, 
 1 
 
43 
 
 PERSPECTIVE 
 
 Of tie Line of Elevation, ferving to give the Heights of 
 all Kinds of Objedls in all Parts of the Plan. 
 
 TH E Ufe of this Line is of the laft Importance, infomuch, that whoever is 
 perfectly Matter thereof will fcarce meet with any Difficulty in any Kind of 
 Elevation. 
 
 As in the putting Planes in Perfpective we made ufe of the Bafe Line ; fo in 
 Elevations, another Line is to be ufed, to direct: us, and carry the proper Heights 
 to all the Objects to be raifed. * 
 
 This Line of Elevation muft be perpendicular to the Bafe Line A B, which is 
 always the firft Line of the Plan, and that next the Eye, and of Confequence the 
 fitteft to carry the Meafures to the feveral Obje&s in the Plan. On this Account 
 the Line of Elevation C D is raifed perpendicularly on AB, -as the other Lines 
 in the Plan fhould be : Infomuch, that it is to be remembred as a Rule, that when- 
 ever, in the Courfe of this Work, mention is made of Perpendiculars, it is to be 
 underftood of Perpendiculars to the Bafe, 
 
 Since *tis this Line of Elevation which is to receive and give the Heights of the 
 Objects to be rais'don the Plan, it muft have the fame Horizon with the Plan 5. 
 for this Reafon, from the Foot of this Line (which is placed either on the right 
 or left) a Line is to be drawn to fome Part of the Horizon, tho' to what Part does 
 not matter, the Effect being the fame in all. In this Figure, the Line of Ele- 
 vation is CD, and from C, the Line is drawn to the Point of the Horizon in E j 
 or it might be drawn to the Point of Sight, if one pleafed. We have here put 
 the Line of Elevation on either Side, and the Point different in each, to (hew that 
 it will anfwerany where. 
 
 If from the Point H, which is in the Plan of the fecond Figure, you would 
 raifeaLineof two Foot Height, fet two equal Parts on the Line of Elevation,, 
 which you hold equivalent each to one Foot, fuch is here CF and from C draw- 
 ing a Line to E, you will have an Elevation of two Foot between the two Lines 
 C and F. 
 
 Now, to give the fame Height of two Foot to a Line raifed from the Point 
 H, from D draw an occult Line parallel to the Bafe Line, till it meet the Line 
 C E in the Point I ; then from the Point I erect a Perpendicular I K : This will be 
 the Height of the Line required, which is to be taken hence in the Companies, 
 and fet off from H toL. 
 
 If a Line likewife two Foot high were required to be drawn from the Point 
 M, the fame Operation being repeated, you will have the Perpendicular N O, 
 which will be the Height required from M. Laftly, performing the fame for the 
 Point P, you will have the Perpendicular QR, for the Height of a Line of 
 two Foot from the Point P. 
 
 The fame Rule will give a Height of 3, 4, 5, 10 or 20 Foot ; all required 
 being to fet fuch Heights on the Line of Elevation, from thofe Heights to 
 draw Lines to the Point in the Horizon, as E, and to proceed with the reft as 
 above. 1 
 
44 
 
 PERSPECTIVE 
 
 Elevation^ a Cube in Perfpedtive* 
 
 HAVING made the Plan according to the preceding Rules, and having put 
 the Line of Elevation upon the Bafe Line, on fome Side of the Plan, as FL, 
 upon the fame Line fetoff the Height of the Cube, viz. FM, and from the Points 
 F and M draw Lines to the Point of Elevation E 5 then from the feveral Angles of 
 the Plan ABCD, draw Parallels to the Bafe Line, till they meet with the Line 
 F E, and from the Points of Interferon F and H, erect Perpendiculars F M and 
 HK; then taking thofe Meafures in your Compafles, fet them perpendicularly 
 upon the Angles ; thus, taking the Height F M, fet it on the two Perpendiculars 
 raifed from A and B, which will give you AG andBG ; then taking the Height 
 H K, fet it on Perpendiculars raifed from C and D, which will give you CO* DO ; 
 laftly, joining the right Lines G O, O G, the Cube will be raifed: 
 
 For the Elevation of any Figure whatever always draw Lines from the feveral 
 Angles of its Plan, parallel to theTJafe Line, till they cut the Line drawn from 
 the Foot of the Line of Elevation, and proceed in all refpects as directed for the 
 Cube, and you will find there is nothing, however difficult and unequal, but will 
 be thus brought into its Perfpective. Examples of which we fliall give in the 
 Polygons following. 
 
 The fecond Figure is another Cube, raifed after a fomewhat different Manner 
 from the firft. The Procefs we mail defcribe in few Words, being nothing con- 
 temptible. 
 
 Having difpatched the Plan the ordinary Way, from the feveral Angles thereof; 
 BCDE, erect Perpendiculars; and on the firft of them, BC, fetoff the given 
 Height of the Cube, viz. BA, CA ; then from the Points A A draw Lines to 
 the Pointof Sight F, or to the Points of Diftance GH, and the Points I and L, 
 wherein they interfect the Perpendiculars of the Angles D and E, will give the 
 Line of Depth, and the Top of the Cube perfectly raifed. 
 
 This latter Method is much lefs univerfal than the former, which has always 
 been in ufe among the oldeft Authors ; yet has it fome Advantages, which we may 
 have Occafion to touch upon hereafter. ' 
 
45 
 
 PERSPECTIVE 
 
 Elevation of a Triangle. 
 
 UNDER our laft Article we promifed to (hew with how much Eafe ail 
 Kinds of Figures may be raifed in Perfpective, Now of thefe, Polygons, 
 or Figures of many Sides, are the mod difficult : We (hall therefore choofe to 
 exemplify in thefe ; and, to obferve fome Order, will begin with the moft fimple> 
 the Triangle. 
 
 Having formed the Plan, as already directed under Art. 21. where we have 
 fhewn the Method of drawing it with a Ledge or Lift : The Line of Elevation, 
 as juft now intimated, muft be fet on one Side, and of any Height at Pleafure, 
 ex. gr. BA, which we'll fuppofe to be 3 Foot: Then from all the Angles of the 
 Plan drawing parallel Lines, parallel to the Bafe Line, to the Line BE, and from 
 the Points of Interfe&ion erecting Perpendiculars between the Lines A E and 
 B E, fet off all their Heights upon the feveral Angles, whence the Parallels pro* 
 ceed : The Height AB, for Inftance, on the Angles G and O, which will give 
 GT andOV; the Height HL, on the Angle K, which will give KXj and the 
 laft Height NP, on the Angle Q, which gives QY. Laftly, connecting the 
 Points R, SandY, and again the Points T, V and X, by Right Lines, you 
 will have the Triangle in its proper Thicknefs, (gc, 
 
 A Pentagon, or Five- Angle, in PerfpeBive. 
 
 THE Pentagon, we have faid, is a Figure with five Sides or Faces, 
 and as manyAngles \ and have directed the Method of forming it in P. 22, 
 As to the making its Elevation, we mould lofe Time to defcribe it, the Figure 
 hereto annexed Sewing abundantly that its Method is the fame with that of the 
 Cube and Triangle, 
 
 The Hexagon, or Six- Angle, in Perfpe&ive. 
 
 THE Hexagon is a Figure with fix Angles, and as many Sides or Faces* 
 as already obferved, P. 23 and 27. where we have given its Diminution, 
 The Method of raifing it is obvious enough from the Figure, 
 
46 
 
 PERSPECTIVE 
 
 The Heptagon, or Seven- Angle, 
 in Perlpe&ive. 
 
 THE Heptagon is a Figure with feven 
 Sides and Angles ; the manner of deferr- 
 ing it, and of putting its Plan in Perfpe&ive, we 
 have already given in Page 24. Its Elevation is 
 performed after the fame manner as that of the 
 Triangle, as appears from Fig. L 
 
 The Octogon, or Eight- Angle, in 
 
 e. 
 
 TH E Octogon is a Figure with eight Sides 
 and Angles, as reprefented in Pag. 25, 26. 
 where the Reader will find two Ways of putting 
 it in Perfpe£tive. Its Elevation is the fame as that 
 of the preceding one. 
 
47 
 
 PERSPECTIVE 
 
 <^> ^ ^ ^ f(j, ^ ^ ftly ^ ^ ^ 
 
 A Double Crofs in Perfpe&ive. 
 
 THIS and the following Figure we add from the Sieur 
 de Maroloisy who has put them in his Works according 
 to our Method. The Truth is, it were fomewhat difficult to 
 put them in Perfpe&ive any other way, by Reafon of the 
 Multiplicity of Angles $ but in this Method all is eafy, by on- 
 ly raifing the Heights from all the Angles of the Plan, &>c, as 
 already ©bierv'd of Polygons, and is evident from the Figure, 
 
 A Stone fluted, or channel? d far-wife r in 
 
 Perfpe&ive, 
 
 NOT having given the Plan of this Figure among the 
 other Plans, we have judged proper to add it under- 
 neath. The geometrical Plan is eafily made, as being only a 
 Circle divided into fix, and the Divifions joined by right Lines, 
 leaving a Point between each two; as, ex.gr. between 1 and 3> 
 leaving 2 ; and from 2 to 4, leaving 3 ; and fo of the other. 
 The reft is obvious from the fecond Figure. 
 
4 8 PERSPECTIVE 
 
 Of Pilasters in PerfpeBive. 
 
 IN the raifing of Columns, Pilafters, Walls, or the like Objects, which are 
 to be of the fame Height, there is no need of a Line of Elevation ; 'tis fuf- 
 ficient to proceed as in the fecond Method for the Cube, that is, having raifed 
 Perpendiculars from the Angles of the Plan, as herefrom A BCD of Fig. i. 
 fet the Height defired on the firft or fecond Perpendicular, as A F or D E ; then 
 drawing a Line from E to the Point of Sight F, to this Line all the Perpendicu- 
 lars from the other Angles are to be raifed : In which Cafe, the Pilafters G and H 
 will be equal to the firft. 
 
 If one choofe not to make ufe of Squares in the Plan, the Meafures muft be 
 laid ontheBafe Line, and Rays be drawn thence to the Point of Sight F, and 
 other Rays for the Diminutions to the Point of Diftance K : Thus, ex. gr. L M 
 being a Side of a Pilafter, Rays are to be drawn from the two Points thereof, 
 Land M, to the Point of Sight F, for the Breadthsof all the Pilafters ; and for 
 the Depth of each, as they are intended to be fquare, the Diftance LM is to be 
 taken and fet off from LtoN; then drawing a Line to K, it will give the Depth 
 of the Pilafter in O ; laftly, from the Points LMOeredt Perpendiculars, and 
 proceed as above directed. If you would have the Width of two Pilafters between 
 one and another, fet them accordingly on the Bafe Line, and after making the 
 Depth of the fecond Pilafter equal to the firft, as here PQ, from the two Points 
 P Q_draw Lines to the Point of Diftance K, which will give the Points R S on 
 the Ray L} and from S draw another little Parallel cutting the Ray M F, as the 
 Line S T ; laftly, from the three Points R, S and T ereding Perpendiculars ; pro- 
 ceed as in the former Cafe. A third, fourth, fcfr. are to be added after the 
 fame Manner, ftill obferving the fame Meafures on the Bafe Line as in the firft. 
 Figure. 
 
 Of Pilasters viewed by the Angle. 
 
 WE have already obferved, that the Plan of Squares is formed by drawing 
 Lines from the Divifions of the Bafe Line to the Point of Diftance., As 
 to the Elevations, the Method is the fame with that juft defcribed : For having 
 fet the Height A B on the firft Perpendicular, Lines muft be drawn from the 
 Point B to the Points of Diftance CD, which will interfecl: and give the Heights 
 of the other Perpendiculars raifed on each Side then giving the Diftances re- 
 quired between the two Pilafters, which are two Squares, raife the fecond ; and 
 by the fame Rule the third. Their Heights will be found by drawing a vi- 
 fual Ray from the Point B to the Point of Sight E, the Interfe&ions whereof with 
 the firft Perpendiculars in the Points F and F, as alfo the Interfe&ions of other t 
 Lines from F and F to the Points of Diftance C and D with the other Perpen- 
 diculars, will give the Heights required, as in the firft Pilafter. 
 
 Thofe done without Plans muft have their Meafures on the Bafe Line, as if 
 they were to have the fame Breadth with thofe viewed in Front. Accordingly, 
 the Breadth G H muft be marked, and a Ray be drawn from G to the Point 
 of Sight E, which will give all the middle Points, or Diameters. Then fetting 
 the fame Breadth from G to I, from the three Points GHI draw Lines to the 
 Points of Diftance CD, which form the firft Plan. On this Plan erect Perpen- 
 diculars, on the firft whereof fet off" the Height, as GK, and from the Point 
 K draw Lines to the Points of Diftance, which Tvill give the Shortnings of the 
 Perpendiculars of each Side. For the fecond Pilafter, do the fame with the 
 Points L and M: And for the third, with the Points N O. The reft is evident 
 from the Figure. 3, 
 
49 
 
 PERSPECTIVE 
 
 Effe& of the Difference Horizons. 
 
 *"T"* HE higher a Man is raifed above an Object, the more he fees of the 
 I upper Part thereof $ of Confequence, the lower he is, the lefs he 
 fees ; and if he be underneath it, he only fees the bottom Part, and nothing 
 of the Top. • 
 
 The firft Proposition is evident from Fig. I. the fecond from Fig. II. and 
 the third from the laft. 
 
 The firft and fecond Cubes are formed after the manner already delivered. 
 The third is alfo done by the fame Rules, tho* they may appear fomewhat 
 more difficult, by Reafon the Object is feen over-head j but, inverting the 
 Paper, or Painting, and drawing Lines to the Point of Sight A, and Points 
 of Diftance B and C, as in the former Methods you -will have the fame 
 Facility. We fay nothing of Objects viewed fide-wife, as having already 
 fo often repeated, that the Method is the fame as of thofe in Front. To 
 render the Practice of putting them in Perfpective more eafy, we have ad- 
 ded two Figures, the one a bare Out-line, the other fhadowed farther. 
 
 Before we quit this third Figure, it is to be obferved, that the Low- 
 iiefs of the Horizon is the Reafon we fee the Bottoms of Objects, as D E F, 
 whereas of the two others, GH, placed in the Horizon, neither Top nor 
 Bottom can be feen : Not the Top, by Reafon of the Lownefs of the Hori- 
 zon; nor the Bottom, becaufe they are the Horizon itfelf. 
 
 There are Abundance of Painters faulty in this Point, making no Scru- 
 ple tofhew the Tops of Objects, even where the Horizon is very low. 3 
 
s° 
 
 PERSPECTIVE 
 
 Elevation Obje&s wtojW £y Hi? -^g/*- 
 
 WE have already (hewn in p. 19, 20. how the Plans are to be form'd, the 
 Lines being always to be drawn to the Point of Diftance, not to the Point 
 of Sight, unlefs for finding the Diameter. The fame Rule is to be obferved for 
 the Elevations, as is evident from the firft Figures, all the Lines whereof are 
 drawn towards the Points of Diftance B and C, and none of them to that of 
 Sight A. 
 
 The firft Figure D mews that thol there bean infinite Number of Parts in any 
 Object feen Angle-wife, they are #11 to be drawn to the Points of Diftance B and 
 C If you would do one after the fame manner, the Rule is this •, having formed 
 a Plan, and raifed occult Perpendiculars, as already directed, fet the given 
 Height on the firft Angle, as E F, and from F draw Lines to the Points B C, 
 for the Heights of the fecond and third Angles, in the Points G •, then from G 
 draw Lines to B and C, and you will have the fourth Angle of the Platform. 
 The other lefler Pieces are raifed after the fame manner, viz. by fetting the 
 Heights on the firft Perpendicular, as from F to H •, and from H drawing Lines 
 to the Points C and B, as before done from the Point F : By fuch Means you 
 will have the Heights of all the Angles, and the Points I and K will give the 
 Thickneffes of all the lefler Pieces, and the Platform of the Middle, by ft ill 
 continuing to draw Lines to the Points B and C. The reft is evident from the 
 Figure, which may ferve for a CaftJe defended with four fquare Towers, or for a 
 Palace cantoned with four Pavilions. 
 
 The two other Objects on each Side the great one are feen Side-wife the man- 
 ner of drawing them is in all refpects like thofe viewed in Front: Thus, railing 
 Perpendiculars from all the Angles of the Plan L, and giving the neceflary Height 
 to the firft of them, as M N, and drawing a Line from the Point N to the 
 Points of Diftance BC, you will have the fecond and third Angles in^the Points 
 OO •, then drawing Lines fromO to the PointsBC, you will have the*Tourth An- 
 gle, which is the Elevation of the whole. This is according to the firft Method ; 
 the fecond would have given the fame. 
 
 The fecond Figure underneath is done the fame Way all the Difference is, 
 that in this the Horizon is fomewhat lower. 
 
 The third (hews the Bottom of the Objects •, but the Method is ftill the fame 
 as in thofe that (hew the Tops, the Lines being drawn to the Points of Diftance 
 sQJR. in the horizontal Line. 
 
SI PERSPECTIVE 
 
 Toraife ObjeBs of any Heights, and remove them to any Dis- 
 tance at Pleafure. 
 
 SUPPOSE it required to have an Objeft two Foot high, one Foot broad, 
 and one Foot deep ; and another three Foot high, one Foot broad, two Foot 
 deep, and two Foot cliftant from the firft Object; and another a Foot broad, 
 five Foot deep, four Foot high, and three Foot diftant from the middle Objeft ; 
 Your Method of proceeding will be thus : Having formed a Plan of Squares, 
 fuppofed each equivalent to one Foot, by Means of the Pb.ntaof Sight A, and 
 Diftance BC ; from the firft Angle erect a Perpendicular according to the fecond 
 Method above directed, which Perpendicular is tocarry the proper Meafures to 
 all the Obiefts, as here D E, wherein the Meafure D F is fet four Times, by Rea- 
 fon the hiheft Objea is not to exceed four Foot. From the feveral Angles of 
 the firft Square FI GD erect occult Perpendiculars j and having fet the proper 
 Meafure, viz. two Foot, on the firft of them, D, from the Point 2 draw a Line 
 to the Point of Sight A, and it will cut the Perpendicular of the Angle G ,n the 
 Po nt H? through which a Line is to be drawn paralle to the Bafe, cutting the 
 Pe mend cular of the Angle I in K, and another Parallel to be drawn through the 
 Po nt", cutting the Perpendicular of the Angle F in the Point L, tten cotu 
 nectTn' the four Points HKL and 2, by right Lines, you will have the firft Ob- 
 feet Now as youwould have a Space of two Foot between the firft and fecond 
 Obiea, two Squares are to be left vacant between them ; and on the firft Angles 
 of he third, Perpendiculars are to be raifed, and the fame done as to the firft Ob- 
 ?oS with this Difference, that the Height of the fecond is to be taken from the 
 fhi d Point of the LineDE, by Reafon it is to be three Foot diftant, and that it 
 s to take up ° wo Squares, finceit is to be two Foot deep. Between this fecond 
 and the third Object the Space of three Squares is to be left, by Reafon there are 
 to be three Foot from the one to the other. From the firft Angles of the fourth 
 Square Perpendiculars are to be raifed as for the firft Object, and five Squares 
 farther another Perpendicular for the Line of the Depth, and the Bound of the 
 fiv Foot, which is the Depth of this third Object. The fourth Point of the Line 
 BE Xe its Height, four Foot, by cutting the Perpendiculars, as in the firft 
 Object The Objects on the other Side are raifed in the fame Manner, and 
 on the fame Proportions as thefe ; but the Wall in the Middle is of an equal 
 Hight eTery where, viz. four Foot, with an Aperture of three Foot >n the 
 
 M in d th; fecond Figure are three Walls of equal Height-, whereof that in the 
 Middle is a Square deeper than the two extreme ones. Between each is an Aper- 
 tu e of hree Foot, for Doors or Windows. On the other Side is a continued 
 ^ntur^en Foot'long, and of an Height anfwerabletc , th< 1 reft Th^ Method 
 of elevating all thefe, is the fame w lt h thofe above. What we call a Wall may 
 lHtewife fcrve for a Hedge, Pallifade, £ft. of a Garden. 
 
5 a PERSPECTIVE 
 
 Of Walls viewed in Front. 
 
 FROM what has already been faid one may raife Walls of all Kinds in any 
 oblique Views; and tho' the fame Method may ferve for the fame Walls 
 viewed in Front, we have thought proper to add this Figure on two Accounts i 
 i(l By Reafon it is not always that Plans are made, and on fuch Occafion a Man 
 would be a little to feek for the Thickneffes. *dl 1; To give the Thickneffes to 
 Gates and Windows, which might occur m fuch Walls. 
 
 To make Walls oarallel to the Bafe Line, or the Horizon, on a Plan, one may 
 give them anv Length at Pleafure on the Parallels to the Horizon For their 
 Breadth, you may take thatof a Square, from the Angles whereof AB, you are 
 to erecl: Perpendiculars to any given Height, as C from C draw a Ray to the 
 Point of Sight D, and CD will give the Diminution of the Wall. 
 
 When there is no Plan, the Thicknefs of the Wall, as E F, is to be fet on a 
 Parallel to the Bafe Line in the firft Corner of the Wall ; then from Fa Line is 
 tobedrawntothe Point of Sight D, and from E, another to the Point of Diftance 
 G and from the Interfedion of the two in the Point H, a Perpendicular to be 
 raifed, and another from the Point F : Then the Height of the Wall FI is to be 
 taken, and from I a Line to be drawn to the Point of Sight D the Inttrfeftion 
 whereof with the Perpendicular H, will give the Diminution of the WaU. For 
 the - Length, you may give it at Pleafure on the i firft Parallel EF. For 
 theDoorfand Windows in the fame Walls, mark the Width and Height as here 
 KLMN, and fet the Thicknefs required on a Parallel, either above or below the 
 Doors or Windows, in the Corner next the Point of Diftance, as here NO or 
 L O laftly, from the Points L and N draw Lines to the Point of Sight D, and 
 from the Points O to the Point of Diftance G, and from the Interferons of thofe 
 Lines in P, fcfc. draw the Thickneffes. 
 
 Another Wall viewed by the Angle. 
 
 HA V I N G the Plan, you have nothing to do but ereft Perpendiculars from 
 the Angles already determined, and to mark the Heights on the ^^Perpen- 
 dicular from the Angle next you, as on the Line QR ; and from the Point K, 
 to draw Lines to thef Points of Diftance S T; the Interfedions thofe Lines ; make 
 with the Perpendiculars raifed from the Angles of the Plan, will give the Length 
 and Thicknefs of the Wall. If you have no Plan, fet the Meafu res both of the 
 Breadth and Depth of Doors and Windows on the Bafe Line, as m this Example, 
 VXis the Breadth, XY the Depth, and Z i the Height of a Window ; then 
 from allthefe Points draw Lines to the Points of Diftance ST; firft from X, 
 which is the Ray of the Bafe ; then from V, a little occult Line cutting the Ray 
 X S in the Point 5, which is the Thicknefs of the Wall. As to the Depth, the 
 Ray YS will give it by its intending with XT in the Point 6; and Z i will 
 oive the Breadth of the Window in the Points 7, 8 5 from which Points X, 5, 6, 
 7, 8, Perpendiculars being raifed, and the Height 2 beingfet on the firft of 
 them X, and from the Point 2 drawing Lines to the Points ST, the 1 Interferons 
 with the Perpendiculars will give the Height of them all. From the Height of 
 the Window, marked 3, 4 > draw Lines taT, and where thefe interfeft the Per- 
 pendiculars 7, 8, Lines are to be drawn 5 and from the Corners 9 to ^, for the 
 Depth 10, draw Lines to T , and from the Point of Interferon n, draw a Per- 
 pendkular. This now may ferve for a Pallifade as well as a Wall* 
 
S3 
 
 PERSPECTIVE 
 
 ^ ^ ^ *^ ^> ^< Jtu ^ 
 
 7# ^/^^ # Z)0<?r Par/ a Wall at Pleafure. 
 
 A Wall is to be raifcd one, two, or three Foot thick, on the Points HI, and 
 to be carried on of the fame Height, as already directed. If then you 
 know pretty nearly the Dimenfions of the Door, fet the Breadth on the Bafe 
 Line, as here in AB of the lower Plan, containing three Foot, and a Side of A 
 and B fet the Breadth of a Frame, or Band, D and C, and from ABC and D draw 
 Lines to the Point of Sight K •, and where they cut the Parallel MN in the Points 
 OO, £sV. erect Perpendiculars of any Heights at Pleafu re : Thus is the Width 
 of the Door already got. For its Height, DFE is to be transferred from the Plan 
 underneath to the Corner of the Wall I, and Lines to be drawn from the Points 
 FE toK ; and where they interfect the Perpendicular MP in the Point Q, draw 
 QJR. parallel to M N, which will give the Height of the Door, and the Band or 
 F>ame a-top. Its Thicknefs, or Depth, will be the fame with that of the Wall, 
 which is G F. And if from G you draw a Line from the Point of Sight K, it 
 will cut the Perpendicular M P in the Point S, through which drawing S T paral- 
 lel to Q^R, you will have the Thicknefs of the Door V. 
 
 To make a Door in a Side-wall, the Inftructions given in Pag. ij. are to be 
 well remembered j importing, that all the Meafures are to be put on the Bafe 
 Line •, and, that Lines being drawn from thefe Meafures to the Pointof Diftance, 
 will give all the Diminutions defired. For an Example, a Door four Foot broad 
 is defired in a Chamber. Setoff four equal Diftances from I to C, and draw 
 Lines from the Dimenfions of the Door C A and B D to the Point of Diftance L ; 
 where the Ray I M interfects thofe Lines, erect Perpendiculars XY, which will 
 give the Breadth of the Door. For its Height, draw Lines from tie Points E and 
 F to the Point of Sight K, and the Interferons with the Perpendiculars will give 
 the Height. As to the Thicknefs of the Top and Bottom, draw the Thicknefs 
 of the Wall, GHand FI, to the Pointof Sight K; then drawing a little Paral- 
 lel to the terreftrial Line, through the lower Corner of the Door X, and another 
 through the upper Corner, you will have XZ, the Thicknefs of the Top and 
 Bottom, to be joined by a Perpendicular, as you fee in the Figun. 
 
 If you would have a Door on the other Side, you have nothing :o do but draw 
 Parallels to the Bafe Line from the Point X to the Ray I N, and then raife them 
 as already directed. The reft is the fame as on the other Side. The Gate is not 
 here reprefen ted in the Middle ; which is a Thing we did defignedy, to obviate 
 the Error of fuch as, without any other Meafures, draw two Diagonals through 
 their Painting, tho* of ever fo great a Size, and make all their Objects equally 
 diftant from the Interferon of thofe Lines, i. e. from the Middl; of the Paint- 
 ing : So that, on their Principle, a Body mould always be mountd to (hew their 
 Work in all its Advantage ; which is a palpable Overfight. For ho' a Painting 
 fhould be forty Foot high, and it mould be placed on the Ground o be feen, the 
 Horizon mould never be above five Foot high, but rather lefs tharmore \ where- 
 as in their Way the Horizon (hould be twenty Foot high. 4 
 
54 
 
 PERSPECTIVE 
 
 To draw Windows/« Perfpe&ive. 
 
 THE Method of defcribing a Window is perfectly the fame with that of a 
 Door •, for if there be any upright Poft, of Wicket, in a Door, „'tis no 
 longer a Door, but a Window : So that you have nothing to do but learn to make 
 a fingle and double Crofs, and you are Mafter of Windows. Suppofe now 'twere 
 required to make one in a Wall AB, of any Breadth at Pleafure, lay down its 
 Breadth on the Bife Line, as.DE, and from the Points D and E draw Lines to the 
 Point of Diftance F, and from the Interferons GG, of thofe Lines with AC, 
 erect Perpendiculars GH, GH giving the Width of the Window, which is here 
 only two Squares, or Panes. As to the Height, it is ufually railed as near the 
 Cieling as may be, but the Breaft-part mould not be above, three Foot and half) 
 this Meafure therefore is to befet On the Perpendicular AB, as from A to I, and 
 drawing a Line from I to K, where that Line interfects G H, will be the Breaft- 
 part. After the like manner drawing a Line from L, the Top of the Window, 
 to the Point of Sight K, its Interfection with GH, will be the Top of the Win- 
 dow ; by which Means we mail have a long Square, or Parallelogram, to which 
 a Crofs being added, will form a Window, To make this Crofs, the Space DE 
 muft be divided into two equal Parts, each being about half a Foot; then draw- 
 ing this Breadth M to the Point of Diftance F, and from the Interferons thereof 
 with the Ray AC, erect Perpendiculars NO for the upright Poft, or Stancher, 
 in the Middle of the Window. As to the Crofs-pieces, you may add as many as 
 you pleafe, only obferving that their Thicknefs muft be equal to that of the up* 
 right Piece ; taking the Meafure M therefore fet it off upon the Perpendicular 
 AB, as is P, and drawing a Line from P to K, the Points wherein it interfects 
 the Perpendiculars GH, GH will give the crofs Bars, and of Confequence the 
 Window is finifhed. For its Thicknefs, 'tis here only to be half that of the Wall) 
 to accommodate which, occult Lines muft be drawn from the Point Qjto K, and 
 little Parallels to the Safe being drawn from the Corners of the Window S, the 
 Point wherein they cut the Line QJEC will give the Thicknefs required. 
 
 This Window ranges even with the Wall on the Infide, which is not very ufual, 
 Windows being now frequently made with Embrafures, or Niches entering into 
 the Wall a Foot, or lefs. 
 
 The Method is precifely the fame in both, only that inftead of taking the In- 
 terfeclions on the Line A C K, they muft here be taken in another, re-entering 
 into the Wall as much as the Window isfnade to re-enter, as appears from the 
 lower Figure, where the Ray O K receives the Meafures laid on the Bafe Line ) 
 and that all the reft muft be drawn to the Point of Diftance F, as in the former 
 Cafe, taking the Thicknefs of the Window between the Perpendicular O, and 
 the other which is the laftV Laftly, when the Window is finifhed, on the 
 Ray OK, and from the Breadth of the Wall OF, raife the Perpendicular A, 
 and draw it to the Point K j then from the lower Corner of the Window, in 
 the Points PP* draw a little Parallel cutting A K in Q, which will be the Thick- 
 nefs of the Wall, covering the Window a little, and (hewing the Thicknefs R P; 
 then from the Point R erecting the Perpendiculars RV, cutting the Ray T K 
 in V: which will be the Thicknefs of the Top of the Window. From the Mea- 
 Aires here laid done, one may make as many as one pleafes, ftill obferving the 
 fame Order* 3 
 
55 
 
 PERSPECTIVE 
 
 I 
 
 Of ClELlNGS. 
 
 \&VX^£3&3£& 7 M whichthey pierce 
 
 S-^Tp^-ntt^^r^n, befirftlaid, and over 
 Suppofe the Walls ratfed AB, on wh i ch J^ n a " r !° 0 f anv p ie ce (which we 
 
 here fuppofe a Foot) it u to be ca rt ed <° the / °£ ° the Point of Sight E, 
 from the Points Cand D occult Lines t . be drawn . ^ be fe£ 
 
 w hichwillgivetheRaysCDGF T £™llTe Meafures of the Joifts, 6fc. 
 on a Parallel to the Horizon f • *7 '" tive here done the three I, K 
 to be laid on the Wall, are to be difpofcd, as we have n ^ 
 
 there, the Line QR»»^ a each other> as foji be judged expedient ; 
 Number, and at lucn uniancc ■ u T L ir i<nefs aDart from each other. To 
 the Rule being ufually to be twice their Th «* nels apar ^ 
 
 mortaife them, take : their i™^™^^ ^ TV ^ ange the Joints, 
 and draw an occult Lme TV-, then be ™^ ^ r e vifibte> draw Lines to 
 X, X, fife, and from al Ithei ' An S les " at „ d [he half of the other Beams, 
 the Point of Sight Y And that they may no ^^Z ^ltUne to the 
 from the Middle of the firft, which is the Point_ I, or PointZ, 
 Point of ••Sigh. :T, wheh will you. may not pafs 
 
 y™toTepZt Y, and you will have what you require. 
 
PERSPECTIVE 
 
 »-¥-« HI S Figure is only added to ftiew the 
 1 Effeft of the Method juft now laid down ; 
 wherein it is obfervable the Number of Stones 
 does not render the Prance at all the more 
 
 ^ T'he Joifts are not mortais'd into the Beams of 
 the upper Story, as they are in the lower. 
 
57 
 
 PERSPECTIVE 
 
 Another Difpolition of Ce i lings in PerfpeElive. 
 
 T H I S Method is performed in all Refpe&s like that juft defcribed, only that 
 the Difpofition of the Members and Pieces that compofe the Cieling i to 
 be changed ; that is, the Beams are laid long-ways, tending towards the Point of 
 Sight, and the Joifts a-crofs, which is the reverfe of the former. 
 
 Suppofe the Walls AB ; on thefe, or on Confoles jutting out from them, fet 
 the Thicknefs of the Beam CD, and through the Points Cand D draw Parallels 
 to the Horizon CE and D F, between which you may put any Number of Beams 
 at Pleafure, as we have here done three, viz. G H and I, from all which Lines 
 are to be drawn to the Point of Sight K } then through the Point P, wherein 
 D P mterfe&s the Perpendicular L P, draw a little Parallel to the Horizon P M, 
 this will be the Bound of all the other Rays, as G N, &c. laftly, from the Point 
 N erect a Perpendicular NO: And fo of the reft. Thus much for the Beams, 
 
 To lay the Joifts a-crofs the Beams, fet their Thicknefs on the Line OR, as 
 V W; and from the Extremes of V draw Lines to the Point of Diftance S j 
 and through the Points of Interfe&ion with the Ray QT draw Parallels to the 
 Horizon, as far as the Beam of the other Side. If you would mortaife them in 
 the Beams, take the Thicknefs of the Rafters within the Beam, as QJX ; and from 
 X draw a Parallel to the Bafe Line, as far as the other Side X X j and between 
 the two Lines QR and XX fet the DivifionsVV, fcfr. which will form YY, 
 tfc. And from all the Points Y drawing Lines to the Point of Diftance S, you 
 will have the Thickneffes of the Bottom and Sides given by the Interfe&ions with 
 the Ray XT in the Points ZZ, through which drawing Parallels to the 
 Horizon, the Ceilings will be finiflied ; as in Fig. II. 
 
 Thus it is that ftmple Timber Ceilings are put in Perfpe&ive. If, after thefe, 
 or in Lieu of thefe, you would have a handfom Platform of Painting, or other 
 Enrichment, you will find Inftruftions for the fame in Page 35. where we fpeak 
 of Gardens: And making Ufe of the Line OR for a Bafe Line, you may do 
 what you pleafe therein. 
 
 For Floors, there are enough already laid down in Pag. 30, 31, 32, 33, and 34. 
 to open, the Mind for the finding many others. Thus far we have had to do 
 with the Rooms, as Hall, Chamber, or the like, the feveral Parts whereof are 
 fully delivered : The Moveables therein fhall be fliewn hereafter. 
 
 I 
 
5« PERSPECTIVE 
 
 §®®®®®®®®®®®®®®®®®®®®^®®®^®®®®®®^i$0^,^^ 
 
 TH I S Figure ftiews the Cieling juft now de- 
 fcribed, diftin£fc and clear of the Lines 
 wherewith the former was embarrafled. 
 
 The Conftru&ion of the Gate fliall be Ihewn 
 hereafter* a 
 
59 
 
 PERSPECTIVE 
 
 * 'At7Z 3z <b 3& 3& $Z M. Jfe 
 
 Circular Gates #W Arches e;/>z^ direcily. 
 
 HAVING given fufficient Inftru&ions for Halls", Chambers, Win- 
 dows, and fquare Doors, or Gates, we proceed to the Pra&ice of 
 
 round ones. , • , 
 
 Suppofe then ABCDEF to be Pilafters on a Plan, to place Arches 
 thereon ; divide the upper Breadth GH into equal Parts, in the Point I, 
 on which fetting one Leg of your Compares, with the other, defcribe a 
 Semi-circle G H, for the firft Arch. 
 
 To make all the reft of the fame Height and Breadth, draw Lines from 
 the Point of Sight HG to the Point of Sight K, and through the two 
 Points L, L, where thofe Rays cut the Perpendiculars C D, draw Paral- 
 lels to GH: Thefe Parallels being divided into two, and Semi-circles 
 ftruckfrom them, as in the firft, you will have the fecond and third Arch. 
 To find the Middle of thofe Parallels L, you have only to lay the Ruler 
 in the firft Centre I, and draw a Line to K, which will cut them all pre- 
 cifely in the Middle M M, and give the Points for the Semi-circles to be 
 drawn from. Thofe viewed in Front, and thofe by the Side, are all per- 
 formed-the fame Way ; as appears from the firft Figure. 
 
 If it be required to make an Edge, or Band, of equal Thicknefs 
 throughout, you are only to ufe one Center as O, from which the Thick- 
 neffes N P of the lower Figures are formed. The reft is all performed as 
 already directed, by drawing Lines to the Point of Sight K. The laft 
 Figures ftiew how all Kinds of fimple Vaults, only confiding of a Semi- 
 circle, are to be formed : As to the Enrichment thereof, we (hall have 
 Occafion to fpeak hereafter. 3 
 
PRACTICAL. 
 
6o 
 
 PERSPECTIVE 
 
 V *W* "W* *W* £ **9f^ * W* *W* 1 
 
 Round Arches over Pilafters viewed in Front, 
 
 np*HE Out-line of the laft Plate readily di reels how this is to be done, 
 X the Method being the fame in both. In the prefent there are a few 
 more Lines, but not any Thing more of Difficulty : For, drawing Parallels 
 to the BafeLine over the Tops of the feveral Pilafters AB, CD, and di- 
 viding the firft of them into equal Parts, from the Middle E, as a Center, 
 defer ibe the fit ft Semi circle A C, without removing the Compafles, from 
 the fame Center, defcribe the Band or Thicknefs AGFC; laftly, from the 
 Center E, drawing Lines to the Point of Sight H, the Ray EH will give 
 the middle Points of all the Parallels for defcribing Semi-circles over them 
 all, from BD to the laft, I. The Method is the fame for that in the 
 Side-view. 
 
 Gothic Arch, or Arch in the third Point. 
 
 r TpHE drawing of this is aseafy as that of the circular Arch. Ha- 
 ving laid down the Breadth K L, fet one Foot of your Compares in 
 K, and directing the other to O, ftrike the Arch LO; then remove your 
 Companies to If defcribe the Arch KO, and you will have an Arch in the 
 third Pointy KOL. Do the fame from M and N, and you will have the 
 Jecondy or inner Arch, MPN. The fecond Figure, in the third Pointy 
 has a Band or Lift all round it, which is defcribed from the fame Centers : 
 Thus, ex.gr. from the Center Rthe Arches SX and TV are fwept; and 
 from the Point S the Arches QV and R X : All the reft is drawn to the Point 
 of Sight Y. 
 
 Another third Point, or terzo Acuto, is reprefented in Figure the 
 Diameter whereof, a b, being divided into three equal Parts X, and one 
 Foot of the Compafles fet in one of the Divifions, as c, and with the other 
 the Aperture c b taken, the Arch b e is ftruck therewith ; then removing the 
 Compafles to d, the Arch da eh ftruck, which is an Arch in the third Point 
 as well as the former ; and either of them may be ufed at Difcrecion, Thofe 
 in old Gothic Churches come neareft the former Kind. 
 
6i 
 
 PERSPECTIVE 
 
 Sequel of the former Figure. 
 
 WE here add an Arbour of a Garden, the 
 Performance whereof is in mil Refpe&s the 
 fame as that of Arches viewed in Front. 
 
62 
 
 PERSPECTIVE 
 
 "To defcribe, and put in PerfpeSiive, round Arches and Doors. 
 
 TH E Circle being fomewhat difficult to put in Perfpective, requires a Num- 
 ber of previous Lines and Points : To find which the more readily, the firft 
 Figure here added is to be underftood ; which fhews, that to deicribe a Semi- 
 circle upon a Diameter AB, there needs no more than to fet one Foot of your 
 Compaflks in the Point C, in the Middle of AB, and with the other to fweep a 
 crooked Line from A to B. And thus is the Semi-circle to be transferred upon the 
 Elevation DE, Fig. II. for a circular Gate or Arch. 
 
 Now to put it in Perfpcdive, it is to be divided into any Number of Parts, 
 and the more the better ; as already obferved in Pag. 28. and as we mall hereafter 
 have occafion to mew, when we are fpcaking of crols Vaults. The prefent Semi- 
 circle we mall only divide into four, and that by drawing a Parallel to A B, raff- 
 ing it in the Point F, which Point will be the Middle of the Semi-circle; then 
 erecting two Perpendiculars from A B, cutting the Parallel Fin the Points GH, 
 and from the Corners AB G H drawing two Diagonals AH, G B, interfeaing 
 each other in I ; from the Point I raife a Perpendicular CIF cutting the Circle in 
 two: And the Diagonals will cut it into two other Parts in the Points KK, thro' 
 which a Line LK is to be drawn Parallel to the Bafe Line : All which Divifions 
 and Meafures are to be transfer^ to Fig. III. to put it in Perfpective. 
 
 Firft then draw a Line from the Angle E to the Point of Sight M, and ano- 
 ther from the Point N (which is the fame Diftance from E, as D is) to the Point 
 of Diftance P •, which latter cutting the Ray E M in the Point E Q^will be the 
 Width of the firft Arch D E in Perfpedive. Then drawing a Line from O to 
 the Point P, it will cut the fecond Arch in the Ray EM, or the Point R. As 
 there is no more Room on the Bafe Line to take the third Arch, a Point muft be 
 drawn from N to the Point of Sight M ; and through the Point R a Parallel to 
 the Bafe LineR S : Now as RSis under the fame Angle withE N, it is the fame 
 Breadth, as has been already proved in the Beginning of the Book', therefore 
 drawing a Line from S to P, it will cut the Ray EM in the Point T, which gives 
 the third Arch. 
 
 Proceed then to raife Perpendiculars V V, &c. from the three Points QJ< T, 
 which interfeding the Ray H M, will give thehigheftof the Arches ; then from 
 the Ray BM, which gives the Bottom of the Semi-circle, draw Diagonals BV, 
 HX, which interfeaing each other, give the Place of the Perpendicular Y F, 
 that divides the Arch into two; and drawing the Ray LM, it will cut the Dia- 
 gonals in two, and the Arch in four laftly, conneaing the Points BZ, FZX, 
 with curve Lines, you will have the firft Arch : And a Method which will give 
 you infinite others. The fame ferves not only for Arches and Doors, but alfo for 
 Vaults, Bridges, and other Things that require the Semi-circle •, for which Reafon 
 it is that we decline fpeaking any Thing farther of the two latter. 
 
 The fame Method may likewife ferve for Church Windows, only one or two 
 upright Pofts are to be added to faften the Glafs to. 3 
 
63 PERSPECTIVE 
 
 To defcribe y and put in PerfpeBhe, double Arches and Gates, 
 i.z.fuch as pew their Thickneffes. 
 
 WH A T we have hitherto done is merely for the Out-line, which 
 being doubled gives the Breadths and Thickneffes ^ of Arches, 
 and what fupports them, by only connefting all the Interferons of each 
 by Right-Lines : For Example, 
 
 Having defcrib'd the firft Line D E, and drawn Lines from D and E 
 to the Point of Sight A, fet the Thicknefs on the Bafe-Line E C, by 
 drawing C to the Point of Diftance B, and in the way cutting the Ray 
 E A in the Point F ; thro' which drawing the Line G F parallel to the 
 Bafe-Line, it will cut the Rays DA and E A in the Points F G, and give 
 the Thicknefs requir'd. Then from F G ered Perpendiculars, and from H 
 draw a Line to A, the Interferon whereof with the Perpendicular F I gives 
 the Height thereof. From this Line you are to find the Line of the Cen- 
 ter of the Semi-circle, by drawing a Line from K to the Point A, which 
 gives the Point L, a Parallel drawn thro' which will have the Center 
 of the hinder Semi-circle upon it, as N is the Center of that before. 
 * This Line M L is to be divided into two equal Parts, by drawing a Line 
 from N to A thro' &X) Then fetting one Leg of your Compaffes in O, 
 with the other defcribe a Semi-circle M L, to be divided like that in the 
 preceding Figure. Laftly, draw Right-Lines from the Divifions of the 
 one to the other, that is, from the fore Semi circle to the hind-one, to 
 connect the two into one ; as in the Figure M is join'd to PQ^toR S, 
 to T V, to X L, to K. * 
 For circular Arches, &c. view'd in Front, as D E F G, there is no 
 need of fo many Divifions, it being fufficient to find the Line M L, in 
 order for the defcribing of the Semi-circle, which refers to the firft N 
 PCh but I have made them designedly, for fear of confounding the Let- 
 terswith the Lines of the lower Figure, where the Arches are view'd ob- 
 liquely, tending all towards the Point of Sight Y. Such Arches would 
 give their Thicknefs by repeating the Operation already laid down for 
 Fig. I. twice over, and joining the Divifions of the one to the other,, as 
 already obferv'd, and as isexprefs'd in the prefent Figure, to which having 
 given the Thicknefs E Z, I have drawn the Line E in Dots, and Z a 
 full Line, in order to avoid Confufion, and to intimate, that whatever 
 is done with Dots, is not intended to be feen when the Draught is 
 finiuYd. ' 4 2 
 
64 
 
 PERSPECTIVE 
 
 Another Method for Circular Arches. 
 
 THE Arches in Front, which we have hitherto defcrhVd, are all performed 
 to the laft Exactnefs; but the Procefs is a little long and tedious : we (hall 
 now add'another, equally juft, but much more expeditious. 
 
 Having described a Semi-circle, or a whole Circle, BH I, from the Centre A, 
 from the fame Centre, and the Extreme of the Diameter B, draw Lines to the 
 Point of Sight C then fetting the Breadth, or Thicknefs requir'd, on the Line 
 B I, as here D A, from the Point D draw a Line to the Point of Diftance E, and 
 through F, the Point where D E and A C interfect, draw a Line parallel to the 
 Bafe, till it cut the Ray B C in the Point G this done, fetting one Leg of your 
 Compaffes in F, and in the other taking the Diftance G, defcribe a Semi-circle, 
 or Circle, which will be the Thicknefs of the Arch, or Sweep : As is feen in the 
 Figures. All the Lines K K, &c. are to be drawn to the Center A, and the 
 others, L, to the Point of Sight C. The fame may ferve for circular Windows 
 built of Stone, in which Cafe the Lines will reprefent the Joints ; as alfo for 
 Tons, Vats, &c. 
 
 Arches view d Obliquely in PerfpeEtive. 
 
 TH E following Method may ferve when a Perfon is ftraightned, and does 
 not defire to be fo very exact y as alfo to avoid a Multiplicity of Lines, 
 which in the preceding Method is indifpenfible^ 
 
 Having form'd the firft Arch N O as already directed, a-crofs it draw little 
 Parallels to the Bafe in any Number at Pleafure, as here Q^C^ &c. then taking 
 in your Compaffes the Breadth of the Spring of the Arch, as P O, fet it off on 
 the little Parallels by which Means you will have the Points RR ; thro* which 
 a Curve Line being drawn, will form the Thicknefs of the Arch. 
 
 'Tis certain, that, according to the Rules of Perfpective, Objects appear the 
 larger as they are the nearer to us •, of Confequence,. therefore, the Line O P 
 fhould be the fmalleft : But the Difference is here fo very fmall, that it is not 
 worth the minding. Befide, we do not give this as a conftant Rule, but only for 
 a Shift in Cafes of Neceffity. 2 
 
6 S PERSPECTIVE 
 Flat ARCH E S. 
 
 THE Method of putting thefe in Perfpedive is the fame_ 
 with that of the Semi-circular Arches, as appears from 
 the Figure A B. All the Difficulty is in finding the Out-line, 
 which is done two Ways. 
 
 The firftbytwo Centers and a String, the Method already 
 mention'd for defcribing an Oval; thefe flat Arches being, 
 in Effect, Semi-ovals. _ 
 
 The fecond is thus : Suppofe the Line C D given you to raiie 
 a flat Arch upon of the Height E F, from the Center F defcribe 
 a Semi-circle C GD, and divide it into any Number of equa 
 Parts at Pleafure, as is here done into twelve; and from all 
 thefe Divifions draw Lines to the Center F ; then again, from 
 all thefe Divifions draw Perpendiculars to the Diameter CD, 
 as are here the LinesOL; this done, defcribe a Semi- circle 
 of the given Height of the Arch, as here HE K; and thro 
 the Interfeaions this leffer Circle makes with the Divifions of 
 the greater, draw little Parallels to meet the Perpendiculars 
 falling from the fame Divifions, for Inftance LO, L O, ftPr and 
 of the feveral Points O connected together form the Arch, as 
 
 ^ The other Figure makes the Arch ftill flatter, and by the 
 fame Rules it may be made of any Lownefs afPleafure. 
 
 The Figure underneath ffiews one of thefe Arches in Per- 
 fpeaive, fuch as it Ihould appear, when finiffi'd, in a front 
 View We fay nothing of the Method, as having a ready in- 
 timated it to be the fame with that for the Semi-circle. 
 
66 
 
 PERSPECTIVE 
 
 IN this Figure we have an Inftance of the fine 
 Effe£t of Arches when well center'd, that 
 is, when they have their juft Rotundity. 
 
 For the Steps and Figures, we (hall have occa- 
 fion to treat of them hereafter. 
 
6 7 
 
 PERSPECTIVE 
 
 To raife Arches upon Pilafters or Columns. 
 
 IT looks as if there were no Pilafters formed in the laft Figure, for 
 which Reafon I determined to add this, which may mew, that the 
 Method is precifely the fame, and that all required farther, is to leave 
 Room for the Breadth, &c. of the Pilafter between every two Arches, 
 which is done by Means of the Plan, or Bafe Line j as already directed 
 for Circular Arches. 
 
 Got hick Arch e s. 
 
 Gothick Arches and Vaults, called alfo Arches in the third 
 Point, are performed in the fame Manner as Semi-circles j fo that 
 having done one, you will do the other with Eafe : The Figure (hews the 
 reft. As to the Out-line, we have already {hewn that nothing is more 
 eafy. The Breadth A B being given to form an Arch of, open your Com- 
 paffes to the Breadth, and fetting one Leg in A, with the other defcribe 
 the Arch BC 5 then removing them to B, defcribe another Arch AC; 
 and the Point wherein the two interfecl:, will be the Point or Apex of the 
 ArchC. 
 
 As the reft is all performed after the fame Manner as the Semi-circle, 
 we mall not repeat it: All the Bufinefs is, that here are Pilafters between, 
 each two, that are not in the other. This may ferve to confirm and ex- 
 emplify what we have already faid, that all that is to be done is to draw 
 Lines fromthefe Divifions on the Bafe to the Point of Diftance O, which 
 will cut the Ray D E in the Points F F, &c. for Perpendiculars to be raifed 
 upon 5 then fetiing off theThicknefs G, and drawing the Ray GE for the 
 Breadth of the Pilafters H, from the fame Point H erecl: Perpendiculars, 
 to be connected to the other by right Lines, &c . as in the Semi-circle* 
 
 4 
 
P E RSPECTIVE 
 
 SXt, A M. 3, * M it?- & St St, ffi 
 
 5ft find CrossVaults in Perfpe&ive. 
 
 TH E Reader muft remember, or have recourfe to, what we have faid in 
 Pag. 28. where, fpeaking of putting a Circle into Perfpe&ive, we divided 
 it, for the greater Exactnefs, into fixteen Parts-, but as in fuch a Divifion there 
 necefiariJy occur a great Number of Lines, we have here chofe to take up with 
 a Divifion of eight Parts, which if it be the lefs exac~l, it will be the lefs confufed. 
 The other Divifion wefhall refume in the following Page. 
 
 Having then formed a Plan of a Circle divided into eight Parts, 1, 2, 3, 4, 5, 
 6, 7, 8, Parallels to the Bafe Line are to be drawn through the feveral Divifions 
 thereof, as far as the Ray B A, which will give the Points CC, &c. on which 
 creeling Perpendiculars CD, CD, &c. the firft of them, BD, being the Line of 
 Elevation, all the Meafures of the Semi-circle BEF muff be fet thereon, by 
 which Means you will have the Points DHG ; from which Rays are to be drawn 
 to the Point A, and in the Interferons of the Perpendiculars CD, you will 
 have the fame Divifions as in the firft, fecond, third, fourth, and fifth Pla n~s. 
 For a Semi-circle, draw curve Lines as in the Arch of the firft Side, the Divi- 
 fions whereof are to be transferred to the other, in order to have two collateral 
 Arches ; from the Springs whereof two Circles are to be defcribed ; the one before 
 G H, from the Cencer M ; the other in the Bottom 5 L, from the Center N. 
 And thus you have the four Arches ordinarily found in Crofs-vaults. All that 
 remains is, to make the Crofs, or crooked Diagonals, refting on the Corners 
 G 5, K L, and pafiing through the K or Groin O. 
 
 Now as the Circle is divided into eight Parts, the Arches, which are but 
 Halves of Circles, are only to contain four Parts ; the Semi-circle GK, there- 
 fore, is to be divided into four Parts, in the Points GPQJRQ* which are to be 
 drawn to the Point of Sight A, as far as the Bottom of the Circle 5 L. Now 
 what follows is the great Secret of the Crofs, viz. That Parallels to the Horizon 
 are to be drawn from all the Interfections of the Circle on the Side 1, 2, 3, 4, 5, 
 in fuch Sort, as thatG, which is the firft Divifion of the Circle, touch the Inter- 
 feclion 1 in a Point; that from 2 a Parallel be drawn to the fecond Divifion P, 
 and the Point S to be marked ; that from 3 another Parallel be drawn to the 
 third Divifion which will give O, the Place of the Key or Groin ; and from* 4, 
 another to the Point T ; laftly, connecting G S O T L with curve Lines, you 
 will have a Diagonal and doing as much for the other Side, you will have the 
 entire Crofs, and the Vault compleat. 
 
 4 
 
6 9 
 
 PERSPECTIVE 
 
 To draw the fame Vault more ac* 
 
 curateJy. 
 
 AM AN, who has a good Notion of the for- 
 mer Method, will find no great Difficulty in 
 the managing this j all that is required being to 
 double the Lines, and take Care of the Interfe- 
 rons, which are here more numerous, by Rea- 
 fon the Circle is divided into more Parts. 
 
 How to form the Plan is taught in Pag. a 8. 
 Add, that Parallels are to be drawn thro' all the 
 Divifions of the Plan from I to 16, as far as the 
 Ray AB ; by fuch Means you will have the Points 
 O, O, &c. from which Perpendiculars are to be 
 raifed. The reft, as in the Method preceding ; 
 over which this has the Advantage of being more 
 exa&, and of drawing the Vault more eafily, 
 by Reafon the Divifions are clofer to each other. 
 
practical; 
 
 6 9 
 
70 
 
 PERSPECTIVE 
 
 To form narrow Vaults. 
 
 THERE are two ProceiTes in this Figure ; the one for contracting or ftraight- 
 ning Side-vaults , the other for giving the Thicknefs to the Crofs. We 
 fliall begin with the firft* 
 
 The two Methods for Vaults already laid down, fuppofe them perfedly fquare, 
 that is, that their Breadth and Depth, or Diftance, is equal ; which holds both 
 in thofe reprefented in Front, and thofe in Side-views : But a Perfon only in- 
 truded in thefe, would find himfelf ftrangelyata Lofs were he put to conftrucT: 
 a Church, where the Side-arches are ufually much narrower than thofe in the 
 Front or Middle. 
 
 ; We proceed, therefore, to offer you an expedient whereby you'll be enabled 
 to make the Side Arches of what Dimenfions you pleafe, and that by Means of 
 the Bafe Line A Suppofe then the front Arch A forty Foot broad, and 
 the Side Arches limited to fifteen or twenty, you are now, according to the In- 
 ftructions in p. 17. to fet this Meafure on the Bafe Line, and to draw a Line 
 from the fame to the Point of Diftance, by which you will have the Depth of 
 the fame Figure in A E. Thus, in the prefent Example, AC being fuppofed 
 twenty Foot, a Line drawn from C to the Point of Diftance, (which here is 
 fuppofed beyond the Limits of the Paper) cuts the Depth twenty Foot in the 
 Point E ; then returning to the Bafe Line, an Arch is to be ftruck at the Di- 
 ftance A C, and the Line, or Radius, to be divided into as many Parts as the 
 larger Arch FG has Divifions, viz. eight 5 and from the feveral Divifions H, 
 Perpendiculars H I to be railed and from the fame Points H, Lines to be drawn 
 to the Point of Diftance, interfering the Ray A E in O, O, &c. Perpendiculars 
 •OP, OP, &c. are to be raifed •, then the Plan of this Semi-circle FG is to be 
 made in fome feparate Place, and the Divifions thereof transferred from E to B. 
 And fince the Plan of the preceding Figure is equal to F G, take the Divifions of 
 half of it, BCDEF, and transfer them upon the Perpendiculars A F •, and from 
 the Points EFDCB draw Lines to the Point of Sight D, and through the Inter-* 
 fections thefe Rays BCDEF make with the Perpendiculars OP, draw curve 
 Lines, which will form the Side Arch. Then drawing Parallels through the Inter- 
 ferons 1, 2, 3, 4, 5, 6, 7, 8, 9, to the Divifions of the Arch FG, you will have 
 Points FRST VXY Z, to form the Crofs after the Manner already mentioned. 
 
 For the Thicknefies of the Nerves, or Branches, a lit:le Line of Elevation 
 mult be made, ab, which I have here added at the Top of the Perpendicular 
 raifed from Q. This Line A B, being drawn to the Point of Sight D, cuts all 
 the other Perpendiculars in the Point c d, and this gi/es the proportionate 
 Heights to each Perpendicular raifed from the Interferons of the Crofs, that 
 is, from the Interferons made to find the Out-line of the Crofs : The firli Ele- 
 vation a b, for Infhnce, gives the firft Perpendicular Ge the fecond Elevation 
 c d gives the fecond Perpendicular F?; and fo of all tht reft in their Order, 
 which all give Points ee; and which being connected by i croolked Line, gives 
 the Thicknefs of the Nerves or Reins of the Vault : As b feen in half the ad- 
 joining Figure. 
 
7« 
 
 PERSPECTIVE 
 
 ^(jjf ^fcl ^ ^ ^1 ^ ^ ^ ^ ^ ^ ^> -^U ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ 
 
 Va ult jRw/ of ^ /r^- 
 
 ceding Rules. 
 
 TH E feveral Rules already deliver'd fuffice 
 for the conftru£Hng a complete Va ult, 
 as that hereto annex'd $ excepting for what re- 
 lates to the Columns, or Imports, which we fhaU 
 have occafion to (hew hereafter. 
 
PERSPECTIVE 
 
 1§ x&x^xJ&^x^^xJ&^g^BjCX^&a: M 
 
 Arches andG ates with three Sides, 
 
 TH E R E is another Sort of Ceiling which fometimes 
 ferves for a Vault over Doors and Galleries, and even 
 Churches, having a pretty good Effect in Perfpective, and eafy 
 enough to perform. I have added it here after the Circle, by 
 reafon it is form'd of a Semi-circle divided into Parts. 
 
 Having rais'd the Walls AB, defcribe a Semi-circle includ- 
 ing the whole Breadth CD; then holding the Compaffes 
 open to the Width of the Radius E C, and fixing one Point in 
 O, with the other ftrike an Arch upwards, cutting the Semi- 
 circle in G 5 and another Arch E H from the Point D ; then 
 connecting the four Letters CDGH by right Lines, you will 
 have a Semi-hexagonal Arch. A Semi-circle is likewife to be 
 drawn upon the Breadth I K, for the Bottom of the Arch ; 
 and to divide it, Lines are to be drawn from the Angles of 
 the former to the Point of Sight F ; between the Interferons 
 whereof with the Arch, right Lines being drawn, will form 
 the Arch I L M K. 
 
 An Arch with five Sides. 
 
 THIS Arch is perform'd after the fame manner as the for- 
 mer ; all the Difference lyes in the Divifion of the Circle, 
 the firft being into three, and this into five. Accordingly the 
 Semi-circle L M being divided into five Parts, N O P and 
 Lines drawn from all thefe Points to the Point R, the reft is 
 perform'd after the manner already laid down. 
 
73 
 
 PERSPECTI V E 
 
 Elevations of Round Objects. 
 
 THE Defire I have of enabling my Reader to put all 
 Things in Perfpedive with the utmoft Eafe, has indued 
 me to fhew how found Figures, as Circles, are to be rais'd of 
 any Height at Pleafure ; and the fame Method may ferve for 
 all other Rotundo's, as Cupola's of Churches, Amphitheatres, 
 Towers, &c. 
 
 Having put the Plan of the Round in Perfpedive, as already 
 directed, and raised the Line of Elevation A B by the Side there- 
 of, from the feveral Angles of the Plan, which are here the 
 feveral Points whereof the Round conlifts, viz. i , 2, 3, 4, 5, 6, 
 7, 8, 9, &c. Parallels are to be drawn to the Line of Elevation, 
 and Meafures to berais'd thereon as already taught, and thence 
 transfer'd upon Perpendiculars rais'd from the Points i, 2, 3, 
 
 4> 5> 6 > 7> 8 > 9> & c - 
 
 The Semi-circle before has but half the Height of that be- 
 hind, and both the one and the other are mere Out-lines with- 
 out any Thicknefs. 
 
 There is no round Figure but may be put in Perfpedive by 
 this Method ; round Figures, we mean, that are parallel to 
 the Horizon: For as to fuch as are perpendicular thereto, they 
 are already taught in the Rules for Vaults. 
 
 4f 44H4W+**444*444W*44*44*44$ 44<i4444444444*$4444*t 444**4444444 
 
 Elevation of Pilasters. 
 
 TH E Circle muft be drawn in the Plan double, as already 
 fhewn in Pag. 29. and between the two circular Lines 
 muft. be plac'd the Plan of the Parts or Members to be rais'd, 
 as thofe here mark'd A B C D, which all tend towards the 
 Center E ; then Perpendiculars to be rais'd from all the Angles 
 of thefe Plans, and their proper Heights fet off from the Line 
 of Elevation F G j as already fhewn in the preceding Figure. 
 
A Va u l t in form of a Shell, 
 
 in Perlpe&ive. 
 
 THIS Figure may ferve for the Hollow of a 
 Church or Grotto, a Nicb, or the like : 
 The Elevation is performed after the manner al- 
 ready directed. 
 
 As to the Plat-Band, or Border, A B, which 
 might ferve for a Cornifh, its Diminution is to be 
 taken on the Line of Elevation in C D, and 
 transfer'd thence to the Pilafters, 
 
 For the Vault, take the firft Arch E F, as be- 
 fore taught, and in the middle of the infide de- 
 fcribe a Semi-circle O, to which draw curve Lines 
 fpringing from off the Pilafters, and you will 
 have the Ribs or Reins of the Vault, as in G H 
 I K. The Heights of the Windows muft be ta- 
 ken on the Line of Elevation between L and M. 
 For the reft, fee the Figure. 
 I 
 
PRACTICAL. 
 
 74 
 
PERSPECTIVE 
 
 Open Domes, or Vaults, in Perfpe&ive. 
 
 AVING made the Plan of a double Circle according 
 to Pag. 29. and marked the Places and Number of 
 Pilafters between the two Lines, all of them tending to the 
 Center A, fetoff the Height intended from the Ground to 
 the Cavity of the Dome, as the Line DE, which is to ferve for 
 a Bafe Line, upon which the Meafures already laid down on 
 BC are to be placed; then from the fame Point of Sight G 
 make another Plan at the Top, like that at Bottom, all the 
 Places of the Pilafters tending towards the Centre H. To form 
 the Pilafters all required is to draw Lines from the Places op- 
 pofite to each other, which will thus give the Breadth and 
 Thicknefs. I have drawn no Lines for the three Fore Pilafters, 
 both to fhew thofe behind, and to Inftance that there mult 
 be both at Top and Bottom. 
 
 To give the Thicknefs of the Rotundo from I to H, and 
 from K to L, fet the intended Height on the Line of Elevation 
 DM - tending to the Horizon in the Point ¥ b and from the 
 feveral Points whereof the Circle confifts, to draw Parallels to 
 the Line D, whereon are to be ereded Perpendiculars, as DM, 
 which are to be transfer d thence, with the Compaffes, to the 
 Perpendiculars raifed from the fame Points KL, N O, PC^; 
 
 and fo of the reft. 
 If inftead of a Round you require a Square, or Polygon, 
 
 the fame Method is to be obferved. 
 
PERSPECTIVE 
 
 That a Number of Objects, and Plurality of 
 Stories, only admit of one Point of Sight. 
 
 IT has already been obferv'd, that one {hould 
 never ufe above one Point of Sight in a Pic- 
 ture, and that the Ignorance of certain Painters 
 is publifhed to all the World, by their making as 
 many Points of Sight, and Horizons, as they 
 make Lines. 
 
 'Tis not long fince I remember to have feen a 
 Painting, wherein there were feveral Rooms one 
 over another, each of which had two or three 
 Points of Sight j and yet the Painter took it for 
 Miracle. The prefent Figure may ferve to cor- 
 real this Error, and to ftiew, that there {hould 
 only be one lingle Point of Sight, to which all 
 the Objects, and all the Rooms, tho 5 there were 
 an hundred over or a-fide of one another, are to 
 tend : As the three Apartments do all here tend 
 to the Point A. The reft is performed as already 
 dire£fced. 
 
77 
 
 PERSPECTIVE 
 
 5K! 
 
 J 5 
 
 To put Chimneys in Perfpe&ive. 
 
 THE Meafures are to be taken on the Bafe Line A B, which, to that End, 
 muft be divided into equal Parts. The Divifions may be accounted any 
 Thing at Pleafure. The prefent is divided into eighteen, which we call Feet. 
 
 To make a Chimney, or Fire Place* in a Wall, A, three Foot within the 
 Room, take three Divifions as A, R, C, and from the Point C draw a Line to 
 the Point of Diftance D, which cutting the Ray AE in the Point F, [ gives a 
 Depth of three Foot. Proceed to fet the Thicknefs of the Jaumb from C, for 
 Inftance, to G ; then drawing a Line from G to D, it will give the Thicknefs of 
 the Jaumb in the Point F. Then fet the Breadth of the Chimney from G to I, 
 four Foot and a half ; and half a Foot, viz. from I to K, for the Thicknefs of 
 the Jaumb; then drawing Lines from I and K to the Point of Diftance D, you 
 will have their Meafures on the Ray AE, in the Points LM : And from the four 
 Points FHLM draw little Parallels to the Bafe Line, as FN, HO, LP, 
 MQ^ For the Breadth of the Jaumbs take a Foot and a half, viz. A R, and 
 the Ray R E will cut the little Parallels in the Points NOPQj from which, 
 and from F L raife Perpendiculars. For the Height of the Mantle Tree, take 
 five Foot on the Bafe Line, and fet them off on the Corner of the Wall from A 
 to S ; and from S to T fet off for the Cornifti. All the reft is obvious from the 
 Figure. 
 
 The other Chimney oppofite to the firft is done after the fame Manner: For 
 thus the Jaumbs are in all Cafes to be managed. And of the Jaumbs may occa- 
 fionally be made Columns, Termins, or, as we have here done, Confoles. 
 
 To find the Hole, or Aperture of the Chimney, with the Depth of the 
 Jaumbs, draw a Line from 7 to the Point of Sight, cutting the Line of Depth in 
 the Point 5, which will be a Foot and a half; then, from the Point of Diftance 
 V, draw a Diagonal through 5, cutting the Ray 2 E in the Point 6 ; and from 
 this Point draw a Parallel, cutting the four Rays 1, 2, 3, 4 in the Points 9, 6, 
 9, 9 : From which Perpendiculars are to be raifed,' and the reft conducted, 
 as above. 
 
 The fecond Figure reprefents what we have been fpeaking of, free and un- 
 embarrafs'd with Lines. 4 
 
PERSPECTIVE 
 
 Stairs/^ Perfpe&ive. 
 
 THER E is nothing gives a Perfpe&ive fo much Grace, or deceives the Eye 
 fo eafily, as a Number of Returns and Breaks j by Reafon thefe introduce 
 a Number of different Lights and Shadows, which give the Objects fuch a Force, 
 that they feemed to projeS or ftand out from the Ground. Now Stairs have this 
 Advantage, that what Way foever you place them, they have always a Variety 
 of Shades, and of Confequence are agreeable to the Sight. We mall add a few 
 as Specimens. 
 
 If you make ufe of Squares, there will be the lefs Difficulty, all required be- 
 ing toraife Perpendiculars of as many Squares as you would have Steps ; then to 
 fet the Line of Elevation, divided into any Number of Parts, on the firft Square, 
 and from the Divifions to draw Lines to the Point of Sight, which will interfec"t 
 the Perpendiculars in the Places where the Seeps are to be. 
 
 *Tis defired, for lnftance, to conftruct a Stair Cafe of eight Steps, the laft of 
 which to be the Breadth of three of the reft ; take the Number of Squares of 
 the Plan, beginning at B, and proceeding i, 2, 3, 4, 5, 6, 7, 8, and allowing 
 three for the laft marked 11, from all thefe Angles erect Perpendiculars, to be cut 
 according to the Divifions on the Line of Elevation BD, in Manner following. 
 jf**M**** The firft Divifion, which, fuppofing the Square to be a Foot, is four Inches 
 high, will cut the firft Perpendicular, and muft be continued to 2, which makes 
 the Top of the Step ; and fo of the reft. The Steps you may make as long as 
 you pleafe, by fuppofing the Square a Foot : Accordingly thefe here, taking 
 three Divifions, are three Feet/ Perpendiculars mould likewife be raifed, as in 
 this lnftance, on the Side B: But that Trouble maybe faved, by taking the 
 Height of the laft Step H, and that of the firft I, and drawing the Line H I, 
 raifing the Angles on the Side I, as E K does on the Side Bj for this done, you 
 need only to draw Parallels to the Bafe Line from all the Steps and Divifions of 
 the Side B, till they interfecl: the Line HI in LMNOPQ, &c. 
 
 One might likewife do without making Squares ; for laying all the Meafures 
 on the Bafe Line, and drawing Lines from them to the Point of Diftance, the 
 fame Meafures would be had on the Line A B. 
 
 The other Figures we are filent upon, thus much being fuffieient for the un- 
 derftanding and executing them all. 4 
 
79 PERSPECTIVE 
 
 oQQaQQQQQ QQQQQg0QQ0Q£6QQSQ£0QQ ^a 0QQ6QQ 0QQ 
 
 Stairs open or perforated underneath. 
 
 TH E Method of managing thefe Stairs is the fame with 
 that already defcrib'd. 
 As to the Aperture, a bare Sight of the Figure is fufficient 
 to fliew how it is to be put in Perfpe&ive. Thefe two may 
 give occafion to the inventing many others. 
 
 Stairs viewed in Front. 
 
 THIS Method is founded on the Ufe of the Line of Ele- 
 vation : As many Perpendiculars are here to be rais'd 
 from the Angles of the Squares of the Plan, as there are re- 
 quir'd Steps, ex.gr. CDEF ; and from the fame Angles Paral- 
 lels are to be drawn to the Line of Elevation A, the Interfecti- 
 ons whereof give the Points OOOO, from which Perpendi- 
 culars are to be rais'd till they cut the occult Rays of the Divi- 
 sions of the Line of Elevation. Thefe Meafures are to be taken 
 in your Compaffes, and fet off on the Perpendiculars rais'd 
 from the Angles of the Plan, each in its Order ; the firft for the 
 firft Step, the fecond for the fecond, &c. 
 
 To find the Returns P P, ^fc.from the fame Angles P, &c. 
 Lines are to be drawn to the Point of Diftance C^, and*notice 
 taken where they cut the Line of the Plan, or the Bottom of 
 the Step ; for Inftance, over the fourth Step is the Plan of the 
 fifth: Now to find its Return P, from the Point P draw a 
 Line to and the Point S, wherein it interfects the Parallel 
 R R, will be the Line of Return S T; and fo of the reft. 
 
So 
 
 PERSPECTIVE 
 
 &x&^x&^x&tf&*% fcSiSa: jc^fSo: 
 
 Stairs /to T^ot /Zw 
 
 THERE are various Manners of ordering fuch Stairs ; two of the eafieft 
 of them follow. Firft, cake the Length of the firft Step, and fet the Num- 
 ber of Steps required upon the fame ; as on the Line A B are here fet Points, 
 CCCC, for four Steps. From thefe Points draw Rays to the Point of Sighc 
 D, which Rays are to be cut by the Diagonals A F and B E in the Points I I, 
 from, which Perpendiculars are to be rais'd, and Parallels drawn to the Line of 
 Elevation G* which give the Points H, to be rais'd as H K. 
 
 On this Line of Elevation G as many equal Parts muft be marked as there are 
 Steps defired, ex. gr. four, here marked i, 2,3, 4. Thefe are all to be drawn to 
 the Point D,. to cut the Perpendiculars H K, and give each its proper Height. 
 
 Thefe Meafures muft be taken in the Compaffes, and transfer**! one after ano- 
 ther, beginning with the firft G, which is to be fet on the firft Perpendicular 
 on the Angle A, viz. A L y then a Parallel to be drawn to the other fide B, 
 (tho' here we only give half of it, to have room for the Plan in the other.) 
 For the fecond Stair the fecond Meafure H 2 is to be taken, and fet off on the 
 fecond Perpendicular I; next a Parallel is to be drawn as before y and fo of the 
 reft. 
 
 Another Manner. 
 
 ' T HE Side M N being given,, make a Parallel OPover the fame, for the 
 Thicknefs or Height of the firft Step : From the two Points O P draw 
 two Rays to the Point of Sight and again others to the Points of Diftance 
 which laft will give a Square after the ufual Way, and form the firft 
 Step. For the fecond, fet the intended Breadth on the Line O P, ex gr. OT, 
 and from T draw a Line to the Point of Sight which Line or Ray T Q_ 
 will cut the Diagonal O in the Point V, the Place where the fecond Step muft 
 be rais'd. The Height of this fecond Degree muft be half of V X, as M O 
 is half of OT.. The Point Y thus gain'd,, a Parallel muft be drawn through 
 it as far as the Diagonal of the other fide drawn from the Corner P then from Y 
 and Z draw Lines to the Points of Sight and Diftance, to form the Square, as 
 for the firft Stair. For the third, fet the Meafure V X on the Line Y Z, ex- 
 tending, ex, gr. from Y to A y and from the Point A draw a Line to the Point 
 of Sight Q, which interfeding the Diagonal of the Point Y, will give the Point 
 B for the third Stair. Its Height will be half of B C, which is always that of 
 O T in Perfpeclive. The reft the fame as in the firft and fecond. 
 
 The third Figure {hews thefe Stairs free of all, the Confufion of Lines and 
 Letters. - 4 
 
8i 
 
 PERSPECTIVE 
 
 Stairs viewed fide-wife in PerfpeSiive. 
 
 TH E Number of Stairs is firft to be laid down on the Bafe-Line, 
 that is, fo many Points are to be made at equal Diftance ; as in the 
 prefent Cafe ABC are. From thefe Points Lines are to be drawn to 
 the Point of Sight D ; then from the Point A another is to be drawn to 
 the Point of Diftance E which Diagonal A E will give the Plan, and 
 the Place of the Stairs, by its Interferon with the Rays B C in the 
 Points 1 5 and by its Interfedion with the Ray F, which is the Foot of 
 the Wall, it will give the Point G, which is the Middle of the Plan of 
 the Stairs. From G a Line is to be drawn to the other Point of Diftance 
 H, which gives the Angle of the laft Stair in the Point K, and the Place 
 of all the reft in the Points 1 1. Laftly, from all the Points I erect: Per- 
 pendiculars. 
 
 Now to give the Heights ; from the Points A B C on the Bafe-Line 
 erect little Lines, ferving for a Line of Elevation ; on thefe lay the Heights 
 according to their Number : A, for Inftance, which is the firft, will 
 only have i ; B, the fecond, will have 2 j and C, the third, will have 3. 
 From all thefe Points 1,2, and 3, draw Lines to the Point of Sight D> 
 and you will cut the Perpendiculars rais'd from the Plan in the Points O 
 which will give the Height of each Step. 
 
 That on the other fide (hews the Thing free of Points and Lines. The 
 fame Method may ferve for divers Purpofes ; as for an Altar, a Throne, 
 the Front of a Church, a Gate, &c. 
 
 Stairs in a Wall in Perfpe&ive. 
 
 MA K E as many Divifions at the End of the Bafe-Line as you in- 
 tend Stairs, as in this Cafe, three between A and B, and from A 
 and B draw Lines to the Point of Sight Cj then, having determin'd 
 the Space the Stairs are to take up, as D E, a Parallel to the Bafe-Line, 
 E F, muft be drawn, which in the Points 1 1 will receive the Interfe&ions 
 of Lines drawn from the Points GH to the Point of Sight C; and from 
 the fame Points 1 1 Perpendiculars, I K, I K, are to be eredted, to re- 
 ceive the Heights of the Stairs, by drawing Points, 1, 2, 3, to the Point 
 «f Sight C, as appears from the Figure. 4 
 
PERSPECTIVE 
 
 A S t a i r-C as e with Landing- Places in Perfpe&ive. 
 
 DO but recoiled the preceding Methods, and you'll find it exceeding eafy to 
 conftruct fuch Stair-cafes : However, to fave the Trouble of too irkfom a 
 Retrofpect, we (hall explain the whole here. 
 
 By reafon Stair-cafes of this Figure ufually run over a Space equal to twice 
 their Width, to raifeone of them in Perfpective, the Horizon muft firft be dif- 
 pofed at pleafure ; then a Square to be made according to the common Rules, 
 and this to be doubled, as directed in Pag. 16 ; then divided by an unequal Num- 
 ber of Squares, that the Wall, which is fuppos'd in the Middle, may be the 
 Meafure of a Square. 
 
 In this Figure each Square has nine Sides, or Squares, on either Hand, which 
 being doubled, give eighteen ; of thefe, four being left at each End for the 
 Landing-places, remains ten Squares, or Stairs, each whereof we fuppofe equal 
 to a Foot every way. 
 
 Having left four Squares, beginning at the Point A, which ferves in lieu of 
 a Wall, erect a Perpendicular B pretty high, then a fecond C, and a third Dj 
 and fo of the other Angles of the Squares, to the Number of ten. This done 
 ■on one fide, the fame muft be repeated on the other and fuch Perpendiculars 
 will give the Depths or Breadths of the Steps. 
 
 For the Heights, if they be a Foot broad, they muft be half a Foot high, or 
 half the little Square A O ; which Height being taken in your CompaflTes, fet ic 
 on the firft Angle, which is to ferve for a Line of Elevation, beginning at the 
 Bottom, or the Point A, and making as many Divifions thereon as you intend 
 Stairs, viz. ten, from the Bottom to the firft Landing-place ; where you begin 
 to mount up the pppofite Side, and the Series of Numbers is continued to twen- 
 ty-three. 
 
 From all thefe twenty-three Points, Lines are to be drawn to the Point of Sight 
 E, and care taken to cut the Perpendiculars in their Order-, that is, having laid 
 your Ruler from the firft Point to the Point of Sight, crofs the firft Perpendicular 
 B to G with a little Stroke, for the firft Step. For the fecond Seep, from the fe- 
 cond Point draw a Line, crofting the fecond Perpendicular C to D. And fo of 
 all the reft on both fides. 
 
 From the Angles of all thefe little Strokes between the Perpendiculars draw 
 Parallels to the Horizon, as far as the Wall F erected in the Middle •, fuch are 
 the Lines II If, which I have only added on one fide, to avoid Confufion : 'Tis 
 thefe Parallels alone that form the Stairs. All the other Lines hitherto drawn 
 lhould be occult, and not to be feen when the Figure is finifhed. 
 
 The Landing-places fhould contain what the laft Perpendiculars come (hort of 
 the Wall, as from GtoH. Their Height, or Thicknefs, HK, is half a Foot, 
 the fame as that of a Stair. 
 
 The lower Figure is the fame with the upper, only that the one has the Ap- 
 paratus of Lines, necefiary for the Performance, which the other is without. 
 
«3 
 
 PERSPECTIVE 
 
 Winding or Spiral Stairs in PerfpeStive. 
 
 ON E Side of the Flight, or Afcent, is to be fet on the Bafe Line, and di- 
 vided into as many Parts as you require Stairs: Suppofe, for Inftance 2 
 A B the Side of the Stair Cafe, and fixteen Steps required in the whole Circuit of 
 the Square each Side, in this Cafe, will contain four confequently AB being 
 divided into four, a Square is to be formed thereof, divided into fixteen, accord- 
 ing to the ufual Rules. 
 
 From all thefe Divifions, which part the Lines of each Side into four, Per- 
 pendiculars muft be raifed to give the Bounds of the Stairs. Suppofe then the 
 Perpendiculars A A, BB, C C, D D, EE; (this E E Hands for three,by Reafon the 
 Point is in the Middle, and ferves as a Newel, or common Centre of them all ;) 
 on the firft Perpendicular A, which is to ferve for a Line of Elevation, the Height 
 of a Stair Q^A muft be fet, and from the Point Qa Line be drawn to the Point 
 of Sight X, which by its Interfeftions with the Perpendiculars QRST V, gives 
 the Dimenfionsof all the Stairs. Thus AQJs the Height of the firft, FR of 
 the fecond, G S of the third, H T of the fdurth, and I V of the fifth. This laft 
 is the Height of all thofe at the Bottom, as A QJs of thofe in the Front. 
 
 Since GS is the Meafure of the third, which is that in the Middle of the Side, 
 it muft likewife be the Meafure of the Centre, and of the Newel of the Flight: 
 For this Reafon, having taken the Meafure G S in yftur Compafles, fet it off in 
 the Centreof the Square as many Times as you would have Stairs in the Flight » 
 ex. gr. eighteen Times for eighteen Stairs. 
 
 All Things thus difpofed, the reft is eafy. For the firft Step you are to take 
 the Divifion AQ, and fet it off upon the Perpendicular D in the Point I, and 
 from I to draw a Parallel as far as the other Perpendicular B ; then from the two 
 Points II draw Lines to the third I in -the Centre of the Square: Thefe three 
 III will form the firft Stair. For the fecond, fince its Angle reaches to the 
 Perpendicular B, which is on the Fore-fide, it muft have the fame Meafure AQj 
 which will be i, 2 ; then from the Point 2 a Line to be drawn to the Point of 
 Sight X, cutting the Perpendicular P in the Point 2 •, from which Points 2, and 
 2 Lines are to be drawn to the 2 in the Centre : Thus will you have formed the 
 fecond Stair. For the third, fince it is found on the Perpendicular P, the Mea- 
 fure F R muft be taken for its Height ; and the fame Procefs obferved as in the 
 former. 
 
 If you would have them round withal, the Square muft be reduced to a Cir- 
 cle ; according to the preceding Rules : And for the reft, the fame Method will 
 ferve for both. 4 
 
84 
 
 PERSPECTIVE 
 
 TOO 
 
 Squares with Circles therein \ in Perfpeciive. 
 
 TH E Method is the fame with that deliver'd among the 
 Planes. The Circle, for Inftance, is to be divided into 
 eight Parts, as in Figure A, wherein the Circle of the Front 
 ©f the Cube gives the Diminution of that a -Top ; and that 
 in the Front, with that a-Top, the Diminutions of all the 
 other Sides; as in Figure B, where the Circle is diminifhed 
 on three Sides ; and in the other C, where it is diminifhed on 
 all three Sides of the Cube, 
 
 The three Figures DEF are perforated each on two Sides, 
 according to the Plan of the Circle A : Thus the Cube D is 
 pierced thro' its Fore-fide ; and thro' that Perforation the 
 Bottom is feen perforated : Thus alfo E is perforated on the 
 Sides ; and F thro' the Top and Bottom, tho' the latter Per- 
 foration be not diftinguifhable, by Reafon the Matter is not 
 fuppofed tranfparent. 
 
 The three Figures underneath reprefent the Pieces cut out 
 of each Cube ; G, for Inftance, out of the Cube D, H out 
 of E, and 1 out of F. 
 
 Upon the whole, the Method of difpofing fquare Figures 
 in Circles appears very eafy ; nor can the Reader find any 
 Difficulty in placing Columns under any Difpofition at all. 
 The Reafon why we have given none before is, that we 
 chofe to render the taking of Elevations as eafy to conceive, 
 and the Practice as little embarrafs'd as poffible. Thus much 
 may ferve for the Beginning of Columns y how to carry on 
 and finifh them fhall be fliewn hereafter. 4 
 
PERSPECTIVE 
 
 Round Stairs in Perfpe£tive. 
 
 TO raife thefe three round Stairs or Steps, in 
 a front View, make a Plan of three Circles 
 within each other, after the Manner already di- 
 rected in Pag. 28. and from the feveral Points 
 that form the Circle draw Lines parallel to the 
 Bafe, as far as the Ray A, which is the Foot of 
 the Line of Elevation A B : This gives the Ele- 
 vations, which are to be taken thence with the 
 Compaffes, and fet off on Perpendiculars raifed 
 from the feveral Points of the Plan. 
 
 Round Steps viewd Side-wife. 
 
 TH E Rules for Obje£ts viewed by the Sides 
 we have often obferved are the fame with 
 thofe for Objefts in Front : However, to ftiew 
 'we are not always obliged to obferve the Divifion 
 of the Circle into fixteen, thefe of the Side-view 
 we have divided into eight. For the reft, 'tis the 
 lame as in the preceding Cafes. The Line of Ele- 
 vation is C D, drawn to the Point of Sight E. 
 
:8* 
 
 PERSPECTIVE 
 
 Winding-Stairs, 
 
 THIS Figure is the fame with the preceding one, which 
 was not fhaded, that the Method of the Operation 
 might be the more confpicuous: For the fame Reafon the 
 Newel of the Stair-cafe was referved for this Figure. It is form- 
 ed by affuming the Point A as a Center, and thence defcribing 
 a Circle ; or rather a Semi-circle, as B C, by Reafon only half 
 of it is to be feen. To the Center of this Semi-circle Lines 
 muft be drawn from all the Divifions of the Square of the 
 firftPlan, as DEFGHIK, which will cut the, Arch BC in- 
 to eight Parts ; and from the Interferons O O, &c. Perpen- 
 diculars are to be raifed ; taking Care they cut precifely in the 
 Points, where the Steps are placed ; the Step I, for Inftance, 
 to be cut by the Perpendicular raifed from its Point in the 
 Semi-circle, as in A ; the fecond Step to be cut by the Perpen- 
 dicular raifed from the Point which K gives in the Semi-circle : 
 And fo of the reft. 
 
 The Doors, Windows, &*c. in the Figure, are all con- 
 ftrucled according to the Rules already laid down. 
 
8 7 
 
 PERSPECTIVE 
 
 Columns^ PerfpeBive. 
 
 WHAT has been juft obferved is not confined to the Cube, but ex- 
 tends equally to any Thing intended to be rounded. For Inftance, 
 if from the Square, A, you would raife a round Piece, AB, defcribe a 
 Circle within the Square, according to the common Rules ; and at the in- 
 tended Height defcribe another Square, with a Circle within it, B. Now 
 to get the two Lines DE, which make the Thicknefs, or Diameter of 
 the Circle, obferve where the Circle cuts the Diagonal of the Square, and 
 take thofe Points for the Lines which form the Sides of the Elevation. 
 Thus C is formed by Perpendiculars raifed from the Interfedions DE of the 
 Circle with the Diagonal of the Square. 
 
 Thus much Regards Side-views. As to thofe in Front, ex. gr. the Fi- 
 gure" F, they are always to take up the Semi-circle GH I, and Perpen- 
 diculars are to be raifed from the Extremes of the Diameter GH; and 
 both in thofe in Front, and thofe in Side-views, Perpendiculars to be rais'd 
 from the Center, to give the Diminutions. 
 
 As to the three Figures underneath, befide that they (hew the former 
 more clearly, and with the Addition of Shadowing, they likewife ferve to 
 point out the Manner of proceeding for Columns. The middle Figure, K 3 
 is quite round, without any Ornament at all. The fecond, marked L, 
 mews, that when a Bafe is required, a double Circle muft be defer ibed 
 on the Square that ferves as alPlinth, whofe upper Part is MN j the In- 
 terval between the Circles to be the Projeclure of the Bafe, and the inner 
 Circle the Plan of the Bafe, from which Perpendiculars are to be raifed. 
 " The third Figure, O, is a Column with its Ornaments ; which every 
 one is to make at his Difcretion j taking Care the Abacus anfwer, as it ought,, 
 to the Plinth. 2 
 
88 
 
 PERSPECTIVE 
 
 A 
 
 Cornices and Mouldings in Perfpe&ive. 
 
 F T E R the Columns, which are the chief Ornaments of Architecture, we 
 proceed to the Cornices, or Mouldings, with their Proje&ures ; which have 
 hitherto been omitted, for Fear of rendering our Elevations perplexed. 
 
 'Tis certain there is fcarce any Building but has fome Moulding or Projective 
 by way of Enrichment, and to render it pleafing to the Eye ; for this Reafon we 
 have here judged proper to add what relates thereto: Not, we mean, to the Con- 
 ftrudion thereof, for that depends on every one's Fancy ; nor to the Meafures 
 and Proportions, for in that Cafe we mould be obliged to give all the Orders of 
 Architecture, and a Thoufand other Things, which the Reader will find elfe- 
 Avhere : But to put them in Perfpective, when any particular Order is pitched 
 
 upon. _ _ 
 
 To put the Ornaments, for Inftance, of a Pilafter in Perfpective, take the 
 Proportions from the Profile of fome other, with all the Ornaments thereof, as 
 AB; whofe Breadth being taken, and a fquare Plan made as ufual, ered Per- 
 pendiculars from all the Angles thereof: Thus will you have the Body, or Shaft, 
 
 of the Pilafter. : • -J 
 
 Proceed now to take the Prefectures, or Jettings ex. gr. the Bale of the 1 llalter 
 C, and the feveral Meafures thereof lay down in DE. To put this in Perfpec- 
 tive all round the Pilafter, from the Point of Diftance F draw a Diagonal to the 
 Point E, and farther at Random, as to G ; then from A draw a Line to the Bot- 
 tom of the Projecture H, and in the Point I, where this cuts the Diagonal, will 
 be the Jet, or Projecture, of the whole Bafe. The fame Line A H gives the 
 Projecture of the Bottom, by its Interfection with the other Diagonal in K. 
 For the Projefture of the Front, from the Point I draw a Parallel to the Rife 
 Line, till it cuts the Diagonal in L : This gives the other Corner of the Projec- 
 ture of the Front. Then drawing Lines from the Top of the Bafe to thefe 
 Points, as from M to L, and from N to K, you will have the Breadth and 
 Height of the whole Bafe. The fame Method ferves for the Capital. 
 
 The Figures underneath fliew the reft and even the Efrec* of what is fa id, 
 free of Confufion. For the Pilafter O, Regard muft be had to that above it, P, 
 where the Line D H has upon it all the Interfe&ions of the Bafe. For this 
 Reafon Lines are to be drawn from the Point of Sight A, which paffing through 
 theDivifions of DH, will exprefs the fame on the Lines D I and N K then 
 Parallels being drawn from the Points D I to ML, nothing remains but to draw 
 the Out-Lines. When there happen Squares, or Fillets, either at Top or Bot- 
 tom, they are formed by Perpendiculars. Thus, for the Plinth, Perpendiculars 
 muft be raifed from the Points LIK, and from the Point of Sight A a Line to 
 be drawn through the Angle of the Plinth to Qj this will give the Height of she 
 Perpendiculars I and K. Laftly, L is to be made equal to I. . 
 
 This Inftruction for the Bafe will fuffice for the Capitals ; the Operation being 
 the fame in both. The laft Pilafter, R, is only meant to (hew one clear of Lines. 
 They are all broke in the Middle, that there might be Room to exprefs both the 
 Bafe, and the Capital 3 the Page not allowing them to be reprefemed whole. 
 
8 9 
 
 PERSPECTIVE 
 
 ^^^^^^^^^^^ 
 
 C *k;Wf c^O^? eJgod* c)^-]^? aO* ^ 
 
 /^rg^ Cornice above the Horizon, in Perfpe&ive. 
 
 THE Method is the fame as that juft delivered ; but being fomewhat trou- 
 blefomby Reafon of the Number of Lines, we have judged proper to re- 
 peat it again here, in order to avoid Confufion. 
 
 To the Purpofe then ; Having taken the Profile of the Cornice, and its Pro- 
 jective, you are to transfer it to the Place where the Draught is to be made * 
 as here the Profile C, &c. is at the Corner of a Wall A B. To find what Height 
 it muft have, and to make it fhew its Bottom, from the Point of Sight D draw a 
 Line through the Extreme of the Profile E, as the Line DF ; then draw a Dia- 
 gonal from the Point of Diftance H, paffing through the Corner of the Wall B, 
 and prolonged till it cut the Ray DE in the Point F ; from which draw the Line 
 FG* which is to reprefent the Angle in Perfpective, and to receive all the Mea- 
 fures of EG. The Corner of the other End of the Wall, KL, is to be drawn 
 to the Point of Diftance I, as being the other Diagonal. 
 
 In Fig. II. it is (hewn, that all the Figures which are on the Line MN, are to 
 be transfer'd, by Means of vifual Rays drawn from the Point of Sight D, upon 
 the Line NO •, in order for Parallels to be drawn through all thofe Points, which 
 are to give -the Cornice complete. But before we go farther, it is to be obferved, 
 as has been already hinted, that all Plat-bands and Squares are formed by Per- 
 pendiculars. Thus, forlnftance, to form the large Square of the Cornice, having 
 made the Doucine, and the Fillet; from the Bottom of the Fillet, which is the 
 Top of the Square, let fall the Perpendicular P Qj Then, to find the Place it is 
 to be cut in, to fhew the Bottom, a Line muft be drawn from the Point of Di- 
 ftance I, through the Point a-fop of the Quarter Round R, to the Perpendicu- 
 lar PQ/, and you will have your Defire. What has been faid of the large 
 Square, holds equally of the kfier ones; as the Denticles, Fillets, &c. which 
 are all to fhew their Bottom. 
 
 The third Figure (hews, that having found all the Points, and drawn Lines on 
 the Line of the Angle, ST, propojtional Mouldings muft be drawn thereon. 
 I mean, that when they project much, as is here the Cafe, by Reafon the Point 
 of Diftance is near, the Mouldings muft be helped out a little ; that is, the 
 Quarter Round muft be inclined a little, the Doucine be erected, the Fillets en- 
 larged ; and the fame done at one End as the other ; ex. gr. the fame on V X as on 
 ST. This done, all that remains, is, to draw Parallels to the Bafe Line. 
 
 The fourth Figure is the Cornice complete. In this we have drawn Parallels 
 from all the Points of the Line of the Angle Y Z ; and one End of the Wall is 
 made to pafs over the Cornice, to fhew, that we are at Liberty in fuch Matters ; 
 and that the Rule is general. 
 
go 
 
 PERSPECTIVE 
 
 To find the Bottoms of large Projectures. 
 
 TO find the Proje&ure of the Corona of the Wall A ; 
 on the Angle of the Quarter Round B, make a Line 
 equal to the Length of the intended Projedure, as BC then 
 from the Point of Sight D, draw a Ray E, paffing to the Ex- 
 treme of the Meafure C : This done, draw a Diagonal from 
 the Point of Diftance F, pafiing through the Quarter Round 
 B ; and the Point G, wherein it interfe&s the Ray D E, will 
 give the Bottom on both Sides, BH: As is more clearly e*- 
 prefs'd in the oppofite Figure K. 
 
 The Proje&ure of the Wall L, is formed after the fame 
 manner as the former, A. All the Difference is, the Projec- 
 tureMN, of the Wall L, is half as big again as that of B C ; 
 to intimate, that the fame Rule makes them as big, or as lit- 
 tle as one pleafes. 
 
 'Tis likewife obfervable in the lame Wall L, how the Return 
 of the Projecture, &c. is found. For Inftance, from the 
 Point O of the Quarter Round in the Fund of the Wall, a 
 Diagonal is drawn to the Point of Diftance P ; and the Inter- 
 feron of that Line with the Ray ED will be a Point, through 
 which a little Parallel to the Horizon R Q^ being drawn, will 
 give the Thing required. 
 
 The fame may ferve for all Squares on Cornices and Mould- 
 ings both great and fmall. 
 
 The Wall S, fhews all the Mouldings on that of L, more 
 diftindly. 2 
 
93 PERSPECTIVE 
 
 The Apertures of Doors in Perfpe&ive. 
 
 HAVING hitherto kept pretty clofe to the Order obferv'd in the actual 
 raifin°- of Buildings of all kinds, we now proceed to (hew how to furnifh 
 a nd difpofe them for the Reception of Guefts. We begin with wooden Doors; 
 hereafter we (hall find occafion to fpeak of other Apertures, as Windows, 
 Cupboards, &rV. then of Moveables, as Tables, Beds, Chairs, Chefts, Benches, 
 
 All Doors made to open and fhut depend on the Pleafure of the Perfon who 
 may open them as far and as little as he pleafes. For this reafon I mall mew a 
 Method of putting them in Perfpedive, at any Degree of Widenefs at Thfcretion. 
 
 Now it is obfervable, that Doors, Windows, Cabinets, Chefts, and, in fine, 
 all Things intended to open and fhut, always defcribe a Semi-circle in opening. 
 The reafon is, that the Side hung by Hinges keeps its Place, like the fix'd Leg 
 of a Pair of Compaffes, while the other Side, like the other Leg of the Com- 
 paffes, fweeps its Arch. Thus in the Plan underneath the Figure, the fix'd Side 
 being at A, and the other at B, if you open the Door quite, the Side B muft 
 defcribe the Semi-circle BCD, whofe Centre is A. Hence it follows, that if 
 the Door be three Feet broad, as in the prefent Cafe, its Semi-diameter A C 
 will likewife be three Feet, and its whole Diameter B A D fix Feet. Of thefe 
 fix Feet in Length, and three in Breadth, a Plan muft be made, confifting of 
 eighteen Squares? wherein a Semi-circle A B C D is to be defcrib'd, to render 
 the making of the fame Semi-circles in Perfpedive the more eafy : Always ob- 
 ferving where the Semi-circle of the Plan cuts the Squares ; that thofe in the 
 Perfpe&ive may be cut after the fame manner, and a Semi-circle be drawn, taking, 
 up the fame Space, traverfing as many Squares, and cutting them in the fame 
 Places. An Inltance of which we have in the Door E, where the Interfedions 
 are mark'd the fame as in the Plan underneath, i, 2, 3, 4, 5, 6, 7. 
 
 When a Door is to be reprefented open, in Perfpe&ive, a Semi-circle muft be 
 ftruck on its Plan, and the Point of Aperture placed on any part thereof at plea - 
 fure : Thus for the Door E the Point of Aperture is fix'd at 2. From this Point 
 2 a Perpendicular muft berais'd, 2 H; and from the fame Point 2, a Line muft 
 be drawn through the Corner of the Door F, and continued till it cut the Ho- 
 rizon in the Point G from which another Line muft be drawn through the other 
 Corner of the Door I, and continued till it cut the Perpendicular rais'd from 
 the Point 2, in the Point H : Thus will you have the Door open, F I H 2. 
 
 All Apertures areperform'd by the fame Rules ; as is farther feen in the Doors 
 K and L. The Door K fhews its Out-fide, and that of L its Infide; yet both 
 are perform'd after the fame manner as the firft. The accidental Point of K is 
 the Point M in the Horizon, and that of the Door L is O. If Bolts, Locks, or the 
 like, be added on the Doors, they muft all be drawn from the fame acciden- 
 tal Point; as the Bolts and Lock of L tend towards O. What accidental 
 Points are, we have already explain'd. Now all Apertures have one fuch Point 
 in the Horizon, excepting two forts : The firft, when the Door is quite open ; 
 in which Cafe its accidental Point is the Point of Sight : The other, when 'tis pa- 
 rallel to the Horizon ; by reafon the Parallels, in that Cafe, never mterfcQ : as 
 in the Door N. 2 
 
92 
 
 PERSPECTIVE 
 
 Cornices with fever al Returns. 
 
 WHEN there happen divers Turns and 
 Returns in the Cornices or Mouldings, 
 their Bottoms muft always be taken from the 
 Points of Diftance. Thus, having drawn Rays, 
 A and B, to the Point of Sight E ; from the Point 
 of Diftance C, or D, a Diagonal muft be drawn 
 through the Angle of the Quarter Round O, till 
 it cut the Ray A or B in I : From which Point, I, 
 a Parallel to the Bafe being drawn, gives the Bot- 
 tom or Proje&ure of the Square; as already 
 {hewn in Pag. 90. 
 
 I would willingly have made a much bigger 
 Cornice 5 as that would not have been a whit the 
 more difficult : But the Compafs of the Page ob- 
 lig'd me to be contented with this. 
 
 If you would have Returns on the Ground, as 
 thefe are above the Horizon; the fame Method 
 is to be obferv'd. For Proof of this, invert the 
 Pacer and vou'll find it have the fame Effe&. 
 
9 l 
 
 PERSPECTIVE 
 
 Cornices Mouldings the Horizon. 
 
 T H E Rules that obtain here are the fame with thofe of 
 the preceding Cafes ; tho', through an Accident which 
 fometimes falls out, viz. a Diverfity of Horizons, there arifes 
 a little Variation ; which fuch as are unacquainted therewith 
 might chance to be puzzled withal. 
 
 We obferve, then, that in viewing a Cornice below the Eye, 
 and of confequence below the Horizon, the Projeclures hide 
 fometimes half, fometimes more, and fometimes lefs of the 
 Body, according as the Eye is more or lefs elevated. 
 
 To find precifely how much is to be covered, and how much 
 not; fet the Profile of the Moulding on the Corner of the 
 Body to be enrich'd therewith; and having found the Line of 
 the Angle, after the manner already directed, draw the Divi- 
 fions of the Profile upon the fame : Thus will you find that 
 the Square, or Plat-band, covers the whole Aftragal under- 
 neath, and only lets half the Fillet be feen. For, drawing a 
 Line from the Point of Sight A, through the Profile B C, it 
 cuts the Perpendicular from the Line of the Angle in D, and 
 fhews how much is to be cover'd. For the Moulding at Bot- 
 tom the fame Method ferves as for that at Top. 
 
94 
 
 PERSPECTIVE 
 
 Apertures of Cafements in PerfpeStive. 
 
 ALL the Difference between the Apertures of Cafements, and thofe of Doors, 
 lyes in this, that Doors have their Semi-circle of Aperture on the Plan, 
 and Cafements in the Air by reafon Windows are rais'd, and Doors ufually turn 
 on the Ground. On this Account, the Semi-circles of Cafements may be either 
 over or underneath them : And in fuch Semi-circles is the Point of Aperture tq 
 be placed. 
 
 Thus, for Inftance, if a Cafement be two Squares, or Panes, broad, as A B, 
 and it be made quite open, it will then take up two Squares more C A, whereof 
 A is the Middle, and the Centre of the Semi-circle ABC. But by reafon the 
 Window is rais'd above the Ground, the Semi-circle muft alfo be rais'd ; as is 
 here actually done in the Semi-circles of the Windows D and E : whereof the 
 fame D, and Eare the Centers ; and which are eafily form'd by erecting Perpen- 
 diculars from the intermediate Squares, till fuch time as they interfect the Rays 
 drawn from the Corners of the Cafements D, E. From thefe Interferons Lines 
 muft be drawn to the Bate- line, and the Meafures of the Squares of the Plan 
 i, 2, 3, be fet thereon. From the fame Points i, 2, 3, Liqes are to be drawn to 
 the Point of Sight F ; which cutting the Parallels, will give Squares to fix the 
 Aperture by. Proceed then to take the Apertures after the fame manner as 
 thofe of Doors. For Example, the Point G being given in the upper Semi-circle, 
 from the fame G, draw two Lines ; the one, G H, perpendicular; the other 
 pafiing through the Corner of the Window E, and cutting the Horizon in fome 
 Point, e. gr. the Point I. From this I, draw a Line through the Corner of the 
 Window K, till it cut the Perpendicular in the Point H, which gives the Cafement 
 open, KEG H. The fame is to be obferv'd with regard to all the reft •, and the 
 Point frill to be taken in the Horizon. Thus, L is the Point for thi Cafement M ; 
 and N, that for the Cafement O. The Cafement P has none at all, as being 
 parallel to the Horizon. 
 
 The Cafements on the other fide are perform'd after the fame Method, with- 
 out any of the Confufion of Lines. Both the one and the other range with the 
 Wall, to facilitate the Operation. The Door at Bottom is done after the man- 
 ner already directed ; and the Cafement according to the Method !aft deliver'd. 
 
 Apertures of Cafements, with Embrafbres. 
 
 TH E Rules for thefe are the fame as for thofe that range even with the 
 Walh excepting that the former are not capable of being qjite open'd, by 
 reafon of the Thicknefsof the Chamfraining, or Embrafure. On this account we 
 never give them a whole Semi-circle," but a Portion anfwerable to the Aperture 
 they admit of. The accidental Point mould always be in the Horizon, for upper 
 Windows, as here in Qand R ; that below is parallel to the Horizon. 
 
9S PERSPECTIVE 
 
 -^a,4a .<et. JR. jft, j& $t Jfe ^i*^ ^ 
 
 JD/wrj other Apertures. 
 
 -THE Openings of Cupboards, Prejfes and Chefts, are at lead as neceffary as 
 1 thofe of Doors and Windows nor had the Omiffion of thofe been a whit 
 more excufable than of thefe. Their Doctrine will be difpatched in two Figures. 
 
 The Cupboards A A, are opened according to the Rules delivered for Cafe- 
 ments, which it would be needlefs here to repeat. We mail only add that the 
 uppermoft is parallel to the Horizon 5 and that the latter tends to the Point of 
 
 ^Thff^Si) on the other Side is opened by two Leaves, one of them rifing up- 
 wards, and the other falling downwards. Each of them defcnbes its Semi-circle 
 from the Centres C and D which being drawn with the Compaffes, the Aper- 
 tures are fixed at any Point at Pleafure •, as here in the Point E ; from which a 
 Ray is drawn to the Point of Sight F, till it interfeft the Semicircles at the other 
 Ends in the Points G. From thefe Points E and G Lines being drawn to the 
 Centres CD, give the Leaves that clofe the Shop. 
 
 In the lower Figure there are three Chejls, differently opened. To open the 
 firft H the Quadrant M is put in PerfpecVive, according to the Meafures ot 
 the Squares of the Plan. Thus, obferving the Width of the Cheft, which is two 
 Squares Perpendiculars are to be raifed thence, and a Semi-circle, or Quadrant, 
 defcribed for the Opening, which is here fixed at the Point N ; and from this a 
 Parallel is to be drawn to the other Quadrant O j and from N and O Lines to 
 be drawn to the Center P. If a greater Aperture is required ; a Semi-circle to 
 be drawn in Lieu of a Quadrant. 
 
 The Cheft 1 has the eafieft of all Openings : For, having taken the Breadth of 
 the Cheft OR, from the Centre R defcribe the Semi-circle QS ; then take 
 anv Aperture at Pleafure, as T, and draw a Line to the Point of Sight V, cut- 
 ting the other Semi-circle in Xj and, laftly, from the Points T and X, draw 
 Lines to the Corners R. . 
 
 If 'tis required to open them farther, you have only to fix the roint or Aper- 
 ture higher in the Semi circle v as Y is in the Cheft K. The reft is the fame as 
 in the firft Cheft. 
 
Bb 2 
 
9 6 
 
 PERSPECTIVE 
 
 &%/fZc /fZ^f%^ jf& fi^ (f&r 
 
 Plans firfl Elevations of Moveables. 
 
 THESE Plans I mould have placed in their order among the reft, but for 
 this Confideration •, that had I treated of them at the Beginning of the 
 Work, without (hewing the Neceflicy thereof, they would have pafifed for ufe- 
 lefs, and accordinglv have readily dropt out of Remembrance. They now come 
 in Seafon, and cannot fail of being well received and learnt with Pleafurej inaf- 
 much as there are no Moveables or Hou/hold Goods but depend upon them. 
 
 The firft Plan, A, may ferve for Beds, Tables, Chairs, Stools, Sec. The other 
 B which is twice as long as 'tis broad, ferves for long Tables, Cupboards, Buffets, 
 Cbefts, Trunks, Sec The third, C, which is long and narrow, ferves for Benches 
 or Forms, Couches, and other Things with fix Feet. • _ 
 
 The Acquaintance the Reader is fuppofed to have with the other Plans already 
 delivered, will render the Performance of thefe eafy ; there being nothing more 
 required than to lay down their Dimenfions on the Bafe Line, draw Lines thence 
 to the Point of View, and fhorten them by Means of the Points of Diftances. 
 
 Thus, e. gr. for the firft Plan A the two Meafures of A and D muft be fet 
 on the Bafe, and Lines be drawn thence to the Point of Sight F. Then from 
 one of the Points of Diftance, a Line to be drawn to one of thofe Meafures, as 
 from G to E •, and through the Points H, and I, wherein it interfefts the Rays, 
 Parallels to be drawn ; by this Means four Squares will be formed, which you 
 may account as much or as little as you pleafe. For a Table, e. gr. they muft be 
 more than for a Stool, i. e. they muft have more Breadth ; the latter being ufual- 
 }y two Inches, and the former four. 
 
 The Plan B is performed after the fame Manner ; excepting that on Account 
 of its Length, which is double its Breadth, a Line muft be drawn from B to one 
 of the Points of Diftance, to find the half, K. For, if a Line were drawn from 
 L it would interfeft in M, and give a whole Square; whereas we only want half 
 of it Parallels then muft be drawn from K to the Points of Interferon with the 
 Ray ; and from the Corner L, a Line muft likewife be drawn to G, interfering 
 the Ray : Thus will you have the firft four Squares. 
 
 The third Plan, O, needs no Explanation ; it being evident that it is formed 
 like the firft, A ; and that the Square muft be doubled to get the fix little 
 
 ^pVom the Figures underneath it appears that Perpendiculars are to be raifed 
 from all the Angles of thefe Squares, to begin to form the Moveables, laid 
 down hereafter. 3 
 
97 
 
 PERSPECTIVE 
 
 Elevations of Moveables. 
 
 IT A V I NG raifed Perpendiculars from the Plan, as already intimated ; 
 11 a Line of Elevation muft be made in fome Part of the Painting, on 
 which the Heights, crofs Pieces, &c. are to be laid. 
 
 Thus the Line CD being a Line of Elevation, and CE and DF 
 Breadths or Depths of the crofs Pieces j from thefe four Points draw 
 Lines to fome Place in the Horizon, ex. gr. the Point G. Then having 
 erected Perpendiculars from all the Angles of the Plan, as in A andBj 
 from the Angles draw Parallels to the Bafe Line, till they cut the Line 
 CG: Thus will you have the Points i, 2, 3, 45 from which Perpendiculars 
 are to be raifed. And thelnterfe&ions thofe Perpendiculars make with the 
 Ray C E, will be the Points to cud the Perpendiculars of the Plans : Whe- 
 ther they be transferred with the Compaffes; or whether they be cut by 
 Parallels, as in the Figure ; where a Parallel being drawn from the Point 
 E, cuts the firft Perpendiculars of the Plans A B in the Points O ; from 
 which drawing Lines to the Point of Sight H, the other Perpendiculars 
 of the Plans will be cut in the Points PP, &c. And doing the like for 
 the Point F, you will at Length have a Cube perforated on all its Sides : 
 Which being well underftood, all the other Pieces that follcw, and even 
 all that can be conceived, will be readily performed. 
 
 It is eafily obferved, that the two Frames or Stands of Tables, I and 
 K, are performed by the fame Rule as thofe above : All the Difference is 
 in the Crofs-bar at Bottom, which is higher in the Line of Elevation in 
 this latter Cafe, than the former. In the latter, for Inftance, we find it in 
 the Line L, which gives MM. For what is beneath j one may either 
 leave the Feet fquare, or round them into Bowls. 
 
 As to the laft Frames, N and Q^there is nothing in them more than in 
 I andK; only that they are viewed by the Angle, and the other in Front. 
 The Plans of thofe, I and K, are drawn to the Point of Sghc R j and 
 thefe latter to the Points of Diftance S, T. 
 
 Thefe Figures furnifti wherewithal to form all the Moveables of a M?- 
 nage. Thus, for Inftance, to make a Bedftead of Fig. I o K, nothing 
 more is required than to give it a proper Height and Breadth. In every 
 Thing elfe the Operation is the fame as for a Couch, a Stool, o>r the like : 
 For a Table you have only a Top to add : For a Joint-ftool, bffidei the Top, 
 it muft be made more in Height than Width. But the ret is all of a- 
 giece. 3 
 
9 s 
 
 PERSPECTIVE 
 
 1 
 
 To make the upper Part of Tables, Stools, &c. 
 
 HAVING raifed Perpendiculars from the Plan, as al- 
 ready dire&ed, and fix'd the proper Height thereon, 
 the Frame will be complete. Now to make an upper Part 
 perfe&ly on a level, and which mall not exceed the Frame, 
 there needs nothing more than to leave the Top of the Cube as 
 it is, without expreffing any Thing thereon ; which will make 
 the upper Part of a Table, Stool, or the like. 
 
 But if 'tis defired the upper Part mall have a Proje&ure, or 
 Ledge ; from one of the Angles of the Frame a Parallel muft 
 be drawn, as AB- and on this Parallel the Meafure or Quan- 
 tity of the intended Projecture muft be fet, as here AB/ Then 
 from the Points of Diftance CandD, occult Lines, AE, AE, 
 &* c. muft be drawn through the Angles of the Square of the 
 Frame here expreffed by dotted Lines. And to make the 
 Meafure A B give the proper Breadth to all the Sides and An- 
 gles of the Table ; draw a Line from the Point of Sight F, 
 thro' the Point B, continuing it till it cut the Line CAE in the 
 Point G. From the Point G draw another Parallel, cutting the 
 other occult Line in H. Then drawing Lines from the Points 
 G and H to the Point of Sight F, the other Diagonals will be 
 interfered in I and K; which will give the upper Part of the 
 Table, with the Projecture firft fet on the Line A B. 
 
 The Thicknefs of this upper Part of the Table is fixed at 
 Pleafure. 
 
 This fame Method may ferve for the upper Parts of any 
 Thing, whether above or below the Horizon ; or whether in 
 Front or in Side Views. 
 
99 
 
 PERSPECTIVE 
 
 Elevation of Buffets, and Cup-boards. 
 
 HAVING made the Plan, and raifed Perpendiculars from all the 
 Angles, as already taught ; upon the Line A B, which is here to 
 ferve for a Line of Elevation, the Meafures or Proportions of the Diftances 
 of the Shelves, with their Thickneffes, &c. as here CDE, muft be laid 
 down. Then from the Points CDE, draw Parallels to the Bafe Line, as 
 far as the upright Poft G F ; and from the Points thus mark'd on G F, 
 draw Lines to the Point of Sight H, as far as the other Poft I K, forming 
 the Breadth of the Buffet. This Breadth is fixed at Pleafure, by laying 
 down the intended Meafure on the Bafe Line. Thus for the Breadth of 
 the prefent Buffet, the Diftance FL is laid down ; and from the Point L, 
 a Line is drawn to the Point of Diftance M ; and the Point I, wherein it 
 interfefts the Ray FH, is the Place of the laft Poft. 
 
 The Buffet on the oppofite Side is performed after the fame Manner. 
 To adjuft the Proportions of the little Cabinet, or Locker, fupported by 
 two Columns in the Middle thereof, take the Points L P, which are in the 
 Middle of QN, or of the Breadth of the Buffet ; and drawing Lines thence 
 to the Point of Diftance O, where the Ray NH is interfe&ed thereby, 
 draw Parallels to the Bafe Line, cutting the Ray TH in the Points V V. 
 And Perpendiculars raifed from thofe Points will give the little Cabinet in 
 the Middle. 
 
 The large Preffes, or Cup-boards, in Fig. IL are performed after the 
 fame Manner as the Buffets above ; only that in the Middle needs a little 
 Explanation, by Reafonit is viewed in Front, fo that there might be fome 
 Difficulty in determining its Depth. We obferve, then, that its Plan 
 muft be formed, as already directed, and as one half is here (hewn. 
 Then, to make crofs Pieces equal to thefe in the Front, occult Lines 
 muft be drawn from the firft upright Poft R, to the firft Perpendicular 
 of the Depth S; and from the Points of Interfe&ion draw little Parallels 
 to the Bafe : Thefe give the Thing required. 2 
 
PERSPECTIVE 
 
 Elevations of Chairs. 
 
 TO raife a Chair ; from the Dimenfions ABC, erect Per- 
 pendiculars, and proceed in the fame Method already 
 directed for Table-Feet, or Frames without Tops. All that 
 is here farther, is the Back of the Chair ; which may be made 
 of any Height at Pleafure. In the prefent Cafe the Height of 
 the Back is equal to that from the Foot A to the Seat K. 
 Which Proportion may ferve equally for Elbow Chairs. 
 
 From the Figure it appears evident enough, that, to form 
 the Back, there is nothing needed but to prolong the Perpen- 
 diculars of the Legs, as here A E ; and from the Point E to 
 draw a Line to the Point of Sight G ; which cutting the Poft 
 raifed from the Plan, or the Foot H gives the Point F. The 
 reft the Figure makes clear. 
 
 If Elbows are required, you have only to prolong the Fore- 
 Feet or Pofts, as the Hind-ones are for the Back : And to 
 draw a crofs Piece, or Bar, as L M, for an Elbow. 
 
 In the fecond Figure underneath, you fee a Form, or Bench, 
 cover' d with Cloth, and two Couches, The Head of one of 
 which is turn'd this Way, and the other view'd obliquely. It 
 would be Lofs of Time to dwell upon the Manner of making 
 them ; the Rules being altogether the fame as thofe already 
 laid down for other Moveables, viz. by making a Plan, railing 
 Perpendiculars, &q. 
 
PRACTICA L. 
 
 ICO 
 
101 
 
 PERSPECTIVE 
 
 Another Method of putting Moveables in Perfpeciive. 
 
 THERE are fome Moveables that fold) or fhmt down, and 
 that ferve for Tables, Seats, Beds, &*c. very eafy to 
 put in Perfpe&ive. 
 
 As to the Elevation, it is perform cl as that of a Cube, as 
 flie wn in A B C D, which is vie w'd in Front ; or E F G H. Then 
 two Diagonals, AC and BD, are to be made for that in the 
 Middle of the Front; or EH, and FG for that of the Side: 
 And thefe will ferve for the drawing of the two Croffes ; tak- 
 ing Care that one enter half through the other, as G K does 
 through H I ; and both of them to be fattened by the Middle 
 to make them fold. 
 
 In the Figure underneath we add a Table upon Treflels, that 
 even the leaft confiderable Moveable might not be wanting. To 
 put them in Perfpeftive, from the Points A, B, which are the In- 
 terval between the Feet of the Treffels, draw a Line to the 
 Point of Sight C; then, laying down the Thicknefs of the 
 fame Feet on the Bafe Line, as here D and E, draw Lines from 
 the lame to the Point of Diftance F, and obferve where they 
 interfecl: the Ray B C ; and from the Points of Interfe&ion draw 
 little Parallels to the Bafe Line h by which you will have the lit- 
 tle Squares or Plans of the Feet, as in A and B: Then between 
 the Diftance D and E, lay down the Breadth intended for the 
 Top of the Treffel, and drawing a Line thence to the Point 
 F, it will cut the Ray BC in the Points G and H; from which 
 Points, Perpendiculars are to be raifed* to any Height at Plea- 
 fure, as here to I. Laftly, from the Angles of the little 
 Squares of the Plan draw Lines to I. The fecond Treffel is 
 performed after the fame Manner as the firft. 
 
 The Form K, and the Table, or Seat L, need not any Ex- 
 planation, k to put them in Practice, as having aothing but 
 what is common with the Pieces above-rnentior/d. 
 
10 2 
 
 PERSPECTIVE 
 
 Mm 
 
 Moveables placed without any Order. 
 
 fIT HEN Moveables are placed orderly along the Side of a Wall, or 
 W in the Direction of the Rays and the Bafe Line, 'tis eafy to put 
 them in Perfpedive by the Rules already delivered : But if they be irre- 
 gularly placed, as in this Figure, you are to proceed as we {hall now 
 direct. Draw the geometrical Plans, R, S, and T, for Plans of three 
 Chairs ; which are to be diminiihed by the Rule already delivered for the 
 irregular Figure, Fag. 40. and the- Plans will be found fituated like the 
 Chairs, or rather the Chairs like the Plans. Now the Plans being in 
 Perfpe&ive, lay^a Ruler along one of the Sides, to fee what accidental 
 Point it gives in the Horizon ; thus, laying a Ruler along the Side A B, 
 we have the Point C in the Horizon for an accidental Point, to which all 
 the Lines of that and the oppofite Side mud be drawn : Thus we fee that 
 A and D are drawn to the fame Point C. 'Tis true each Plan placed irre- 
 gularly mould have two accidental Points; but they are frequently fo far 
 off in the Horizon, that 'tis a Chance you don't find them both. The 
 prefent Plans have each of them one ; as A B has C ; and AD, the other 
 Side, would have another, if our Paper were broad enough r E F gives G, 
 and IH gives K. As to the little Squares 1, 2, 3, 4, they are the Plans 
 of the IFeet of the fame Chairs, and may be made broader and narrower 
 at Pleafure. 
 
 Proceed then to erect Perpendiculars from all the Angles of the Plan, 
 and on the Side add a Line of Elevation, M N, whereon to lay the Di- 
 menfions of the crofs Pieces; as O, for the lower Bars j P for the Bars 
 of the Seat; and Q, for the Backs of the Chairs. Things thus difpofed, 
 from the Angles of the Plan draw Parallels to the Bafe Line, as far as the 
 Line of Elevation, and in the Points of Interferon erect Perpendiculars : 
 Thefe will give the Dimenfions, as already obferved of the former Figures. 
 
 All the Lines* of the Sides are to be drawn to the accidental Point of the 
 Plan : Thus, in the middle Chair, all the Sides are drawn to the Point G, 
 which is the Point of the Plan : As appears from the Figure. 
 
 3 
 
103 
 
 PERSPECTIVE 
 
 Moveables laid or tumbled on the Ground. 
 
 FROM the fame Plan of Chairs (landing on their Feet, it is eafy to 
 form thefe, which are laid on the Ground. 
 From the feveral Angles of the Plan erecT: Perpendiculars, and give 
 the Side on the Ground the fame Dimenfions as that bore up above it. 
 For Example, having ereded Perpendiculars from the Angles, you 11 
 have the Breadth M in the Chair laid on its Side, which is drawn to 
 the Point K : This Meafure M, being doubled, gives O for the Bar at 
 the Bottom of the Chair j and the Perpendiculars raifed from the Plan, 
 give the Bar of the Seat P : From which Points, Lines drawn to K, will 
 cut the other Perpendiculars of the Front in the Places required to fhew 
 the fame Bars on all the Sides they are viflble on As to the Height of 
 the Back of the Chair, make it the fame with the Height of the Seat; 
 but for the Back of that in the Middle, you are to draw a double Dia- 
 gonal, andobferve where it cuts the Rays, or Sides, RS. lne relt is 
 
 ^ThTtwo other Figures underneath, with their Feet aloft are eafily 
 performed: One of them is drawn to the Point of Sight T, the other to 
 the Point of Diftance V X. The Line of Elevation is Y Z. 
 
 The Method of raffing them is the fame as for thofe upon their Feet: 
 That is Perpendiculars muft be raifed from the Angles of the Han ; and 
 from the fame Angles, Lines be drawn to the Line of Elevation: By which 
 you will obtain the Dimenfions of each of the upright Parts, and the 
 Places of the crofs Parts both of Top and Bottom. 
 
PERSPECTIVE 
 
 Altars in Perfpeftive. 
 
 TH E Method for Altars is the fame as for Frames of long Tables. All there is farther in the for- 
 mer is the Circle in the Middle, the Edges of the Clcth and the Laces : Of each whereof in its 
 Place. 
 
 Firft for the Altar, here viewed in Front, there is but little Difficulty ; for having adjufted its Height 
 and Length, there remains nothing but to draw Lines from all the Points on the Bafe Line to the Point 
 of Sight E ; and from the Interferons thofe Lines make with the Bottom of the Altar, erect Perpendi- 
 culars. As to the Circle in the Middle it is ftruck with CompafTes : The reft is obvious. 
 
 For a Side Altar fet the intended Breadth and Height in the Place where you would have it begin ; as 
 the Breadth A B, and the Height B D in the Figure. Then, from B, D, and C, draw Lines to the Point 
 of Sight E : and fince B F is the Length of the Front Altar, and we would make this equal thereto, from 
 the Point F, draw a Line to the Point of Diftance G,„ and obferve where it interfects the Ray BC ; and 
 from the Point of Interferon raife a little Perpendicular to touch the Ray D in the Point H. Then 
 drawing a little Parallel from H, it will give the Point I in the Ray C; and by fuch Means you will 
 have the Top of the Altar, C D H I. For the two Ornamencs that are on each Side the Circle, they 
 are found on the Ray B E, by drawing Lines thence to the Point of Diftance G. M gives the Breadth 
 of the Border of the Altar Cloth. Now taking the Meafure B M, fet it off from D to O, for the 
 Breadth of the Cloth at the Top. As to the Circle, we need not repeat what has been already faid of 
 the Method of putting it in Perfpective. We (hall only here obferve, that Lines muft be drawn from 
 all the Divifions thereof to the Point of Diftance G ; and in the Interferons with the Ray B. Perpen- 
 diculars to be raifed. Then, the fame Dimenfions to be taken and fet off between B and O ; as PP P, 
 And from all thofe Points Lines to be drawn to the Point of Sight E 5 obferving where they cut the 
 occult Perpendiculars, and connecting the Points with a crooked Line, which gives the Circle in Per- 
 fpective. The Method of diminishing would be the fame, if in Lieu of Laces and a Circle there were 
 an Embroidery. 
 
 In the Figure underneath the fame Altar is fhewn free of Lines, and Points, and farther adorned with 
 a Crucifix and two Candlefticks. In order to this, the Corner Line of the Altar, QJt, muft be pro- 
 longed. Then, from the Point of Diftance G, a Line to be drawn thro' the Corner of the Altar T, and 
 continued till it cut Q.R ; and the Line Q_R will be the Length of the Altar, equal to B F in the firft 
 Figure. Hereon muft the Dimenfions of the Crofs. and the Candlefticks be laid ; e.gr. V for the Crofs 
 and S S, C3>. for the Candlefticks. From all the Points S and V, Lines to be then drawn to the Point 
 of Diftance G, and through their Interferons with the Ray QJi, little Parallels to be drawn ; which 
 cutting the Ray S E, give Squares upon the Altar, X X, &c. for the Crucifix, and Candlefticks. Thy 
 Square muft be left for the Foot of the Crucifix ; and from the Middle of the Square, the Crucifix is to 
 be raifed. For the Proportions of the Arms of the Crucifix, erect occult Perpendiculars from the Angles 
 of the Square, as here Y Y ; and draw Lines to the Point of Sight E, for the Candlefticks. Then turn 
 the Squares, for their Feet, into Circles, and obferve where they interfeel the Diagonal : For Perpendi- 
 culars erected from the Points of Int.erfec~r.ion, give the Breadth of the Bafons or Stands; and Lines drawn 
 to the Point of Sight, the Height. Laftly, from the Middle of the JFoot erect a Perpendicular for the 
 Body of the Candleftick, and the Taper therein, which is to be made high or low at Pleafure. To 
 proportion them, draw a Line from the Top of the firft to the Point of Sight E. The reft as already 
 faid. The Figure will call to mind the Methods. 
 
 104. 
 
PERSPECTIVE 
 
 Shops w Perfpe£tive. 
 
 TR ADESMENS Shops are ufually encompaffed with Shelves, Boxes, or 
 Drawers, wherein their Goods are difpofed. 
 The Rule for defigning Boxes, or Shelves, is much the fame as that already 
 laid down for Doors, and Windows ; e. gr. in Lieu of the Thicknefsof the Wall 
 ufed in making a Window, you are here to put the Board AB, and from the 
 Point B, to draw a Line to the Point of Sight, C. Then, for the Bottoms of 
 the Boxes ; having laid down the Diftances, or Proportions of the Boards, 
 inE, F, G, from thefe Points draw Lines to the Points of Diftance D. Thefe 
 make Inter lections, H, I, K, with the Ray B : From which Interfe&ions, Per- 
 pendiculars are to be raifed. 
 
 For the crofs Boards, fet any Number thereof at Pleafure, on A B, or only 
 on the firft Perpendicular B O ; fuch are, here, L, M, N, O : From all which 
 draw Lines to the Point of Sight C, and their lnterfe&ions with the Perpendi- 
 culars, in the Points P, P, csV. give the Boxes. So that nothing remains but to 
 draw little Parallels to the Bafe Line which give the Corner of the Box, fepa- 
 rating the Side from the Top and Bottom. 
 
 As to the Front Boxes, there only needs to draw Rays from the Points or Mea- 
 fures, and in their Interfe&ions with the Line QS, to erect Perpendiculars R and 
 S. The crofs Pieces are had, by drawing Parallels from all the Divifions on the 
 Perpendicular K as are, here, Pi, P2, P 3, P 4. 
 
 As to the Boxes on the oppofite Side, where there are fquare [upright Pofts to 
 fuftain the Shelves, their Width is had by drawing Lines from the Meafures TG 
 to the Point of Sight C. And to get their Plan, or Square, Lines are to be 
 drawn from the Meafures AEF to the Point of Diftance V, which give the In- 
 terfeftions XYQ^on the Ray T C. Through thefe Interferons, little Paral- 
 lels muft be drawn till they cut the Ray TG in Z ; and from the Angles of thefe 
 little Squares Perpendiculars are to be erected, which give the upright Pofts, as 
 in the Figure. 
 
 The Figure underneath (hews a Shop quite ficted up, and ready to receive 
 Goods of any Sort : For a Bookfeller, it muft be flocked with Books ; for an 
 Apothecary, with Drawers and Gallipots 5 for a Draper, with Pieces of Cloth, 
 Stuff, &?<r. 4 
 
io6 
 
 PERSPECTIVE 
 
 Buildings viewed on the Outfide. 
 
 HAVING now confidered every Thing relating to the Infidesof Buildings, 
 Churches, Houfes, csV. we proceed to give Rules for the Out fides. 
 Many of the Methods already laid down for the Infides may likewife fervc 
 for the Outfides: Thus the Method for Doors and Windows in any Part of a 
 Wall is itfelf fufficient for the Outfides of all Kinds of Buildings ; inafmuch as 
 the moft of what appears of the Outfide of a Building is Doors and Windows. 
 In Cafe it be enrich'd with Orders of Columns, Cs?<r. thofe, too, we have taught 
 to manage. 
 
 If there be Windows in Front, as A, and*tis defired to have others in the 
 fame Proportions on another Side, the Proportions AAA muft be transfer 'd to 
 the Bafe Line, as here to B B B, and Lines be drawn thence to the Poin of Dif- 
 tance C : And in the Points FFF, where they interfect the Ray DE, Perpen- 
 diculars to be raifed for the Uprights in the Window. 
 
 For the crofs Pieces \ thofe in the Front Window muft be continued to the Per- 
 pendicular D, by which Means you will have the Points II; from which Lines 
 are to be drawn to the Point of Sight E, which cutting the Perpendiculars F, 
 give the crofs Bars in the Side-window. 
 
 If the Number of Windows were much greater nothing farther would be 
 required but to continue their Rays, in order to make the Meafure and Height 
 of the crofs Pieces the fame in all. An Inftance of which we have in the Houfe 
 on the other Side, which has two Windows from the fame Rays. As to the 
 Breadth, or Thicknefs of the Pofts and crofs Bars of Windows in Front, it muft 
 be fet on one of the Travers, as here on K H ; and from the Corner of the 
 Window K, a Line be drawn to the Point of Sight E ; and from the Point H, 
 another to the Point of Diftance C, for the Window A, and to the Point of Dif- 
 tance L, for the Window on the other Side ; and in the Point, where thofe two 
 laft Lines interfeft, a Perpendicular, HM, muft be raifed. Then, from all the 
 Corners of the Window Lines to be drawn to the Point of Sight, and from 
 the Points Q^Q, (Jc. where they interfeft the Perpendicular HM, Parallels 
 muft be drawn to give the Thickneffes of the crofs Bars. The Thicknefs of the 
 middle Poft, N, will be had by drawing a Line from the Corner, N, to the Point 
 of Sight ; and in the Points Q_Q, where it cuts the Thickneffes of the crofs 
 Bars, erecting Perpendiculars Q^R, Q^R. 
 
 To fix the Thicknefs of the Windows on the other Side, it muft be fet in the 
 Corner of the Wall, on the Perpendicular D, as the Diftance 10; and from 
 the Points O O, Lines muft be drawn to the Point of Sight E. Laftly, lit- 
 tle Parallels to be drawn from all the Corners of the Windows, asS, T; which, 
 interfeding the Ray O, give the Thicknefs in the Point S. Thefe Rules may 
 lervefor all Kinds of Windows, both high and low. 
 
 In the Figure underneath is fliewn a Door diminiflied according to the Rules 
 delivered heretofore. As, in Effect, every Thing belonging thereto is very eafily 
 underftood, and readily practis'd, on fome or other of the preceding Methods. 
 
 -4 
 
PRACTICAL. 106 
 
i©7 
 
 PERSPECTIVE 
 
 Roofs of Houfes in PerfpeSiive. 
 
 ROOFS are made or different Heights according to their Material?. Thofe of Slate are the moft 
 upright of all. Their ufual Meafure is an equilateral Triangle ; i. e. their Slope, or the Declivity 
 of the Roof, is equal to the Width of the Houfe. Thus, in the little Figure at the Bottom of the pre- 
 fent Plate, C A, or C B, is equal to A B. Others make the Breadth A B equal to the Punchion, or middle 
 Top, D C, which is higher. But that Practice is much lefs ufual than the former. For flat Tiles, we 
 only make the Roof two thirds of the Height of thofe of Slate, or of the Width of the Houfe ; as in 
 A E B : For Thatch, the Height is ufually but half the Width : And for Pan-tiles, only one third ; as 
 A 9 B. 
 
 Before we go any farther it is to be obferv'd, that what we call Punchion, or middie Top, is a Tim- 
 ber rais'd perpendicularly on the Beams that fuftain the Ridge, and wherein the Rafters are all jointed. 
 Rafters are the Pieces of Wood which form the Declivity of the Roof, as H I. The other Pieces in 
 the Corners, which go to the middle Top, are called Stays, and are ufually longer than Rafters, 
 asHK. 
 
 There are three Kinds of Roofs in ufe j Pavilions, Pinnacles, and Pent-houfe-form. The firft have 
 four Sides, the fecond only two, and the laft but one. 
 
 To put a Pavilion, or Turret, in Perfpective, the Place of the middle Top muft be known, that the 
 Stays may be drawn to the fame. For this reafon it was that I made the geometrical Plan L M N O j 
 to fhew, that a Square, LMNP, is to be made of the Breadth of the Houfe L N, and two Diagonals 
 drawn through the fame, interfering in Some put the Punchion in Q, but that advances it too far, 
 and renders the Declivity of the End too fquat. It has a much better Grace when more upright. With 
 this View, it mould be approached towards the Wall L N a third part of the Diftance Q R, which will 
 bring it to the Point Sj from which Point a Perpendicular, S, muft be drawn upon the Line N P. 
 Then, the Meafures LT and T M to befet on the Bafe-Lines, and Lines drawn from them to the 
 Point of Diftance, which is here more remote than ufual ; and from the Points, wherein they interfect 
 the Ray V, Perpendiculars to be erected to the Top of the Wall, which wi[l give the Points XX ; from 
 which, Parallels to the Bafe-line are to be drawn as far as the other Ray I. Then, from the Middle of 
 the Wall Y, a Line to be drawn to the Point of Sight, cutting the Parallels in the Points Z, Z, &c. from, 
 which Points the Punchions are to be rais'd. To give them the proper Height regard muft be had to 
 the Materials intended for the Covering, and the Height be adjufted thereby, according to the Propor- 
 tions already hVd. Thus, fuppofethe Covering, Slate, an equilateral Triangle, 1,2,3, muft be made of 
 the Breadth of the Wall j and from 3, a Line be drawn to the Point of Sight, cutting the Punchions in 
 ihe Point 4. To which Point, Lines being drawn from the Corners of the Houfe, will give the Form 
 of the Pavilion. 
 
 For Pinnacle Reefs there need not fo much ado. You are only to make an equilateral Triangle, 5, 6,7, 
 of the Breadth of the Wall 5, 6, and the like for the other End of the Wall, which will give you the 
 Point 8. Then joining 7 and 8, you will have the Form and Meafure of the Roof. 
 
 The Figures on the other Side fhew the fame Thing unembarrafs'd with Lines. The Projecture Hand- 
 ing beyond the Roof is made at Difcretion. 
 
 The Frcnt-houle iscover'd with a Pavilion, perform'd after the fame manner as that on the Side. 
 - In the prefent Figure, where the Letters are, the Horizon is placed very high, to fhew the Togs 
 ©f the Houfes, and render the Practice more eaiy, and conceivable. But, as it is not often fuch a Cafe 
 happens, I have added the other Figure at the Top, wherein theHorizon is as low as ufual : Tho' the 
 Rule in itfelf is the fame as that already delivered . a 
 
io8 
 
 PERSPECTIVE 
 
 IN the preceding Figure the Pinnacle Roofs are viewed in Front y and their 
 Height, where covered with Slare, fixed to that of an equilateral Tri- 
 angle. Where the Covering is Thatch, or Tiles, the Heights arc laid 
 down on the Figure underneath. 
 
 Now, to make thefe latter Roofs with Returns, the Width of the Bot- 
 tom of theHoufe muft befet on the Bafe Line, as here AB ; and of this 
 Width a Triangle is to be formed with the other Dimenfions, according 
 to the Form of the Roof. The prefent is an equilateral Triangle, where- 
 of CD is the Height intended to be fet perpendicularly on the Corner of 
 the Houfe, at the Height of the Wall, as here E F. Then the Breadth 
 of the Houfe is to be laid down in C, which is the Middle of AB; and 
 from thence a Line to be drawn to the Point of Diftance j and in the 
 Point G, where it interfeds the Ray A, a Perpendicular muft be raifed. 
 Laftly, from F, a Line to be drawn to the Point of Sight X ; the Inter- 
 feron whereof with the Perpendicular H, will be the Point, or Tip of 
 the Pinnacle ; to which Lines muft be drawn from the Corners of the 
 Houfe, E L If you would have Eaves, they are eafily added : As is feen 
 in the Figure on the other Side, D. 
 
 For Pentices, you have only to draw a Line for the Height of the 
 Roof, as here the Line L M, and give it any Declivity at Pleafure. In 
 the prefent, the Height of the Roof MN, is the fame with the Breadth 
 of the Building, N O. If then, from the Points M O, Lines be drawn 
 to the Point of Sight X, the Perpendicular of the Depth will be cut in 
 the Points P and which being connected by a right Line will form 
 the Roof. The Figures on the oppofite Side £hew Houfes covered after 
 fuch Manners. 
 
 Thofe a Top are only intended to (hew that the fame Rule is to be 
 obferved, tho' the Horizons be changed. 
 
 A Church k feen in the Middle, which is covered or roofed with Pi- 
 nacles ; and the Wings with Pentices. 
 
 There is alfo a Pavilion viewed end-wife j mention whereof has been 
 made in the preceding Page. a 
 
A 
 
 109 PERSPECTIVE 
 
 To put a Street in PerfpeSiive. 
 
 Bare Sight of the Figure muft fuffice to fliew 
 the Method, which is exceeding eafy. All 
 you have to do is to make a Plan of fimple 
 Squares, the common way 3 and to take one, or 
 two, or three of the Squares for the Breadth or 
 Length of each Houfe $ and on fuch Breadth, 
 &c. to fet off the Meafures of the Doors, and 
 Windows ; and to get the Diminutions by draw- 
 ing Lines from the feveral Meafures to the Point 
 of Diftance $ as here from B C D E and F. 
 
 The firft Angle of each Houfe may ferve for a 
 Line of Elevation, as the Angle G in the firft 
 Houfe. As to the Roofs, we have already faid 
 how they are to be manag'd. 
 
 If you require any crofs Streets, one, two, or 
 three Squares are to be left vacant, and nothing 
 upon them, as are here H and I. 
 
 The Figure underneath is to fhew, that where 
 Houfes are to be made advance, or fall back, you 
 have only to put their Elevations forwarder or 
 backwarder on the Plan of Squares. Thus L ad- 
 vances a Square farther than K, and M farther 
 than L 5 and fo of the reft. 
 
no PERSPECTIVE. 
 
 That remote Obje&s do not pew 
 
 their Thicknefs, 
 
 IT muft be here remember'd, that Obje&s near 
 the Horizon, that is, fuch as are extremely re- 
 mote, are not to mew any Thicknefs when view'd 
 in Front. Thus, for Example, the Houfes A, B, . 
 C, D, mould not have any Thicknefles of the 
 Windows, Doors, &c. but only mere Lines. The 
 Reafon is, that the vifual Rays proceeding from 
 the front Parts of the Object become united m 
 the Eye with the collateral ones. 
 
 I mould have given a ftri& Demonftration 
 hereof, had I apprehended it any way neceffary. 
 But as I don't fee of what ufe it would be, and 
 as I ftand engag'd from the Beginning of the 
 Book not to enter into fuch Demonftrations, by 
 reafon I fuppofe I have to do with People who are 
 but indifferently prepar'd to underftand them, I 
 decline it* 
 
Ill 
 
 PERSPECTIVE 
 
 Buildings viewed by the Angle. 
 
 OF ihefe two Building feen Angle-wife the firft is performed after the Man- 
 ner already delivered for Squares viewed the fame Way, and Elevations of 
 other Things in Side-views. However, to fave the Trouble of recurring to the 
 one and the other, we fhall here obferve, that to perform fuch Buildings the 
 Meafures muft be fet on the Bafe Line, and from each of them, Lines be drawn 
 to the Point of Diftance, and from the Points of Interferon Perpendiculars 
 to be raifed : The firft Angle ferving for a Line of Elevation. Thus, in the 
 prefent Building, the Breadth being AB, and the Length, BC, double its 
 Breadth ; from A and B, Lines are to be drawn to the Point of Diftance D ; 
 and from B and C to the Point of Diftance E •, and from the Interferons B F 
 and G, Perpendiculars to be raifed for the Corners of the Houfe. As to the 
 Dimenfions of the Doors and Windows, they muft be laid down on the Bafe 
 Line between A B and B C; and Lines be drawn from them all, to the Points of 
 Diftance D and E. Then, obferving where BDor BE are interfered thereby, 
 raife the Pofts of the Windows therein. The Perpendicular of the firft Angle B 
 ferving for a Line of Elevation, will give the crofs Pieces, and the Height of 
 the Windows. The reft is obvious. 
 
 As to the Figure underneath,- the Method is the fame as for Chairs placed ir- 
 regularly ; i. e. having made the Plan, put it in Perfpeclive as irregular Objects 
 are put : Then, laying a Ruler along each Side of the Plan, obferve where it cuts 
 the Horizon, and marking the Point, draw Lines thereto from each Part of that 
 Side of the Building. Every Side or Face of a Building has its particular 
 Point. Thus the Plan being put in Perfpective, the Side, HI, gives the Point 
 K on the Horizon, to which all the Rays on that Side muft be drawn. The 
 other Side, IL, fhould likewife have its Point ; but for want of Paper-room, 
 we could not here exprefs it. Thefe two Points found, a Ruler muft be laid 
 thereon, and an occult Line drawn over the other Side of the Building parallel 
 upon the Plan to that which gave the Point in the Horizon, and continued to the 
 Bafe Line •, as from R/tthrough L to M ; and from the other Point continue an 
 occult Line through H to N. Then fetting the Number of Windows of the 
 Side HI, between Nandl ; and between I and M, fetting the Number of Win- 
 dows on the Side I L, draw Lines from all thefe Points, or Meafures on the Bafe 
 Line to the Points in the Horizon : And proceed as in the Figure above. 
 
 4 
 
112 
 
 PERSPECTIVE 
 
 To put Walks, with Rows of Trees, in Per- 
 
 fpeBive. 
 
 TH O' the preceding Rules might furnifh fufficient Inftruct ions for putting 
 Walks with Trees in Perfpective ; we have judged it not arnifs to add a par- 
 ticular Rule which may render the Method ft ill moreeafy. 
 
 If only a Tingle Row of .Trees on each Side be required, there is no need for 
 making a Plan of Squares, or Checquers : What is directed in Pag. 17. will 
 
 But where a Number of Walks are to be (hewn, we think it advifeable to form 
 a Plan in occult Lines, with Trees, as already taught in Pag. 31. and from the 
 Diagonals of the little Squares formed thereby, to erect Perpendiculars, as is 
 fhewn in A B. If you defire to have the Trees farther or lefs apart, increafe or 
 diminifh the Diftancesof the Squares on the Bafe Line. 
 
 When you have given the Stem of the firft Tree its proper Height, as AC, 
 draw a Line from C to the Point of Sight D, which Ray CD is to bound the 
 Stems of all the other Trees. The firft Tree, A B, mews that you may give 
 them what Turn or Form you pleafe between the two right Lines i and that they 
 are not to be drawn with the Straightnefs of a Ruler. 
 
 The Figure underneath is performed as that above, all the Difference is, <hat the 
 Squares of the upper are direct, or in Front ; and thofe of the under, viewed 
 Angle-wife : Whence the Meafures on the Bafe Line, in the latter Cafe,' muft be 
 all drawn to the Points of Diftance E and F Perpendiculars to be raifed from 
 the little Squares, and the reft as above. 
 
 In the fame Perfpective, wherein are Walks drawn to the Points of Diftance, 
 one may add others, drawn to the Points of Sight. Thus the middle Walk tends 
 to the Point G, which is the Point of Sight j and the others to the Points E, F, 
 
 fuffice. 
 
 which are thofe of Diftance. 
 
 4 
 
PERSPECTIVE 
 
 Ttf Gardens in PerfpeElive* 
 
 IN the Doctrine of Plans has already been (hewn the Manner of diminiftiing, 
 or putting the Plan of a Garden in Perfpective, by an eafy Rule fuppofing 
 that you have the Plan thereof. But, as I always endeavour to avoid geometrical 
 Plans, by Reafon it takes up too much Time to make them, I have added the 
 prefent Figures : Whereby it appears, that having made a Checquer, or Plan of 
 Squares, you may take as many or as few of them as you pleafe for the Beds of the 
 Garden : As here, A and B have each of them three Squares every Way i the reft 
 ferving for Walks, as C C. If you would have Compartments, or Knots in the 
 Beds, you are to ufe the little Squares or Divifions of each Bed •, cutting them, 
 and forming of them the Figure required ; as is ftiewn in the Squares of AandBj 
 and thofe of the other Side, D and E. The Pallifades and Arbours are cut thro' 
 the Breadth of the Walks, 
 
 Beds with Borders. 
 
 WHEN Borders are to be given the Beds, the intended Heights and Breadths 
 muft be fet on the Corner j and from thofe Meafures, Lines be drawn to 
 the Point of Sight. Thus, in the lower Figure, F G being the Breadth and 
 Depth of the Borders of the Bed H, Lines muft be drawn from the Angles of 
 the little Square F and G to the Point of Sight I ; and go on with the reft, as 
 abovefaid. 
 
 For Arbours, upright Pofts, or Perpendiculars, OO, 6fr. muft be raifed from 
 the Angles of the Squares of the Walk. The reft as already directed for Arches 
 viewed Side- wife, in Pag. 60. 
 
 The Grove in the Middle is performed by erecting Perpendiculars from all the 
 Angles of a Checquer, &V. 
 
PERSPECTIVE 
 
 To /^Fortifications in PerfpeBive. 
 
 \\7T E need not here repeat the Method of di- 
 W minilhing, or putting in Perfpe£tive, the 
 Plans of all Sorts of Fortifications : What has al- 
 ready been faid in Pag. 39. is clear enough. 
 
 To raife them there is no more Difficulty than 
 in a bare Wall ; only more Time is required, by 
 Reafon of the greater Number of Angles which 
 are to be drawn all to the Line of Elevation, to 
 give their Heights thereon j as has been mentioned 
 over and over in treating of other Works. 
 
 The little Line of Elevation is divided into 
 four Parts : The firft, from 1 to 2, is the Height 
 of the Parapet of the covered Way ; from 2 to 3, 
 is the Height of the Rampart j from 3 to 4, the 
 Height of the Parapet of the Rampart ; and from 
 5 to 1 5 the Depth of the Ditch. 
 
H5 
 
 PERS PECTIVE 
 
 To make Deligns in PerfpeBive. 
 
 THERE is no Matter fo excellent, but makes Defigns of the Works he 
 would fucceed in. If this be ufual in moft Arts, 'tis neceflary in this, by 
 Reafon of the great Number of Points, and Lines to be ftri&ly obferved, and 
 nicely managed, without which nothing is to be done in any wife pleafing to a 
 Perfon that has any Tafte or Skill therein. 
 
 Since then there is a Neceffity of making Defigns, we are to look out for what 
 may be afliftant therein. And as every Body knows that the Length and Te- 
 dioufnefs of fuch Works lyes in the drawing of Parallels and Perpendiculars, I 
 have fought both in Authors, and in Experience, for a Method of doing the 
 feme as expeditioufly as poflible. The Refult is, that nothing of this Kind has 
 appeared to me worth the recommending, but the Plate and Square, which Viator 
 feas left us in his Writings ; which are Things fuch People, as have Occafion to 
 fpend much Time in defigning, will find a deal of Eafe and Benefit from. 
 
 Tho' the Figure gives a tolerable Notion of the Thing, and the Method of ufing 
 it, it may be convenient to give fomething more exprefs thereon. The Plan AB 
 CD, then, is to be perfectly on the Square, a Foot and a half long, fifteen Inches 
 broad, and half an Inch thick. The Wood to be dry, firm, and fmooth. To 
 make it the fofter, and favour the Pen, a Sheet of Paper may be ftuck on it. 
 The Square EF is a Ruler a Foot and a half long, an Inch broad, and a Quar- 
 ter of an Inch thick, fitted at right Angles in another Ruler, GH, eight Inches 
 long, one broad, and three Quarters of an Inch thick. Now to draw Lines* 
 this laft Ruler, G H, is held clofe to the Board A B G D, in which Cafe the 
 other Ruler, E F, is certainly right, provided the Board and Ruler be exactly 
 formed. , 
 
 When you go to Work, fallen the Sheet of Paper, I K L M, on the Board 
 with four little Pieces of Wax, NOPQj then may you draw Lines from any 
 Point, fecurethat they are right. And for Perpendiculars, you have only to lay 
 the Handle, or Crofs of the Ruler, GH, on the Side GD, in. which Cafe E F 
 will be perpendicular to C D. A 
 
 For myfelf, I find a wonderful Eafe herefrom. The Truth is, withqut fuch 
 a Contrivance, a Man muft never be without the CompaffesTrlrhis Hantf. All 
 the Trouble now remaining is for the vifual Rays. And for thefe, fome ufe a 
 Ruler perforated at one End, and fattened by a Needle to the Point of Sight. 
 But this is to run into a Trouble greater than what you would avoid. The com- 
 mon Ruler does every whit as well. 
 R is a common Ruler. 
 T a Pair of common Compares* 
 
 V Another Pair of Compajfes, with a drawing Pen therein"; for circular Lines. 
 Thefe are all the Inftruments neceflary for making of Defigns in Perfpeclive. 
 
PRACTICAL. 
 
 1 1 
 
 G'g 2 
 
 ■ 
 
 m 
 
PERSPECTIVE 
 
 Reduction of PerfpeBive Draughts out of Small into Great; and out of 
 
 Great into Small, 
 
 AS Defigns are made with more Eafe in little than in great, 'tis but reafonable they mould always 
 be fo made. This has put me on giving a Method of enlarging fmall Defigns on the Canvas. 
 The Method commonly ufed by the Painters is to divide their little Defigns, and the Canvas they in- 
 tend the large ones to be on, into an equal Number of little Squares, and to transfer what is in the 
 Squares of the Defign, into the correfpondent Squares of the Canvas. This Way fome greatly approve of. 
 
 Here follows another, which, in my Opinion, is eafier and furer. Provide a Scale proportionate to 
 the little Defign, and another proportionate to the Canvas. To make a Defign the firft Thing to be de- 
 termined is the Scale, which is to fix the Meafures of all the Parts of the Work. Thus, in the little De- 
 fign A, the Scale B C of five Parts, which we may call Feet, is the firft Thing made. From this Scale 
 are taken the Horizon, the Height and Diftance of the Trees, the Breadths of the Walks, &c. 
 
 To enlarge this Defign the Method is this : Confider whether or no the Draught is to have its natu- 
 ral Horizon, i. e. Whether, when the Bottom of the Painting is on the Ground, the horizontal Line be 
 the Height of the Eye, which is about five Foot. Then, of the five Divifions between B and C, make 
 a Scale of five Foot, F G, that thus, having taken all the Meafures and Proportions in the fmall one 
 you may transfer them to the great one, after the following Manner. 
 
 The two Scales thus fixed, the firft Thing to be done is, to take in your Compaffes the Diftance be- 
 tween the Bafe Line D, and the Horizon E, and to apply the Compaffes thus opened, to the little Scale 
 B C, nothing what Number of Parts it includes, as here it does five. Take therefore five Divifions on 
 the large Scale FG in your Compaffes, and fet them on each Side the Painting, or large Defign, begin- 
 ing at the Bottom of the Cloth H H, and ending in 1 1. From the Points 1 1, ftrike, or fcore a Line 
 with a chalk'd or blacken'd Packthread. This Line 1 1, will mark the Horizon in the large Draught. 
 Then take the Diftance, or Depth, K L, of the little Defign, which gives the Foot of the Houfe, and 
 fet it on the little Scale : Note how many Divifions it includes, and take the fame Number from the 
 large Scale, and fet them on the Edges of the Canvas, H M, HM, which you muft ftrike with a Pack- 
 thread, for the Depth of the fecond Tree. Proceed to take in the little Defign, the Diftance N O, and 
 fet it on the little Scale, then take as many in the large one. Again, N O includes two Parts of the little 
 Scale ; accordingly two Parts are to be taken on the great one, and fet off from H to P, which muft be 
 ftruck as before. Do the fame for all the Parallels to the Bafe Line, as the other Trees, Windows 
 Roofs, &c. 
 
 As to Perpendiculars to the Bafe Line the Method is the fame as for Parallels ; only that they are to 
 be ftruck or fcored not from the Side, but from the Top and Bottom. Thus, for the two Corners of 
 the Houfe, the Interval between them being taken in the Compaffes, muft be fet on the little Scale, and 
 being there found equivalent to feven Divifions and a half, as many Divifions muft be taken from the 
 great Scale, by which you will have HS T S, to be ftruck as before. And the like muft be repeated for 
 all the other Perpendiculars, as Buildings, Trees, Pallifades, &c. 
 
 To find the vifual Rays, which are the Lines proceeding to the Point of Sight V, faften a Pack- 
 thread to this Point V, of the Length of the Painting, and with this ftrike or fcore al! the Rays very 
 exa&ly. Thus, for the two Rays D X, which give the Breadth of the Trees in the little Defign, take 
 the Diftance D X, fet it on the little Scale B C, and take an equal Number of Divifions from off the 
 great Scale, this will give you H Y; to which Points Hand Y, Lines are to be ftruck with the Pack- 
 thread, from the Point V. For the Ray of the Pallifades, take the Diftance D Z, and fet it on the 
 little Scale, and take as many Divifions from the large Scale ; by this Means you will have H f, which 
 are to be ftruck from the Point V, as before. 
 
 Every Thing in a Perfpeftive ordinarily comes under one or other of thefe three Sorts of Lines, Paral- 
 lels, Perpendiculars, and vifual Rays: And having fhewn how to defcribe thefe with a good deaf of Eafe 
 on the Canvas, there remains nothing formidable in the reducing fmall Defigns into great. 
 
 As to the reducing great into little, you have only to invert the Procefs ; that is, take the Meafures 
 firft on the large Scale, and diminifh them proportionably on the fmall one. Thus, if the Horizon of 
 the large Defign were five Divifions of the large Scale, five Divifions of the fmall Scale were to be ta- 
 ken for the Height of the Horizon of the fmall Defign. And fo of the reft. 
 
ii7 
 
 PERSPECTIVE 
 
 A? 
 
 Apparatus to the univerfal Method of the Sieur G. D. L. 
 
 AS many of the People, for whofe Benefit lintend this Work, may not be deep enough to fee clear- 
 ly into this univerfal Method, the Author, I believe, will allow'me to make it as eafy as I can, 
 that they may be the better enabled to reap the Benefit thereof. 'Tis for this Reafon I have added the 
 two following Figures, which will call to mind what has been already touched upon in the fecond, third, 
 fourth and fifth Advertifements. The Ddign whereof was to facilitate this Method, and accordingly 
 in them is ftiewn how to take all the Meafures on the Bafe Line ; and that as many Rays as cut the Dia- 
 gonal C F, fo many Squares are formed in the Depth of the Draught ; which Squares may be made of 
 any Magnitude at Pleafure. 
 
 Now, not to have fo far to feek, view the firft Figure, where the Bafe Line is A B, the Point of Sight 
 G, and the Points of Diftance E F. This Bafe Line I divide into twelve equal Parts, which I fuppofe 
 equivalent each to one Foot, and from all the Divifions draw Lines, or Rays, to the Point of Sight, 
 whereof A and B are the laft. Now, if a, Line mould be required that is funk a Foot deep in the Draught, 
 draw a Line from the firft Divifion, B D, to the Point of Diftance F ; and where this Line D F cuts the 
 Ray BG, will be the Point for a Line to be drawn through, that is funk a Foot. If another, two Foot 
 deep, were required ; take three of thefe Parts on the Bale Line, and from the third draw a Line to the 
 Point of Diftance F, and the Point where it interfe&s B G, will be the Place for that Line. Confe- 
 quently, if from C a Line be drawn to F, the Point where CF cuts B G will be a Line fix Foot deep. 
 
 If of the other fix Parts remaining of A C, you make twenty four, by dividing each into four, and 
 yet account each Divifion a Foot, you will have twenty four Feet between A and C ; fo that if a Line 
 ihould be required eighteen Foot deep in the Draught ; I would reckon eighteen little Parts from A, 
 and from the eighteenth would draw a Line to the Point of Diftance E, which by its Interferon with 
 A G would give one Point for that Line. If a Line were required twenty four Foot deep, the whole 
 Line A C m ult be taken, and from C a Line be drawn toE, and from H, the Point wherein CEcuts 
 A G, the Line H I muft be drawn, to appear twenty four Foot deep in the Draught. 
 
 In Perfpeaive, the Line H I is equal to that of A C, i. e. contains as many Parts, or Feet. So that 
 if from la Line be drawn to E, the Interferon of I E with A G, will give the Line KL forty eight 
 Foot deep. And if from the Point L, a Line be drawn to the Point of Diftance F, by its Interfe&ion 
 with the Ray A G, you will have a Line twenty four Foot farther off than the other. 
 
 If you would have a Line thirty Foot deep, from the Point A reckon fix fmall Divifions, and from 
 the fixth draw a Line to the Point of Sight G, obferving where it cuts the Line HI, as here in the Point 
 M. Then from M draw a Line to the Point of Diftance E, and the Line M E will interfed the Ray 
 A G in the Point N, through which the Line required muft be drawn. If a Depth of forty Foot were 
 required, from A fixteen Divifions were to be reckoned, and the reft, to be done, as before. If fixty 
 Foot be required, twelve Divifions muft be taken, and from the twelfth a Line be drawn to the Point of 
 Sight G, as far as the Line K L, which will give the Point O. Then, from O, a Line to be drawn 
 to the Point of Diftance, and its InteHe&ion with the Ray A G, will give the Line. 
 
 As to the fecond Figure, from what has been faid it is eafy to find a Point of any Depth or Diftance 
 at Pleafure. It remains to (hew how the fame is found within or without the Rays A G or B G. In order 
 to this, the Line B C is to ferve as a Scale of fix Foot, one of which we divide into twelve Inches ; that 
 wc may have the half, third, fourth, cffV. of a Foot. Things thus difpofed, if it be required to fhew 
 a Point feventeen Foot diftant, and a Foot and half within the Ray AG, a Line muft be drawn from 
 the feventeenth Divifion of the Bafe Line, to the Point of Diftance E, and where the Ray A G is in- 
 terfered thereby, in P, the Line P Qjo be drawn. Now, fince a Foot and half is required within the 
 Ray A G, I take the Extent on the fame Line N QJn my Compafies, and fetit off from P to R, which 
 Point R is the Point required. If a Point twenty nine Foot diftant, and feven and a half within the Ray 
 A G be required, a Line muft be drawn from C to the Point of Sight E, and through the Point where 
 it cuts A G, a Line being drawn, gives twenty four Foot. Then, from A taking five letter Parts, a 
 Line muft be drawn from their Extent to the Point of Sight G, till it cut that Line in the Point S ; and 
 fromS a Line is to be drawn to the Point of Diftance E, and from the Point wherein i t cuts the Ray 
 AG, a Line, TV, muft be drawn. And fince feven Foot and an half are required beyond the Ray A, 
 that Space muft be fet on the fame Line from T, towards V to the Point X, which Point X will be the 
 Point defired. After fuch Manner, may any Diftance at pleafure be determined." 
 
n8 PERSPECTIVE 
 
 An umverfal Method of performing PerjpeBive 'without having the Point of Diftance out of the Painting, or 
 Ground of the Work ; made pub lick by the Sieur G. D. L. 
 
 IN this Method a geometrical Plan is required, or at leaft a Scale of Meafures both for the Plan, and 
 the Elevation, in order for the one or the other to be put in Pjerfpective. 
 For an Object or Subject, we fhall take the Author's own Example, which is afquare Cage, termi- 
 nating a Top in a Point, or a Building with a Pavilion Roof. The Meafures whereof fhall be given by a Scale. 
 
 Now having made the Plan of the Cage, milk, which is here added at the Top of the Figure, a 
 Line, a b, muft be drawn at the Diftance the Objedt is to appear at in the Draught, as here the Line, a b, 
 x 7 Foot, which is to be the Bafe Line, or Bottom of the Piece, and to be placed according to the Afpect the 
 Object is to be viewed in. Then, from the 2 Extremes of the Line a b, 2 indefinite Lines muft be 
 drawn parallel to each other, as the Line ag, and bg. On 1 of which Lines, as a g, you are to draw 
 little Parallels to the Bafe Line, proceeding as far as the Angles of the Plan, and by Means of the Scale 
 fee how far each Angle of the Plan is removed from this Line a g, and mark the fame on each Line. Then, 
 from the Place the Painting is intended to be viewed from, which is here the Point c, 5 Footdiftant from 
 b, defcribe a Perpendicular to a b, viz. the Line c t ; and to this Line allow as many little Parts of the 
 Scale, as the Spectator is to be diftant to view the Painting, viz 24 Foot. At the Extreme of which 24 
 Foot, which is the Point/, erect a little Perpendicular, of the Height of the Eye, viz. the Line//, 
 equal to 4 Foot and an half. 
 
 The Cloth, Wall or Paper thus difpofed for putting the Plan in Perfpective, and making the Elevation 
 on the Plan, divide the Bafe Line, A B, into as many Parts as a b in the Plan is divided into, viz. twelve, 
 each accounted a Foot ; and over the Points A and B, fet the Height of the Line / /, viz. four Foot and a 
 half; that is, taking in your Compaffes four and a half of the Divifions of AB, fet them perpendicularly over 
 the Points A B, by which Means you will have the Points E and F. Draw the Line E F, therefore, parallel to 
 A B, and it will be the Horizon. Then, as in the Plan, the Point C, which is the Place the Draught is to be 
 viewed from, is five Divifions diftant from b, you are to reckon as many Parts from B ; and from the fifth, 
 C, erect a Perpendicular to A B, which cutting the Horizon in the Point C, gives the Point of Sight to 
 which all the Rays AG, and B G, reprefenting the Parallels of the Plan ag, and b g, muft be drawn. 
 
 As to the Point of Diftance, it will be the Point F, and as the Line c t is 24 Foot long, 6 Divifions 
 muft be taken from the Line A B, viz. from A to D, and each fubdivided into 4 ; which 24. Parts 
 are to ferve as a Scale for the Depths or Diftances, being fufficient for the fame, tho' they were infinite. 
 And the 6 Parts remaining between B and D, will be a Scale for the Feet, according as the Lines drawn 
 from the Points found for the Plan, fhall cut the Rays drawn to the Point of Sight G. For as this 
 Scale is a Pyramid, whereof B D is the Bafe j the Meafures diminifh in Proportion as they are farther off. 
 One of the Parts is divided into Inches, that all the Meafures may be there, as on the Plan. 
 
 By the Scale of Diftances, the Points of the Plan are found, and by the Scale of Meafures the Lengths 
 of the Lines both of the Plan and Elevation. 
 
 Now to put the Plan in Perfpective, all the Meafures of the geometrical Plan muft be obferved. The 
 firft Angle of the Plan r m is 17 Foot diftant from the Point a, on the Line ag. For this Reafon we 
 reckon 17 Parts, beginning at A, and from the feventeenth draw a Line to the Point F, cutting the 
 Ray A G in R. From this Point, R, a Parallel to the Bafe muft be drawn : And by Reafon the Plan m 
 is within the Ray ag, by a Foot and an half, therefore, on the Side B Dof the Line R, muft a Divifion 
 and an half be taken, and fet off within the Ray A G, which will give the Point M, reprefenting the 
 Angle of the Plan m. As to the Angle l 3 which is 26 Foot diftant from the Point a, a Line muft be 
 ■drawn from the Point D, which is 26' Foot from A, to the Point F; and where the Ray A G is inter- 
 fered thereby, viz. in the Point y, a Parallel is to be drawn. Now as the Pointj is not remote enqugh 
 by 2 Foot, a Line muft be drawn from the fecond Divifion of the Scale to the Point G, and where this 
 Ray cuts the Parallel^, viz. in the Point Q,, the Line QJF to be drawn, which will give the Point H 
 on the Line A G : From which Point H a Parallel to A B muft be drawn, and on the Side B D of the 
 fame Line H, muft the Divifions for 14 Foot and an half be taken, viz. from the Point H to L. 
 
 For the Point k, which is 29 Footdiftant from A, a Line muft be drawn from the fifth Part of the Scale 
 A D, to the Point G, and where this Ray interfects the Parallel y, viz. in the Point O, the Line O F muft 
 be drawn, which gives the Point N on the Line AG. Then from N draw a Parallel, the Side whereof, 
 BD, 7 Foot and a half mult be taken, to be fet off without the .Ray AG, viz. from N to K. 
 
 For the Point /*, which is 38 Foot from a, take 14 Divifions on the Scale AD, and from the four- 
 teenth draw a Ray to the Point G, which cutting the Parallel in the Point S ; from that Point draw a Line 
 to F, cutting the Ray A G in T, which is 38 Foot from the Point A, inafmuch as the Parallel y is 24; 
 to which, 14 being added, gives the whole 38. And fince the Angle i is 4 Foot and an half within the 
 Ray AG, that Extent muft be fet on the SideD B of the Parallel T, viz. from T to I. 
 
 To form the Plan, thofe four Points MLK I muft be connected by right Lines, and Perpendiculars 
 eredled from their Angles, as My?, L ff, Kfr, and I Jp ; each of which will be feventeen Foot, as is ex- 
 prefs'd in the Plan by the Line X. Then, from the Extremes of thefe Perpendiculars, draw two Dia- 
 gonals ft, fp, and ff,fr, which interfering in Z, from the fame Point Z erect a Perpendicular, Z jE, 
 thirteen Foot and a half. Laftly, drawing Lines from all the four Angles ft, ff, fp, and fr, to the Point 
 JE, the Cage will be formed in Perfpective. If you would have it funk a Foot under Ground, add a 
 F«ot underneath each Point of the Plan, and connect them by Lines. 2 
 
ug 
 
 PERSPECTIVE 
 
 *To give any precife Dijiance required, without removing the Point of Sight- 
 
 out of the Piece. 
 
 SUCH as are difpofed to make ufe of this univerfal Manner ought to know, that the Number of 
 Feet you take on the Bafe Line are to have a regard to the Point of Diftance propofed. 
 To make the Proportion underftood : In the firft Figure are put two Points of Pittance, the one fix, 
 the other twelve Feet, which have an eafy Ratio to each other ; inafmuch as the fix Parts being each di- 
 vided into two, you have twelve. 
 
 Suppofe then the Line A B divided into twelve Parts, and from each Divilion Lines drawn to the 
 Point of Sight C; take half thefe Divifions, A D, and from D to the Point E, which is the Diftance of 
 fix Feet, drawDE. 'Tis certain its Interjection with the Ray AC will give the Diminution of the 
 Squares viewed at fix Foot Diftance. And if from Da Line be drawn to F, which is the Diftance of 
 twelve Feet, the Line D F cutting the Ray A C will give the Diminution of fix Squares, view'd at a 
 Diftance of twelve Foot. And if the Diminution of twelve Squares, viewed at twelve Foot Diftance, 
 were required, fom the Point B, which is the whole Bafe Line, a Line muft be drawn to F, and its 
 Interferon with the Ray A C, in the Point H, will give the Thing required. Or from I a Line I F is 
 to be drawn, which will give the fame Point H, the Line HK, in each Cafe, being the Depth of twelve 
 Squares, viewed at twelve Foot Diftance. Hence we obferve, that twelve Squares, viewed at twelve 
 Foot Diftance, meet in the fame Line HK with fix Squares viewed fix Foot off, and that all the Lines 
 cf the fix Squares, given by the Interferon of the Diagonal D G, have a Relation two by two to thofe 
 given by the Diagonal DF, The Reafon why the Diagonal DF gives two Lines for one of thofe 
 DG, is, that the Diftance is double. If it were triple, it would give three, and four if quadruple. 
 Now, to find the fame Interferons, and the fame Number of Squares on the Side B D, as are on that A D, 
 without having the Point of Diftance out of the Piece, you have only to divide each of the fix equal 
 Parts between B and D into two, by which Means you will have twelve Parts : Then draw occult- 
 Lines from each Divifion to the Point of Sight C, and drawing Parallels to the Bafe Line thro' all the 
 Interfe&ions the Diagonals make with all thofe Rays, you will have twelve Squares Depth in the fame 
 Line as if the Diftance were twelve Foot, tho' in Reality G be but fix. The Reafon is, that in multi- 
 plying the Rays you multiply the Squares, and multiplying the Squares you remove the Diftance far* 
 ther. Such is the Reafon why having made twelve Parts of the fix that were between B D, there are pro- 
 cured twelve Squares, which have the fame Depth as if at twelve Feet Diftance. And if a Diftance of 
 twenty four Feet were required, you have only to divide each of the Parts between B and D into two, . 
 which making twenty four Parts, from the twenty fourth draw a Line to the Point D, and the Point K, 
 wherein it interfe&s the Ray B C, will be the Depth of twenty four Feet. 
 
 In the fecond Figure the fame Meafures are laid down on the Line L M, as on A B of the firft Figure, 
 and thefame Depth and Diftance on the Side MN, as on the Side AD, which gives the Line HKj to 
 fhew, that if a Line were drawn from the fifth Part, as QG, or from the feventh, as R G, the true 
 Depth would not be had, which is at K. For R G would not fink it enough, and QjG would fink too 
 much; even tho' of thofe five or feven Parts there were made twelve or twenty four. 
 
 For this Reafon you are always to obferve to take a Number which may be multiplied by the Di- 
 ftance, as here the Diftance of 6 may ferve for 12, 18, 24, 30, 36, 42, 48, &c. the Diftance 5 may 
 ferve for 10, 15, 20, 25, 30, &c. and the Diftance 8 for 16, 24, 32, 40, 48, &c. In this Way you . 
 cannot fail ; for fuppofing the Point of Diftance cannot be nearer the Point of Sight than G is to C, it 
 follows, that if G be fix, feven, eight, or ten Foot from C, that then half the Bafe Line will have 
 the fame Number, which is to be divided proportionally to the Diftance intended. For Inftance, if there 
 be eight Foot from N to L, and I require a Diftance of thirty two Feet, without moving G out of 
 its Place; I divide each of the eight Parts, or Halves of the Bafe Lines, asLN, into four, accordingly, 
 four Times eight make thirty two Rays. So that the Diminutions of the Squares will be thirty two Foot 
 diftant. 
 
 Thefe little Divifions do none of them remain after the Painting is finifhed, only the principal Divi- 
 fions of Feet, which are drawn to the Point of Sight, and the Diminutions, that is, the Parallels to the 
 Bafe Line, which ftill ftand. 1 
 
120 
 
 PERSPECTIVE 
 
 A very curious Method of drawing all Perfpe&ives in the mojl natural Man* 
 
 ner, without obferving the Rules. 
 
 HAVING given you all the Rules to be obferved in drawing of Perfpeo 
 tives in the exacted Manner, I have thought fit to add this and the fol- 
 lowing Method of drawing the fame very elegantly and exactly, without being 
 tied to the Obfervation of any one Rule. 
 
 It may be of good Service to fuch as love Painting, and take Pleafure in prac- 
 tifing the fame, without being willing to be at the Pains of opening the Com- 
 pafies, or taking up the Ruler, to draw Lines. For in this Method neither the 
 one nor the other are required ; and yet the fineft Draughts may be made here- 
 by, of Buildings, Gardens, Landskips, &c. 
 
 Before we come to the Method kfelf, it muft be obferved, that the principal 
 Requifite therein, is a large Piece of fine clear Glafs, fitted in a fine wooden 
 Frame, expreffed at the Bottom of the Plate by the Letter A. This Frame is 
 to Aide between two Cheeks, or Pieces of Wood an Inch and a half thick, which 
 are raifed at the two Extremes of a Board the Breadth of the Frame, i. e. about 
 a Foot broad, as fhewn in BC, which is difpofed to receive the Frame A. In 
 the Middle of the Board one or more fquare Holes muft be made, as in E, to 
 receive the flit Ruler F, fo as it may be raifed or lowered at Pleafure. At the 
 Top of which Ruler is a Circle of three or four Inches Diameter, but no Thick- 
 nefs, being made of Tin, or the like, and having a little Aperture, about the 
 Size of a Pea, in the Middle. The whole is reprefented together in G. 
 
 Now, tho' the mere Figure (hew the Application, yet we (hall defcribe the 
 Method of Proceeding. Hiving, therefore, placed the Inftrument G before 
 the Object you would draw, look thro' the little Hole, or Sight, F, and if you 
 fee all the propofed Objects reprefented on the Glafs, the Inftrument is fixed, 
 otherwife, bring the Sight nearer the Glafs, till you fee the whole of what is re- 
 quired. The Piece thus rectified, you are to draw on the Glafs every Thing that 
 you fee thereon thro' the Hole F ; which has the fame Effect here, as the Point 
 of Sight in the other Methods. And it is certain, every Thing thus drawn on the 
 Glafs, the Eye being fixed to the little Hole, will be according to the ftrid 
 Rules of Perfpective. 
 
 Every Body knows how to take, or copy off what is thusdefign'd on the Glafs. 
 'Tis beft to draw the Lines and Figures on the Glafs with Pen and Ink, then 
 wetting the Backfide of the Glafs a little, and laying a moift Sheet of Paper on 
 the Side that has the Defign, rub or prefs the Paper gently thereon with the Hand, 
 and the whole Draught will be imprelfed or transferred from the Glafs upon the 
 Paper. 
 
 Some advife to make ufe of a Pencil and Colours, and in Effect, every Body 
 is left to their own Difcretion. 'Tis enough to know the Method in general. A 
 Defign of a Palace is as.eafily taken this Way as 'a Landskip, and a Church as 
 a Houfe or Chamber: All required in any of them being to pitch on a Place 
 where the whole Thing to be reprefented may be feen, and to bring the Sight to 
 t he proper Nearnefs to the Glafs. 
 
 A Painter may ufe the fame Method for the drawing of Figures, Poftures, &c. 
 from Nature, Statues, Relievo's, and, in fine, every Thing: It being certain, 
 that a little Practice will render the Method exceeding feafible and eafy. 
 
PRACTICAL. 120 
 
121 
 
 PERSPECTIVE 
 
 Another elegant Manner of praciifmg Perjpeclwe, 
 without underjlanding it. 
 
 nr HIS Method is as curious as the former, and fome even prefer it, 
 byReafon there is a double Draught required in that, one on the 
 Glafs, and a fecond copied or imprinted from it. Whereas in the prefent 
 Method only a fingle Draught is made, and that as exa&ly as the former. 
 
 I mail not defcribe the Structure of this Inftrumenc, it being the fame 
 with that already mentioned; excepting that the Frame, inftead of a Glafs 
 fitted in it, muft be divided into a Number of little Squares by fine Threads 
 . drawn at equal Diftances from each Side of the Frame, acrofs each other, 
 forming what we call a Reticula, or Lettice.* As to the Number of Squares, 
 it is left to Difcretion : All we need add is, that they muft not be too 
 large that you may work the more exactly, nor too fmall for Fear of 
 being confufed. 
 
 For the Practice, place the Piece H in fuch Manner as that you may 
 fee all the Obje&s you mean to defign, thro' the Hole of the Sight I. If 
 the Defign mould be larger than the Compafs of the Frame, or Reticula, 
 or Checquer, Squares muft be made on the Cloth, or Paper, larger than 
 thofe of the Frame. If the Defign be intended fmaller on the Cloth, &c. 
 than the Frame is, make the Squares lefs ; otherwife they are to be of 
 the fame Size. But in all the Cafes make the fame Number of Squares 
 on the Paper, &c. as you fee in the Frame when you look through the 
 Sight I. Thus, transferring proportionally from the Squares in the one, 
 to the correfponding ones in the other, the Perfpective will be as juft as if 
 you had gone by the ftrict Rules, and ufed the Compafs, Ruler, &c. 
 
 The two Figures (hew how the Piece His to be placed, in order to de- 
 fign on a Table. The Expedient is of excellent Ufe in Painting, and ferves 
 to draw very exactly, any Perfpective Draughty to copy Paintings, draw 
 to the Life, &c. 
 
 Some People will be apt to urge, that the Method is not new j there 
 being few Painters but what know how to enlarge or diminifh Paintings 
 by Means of the Checquer, or Squares. All this we muft allow, but 
 muft take the Liberty to fay, that we don't know of any that ever yet ufed 
 the Sight ; which, however, is the great Means of doing any Thing in 
 Perfection. 
 
M E A S UR E S 
 
 AND 
 
 PROPORTIONS 
 
 0 F 
 
 FIGURES 
 
 FOR 
 
 Perfpe&ive Draughts, Paintings, and 
 
 Relievo's. 
 
122 
 
 PERSPECTIVE 
 
 Figures in FerfpeBives. 
 
 HAVING now (hewn to draw all Kinds of Perfpeftives, with their Ornaments, and other Circunv 
 ftances neceffary to pleafe the Eye, there remains nothing to deceive it entirely, but to add Figures. 
 But before we go farther, we muft diftinguilh between Figures it being one Thing to reprefent a Hi- 
 ftory. and another to aim to deceive the Eye by a Piece occafionally placed in a Gallery Hall, Garden, 
 or the like. In thefe latter, ftill Figures do bell, whereas in a Hiftory-Piece they muft all be, as it were, 
 animated by the Diverfity of their Poftures, &c. e . . 
 
 The Number of Horizons which our Painters frequently introduce in the fame Piece, leads them in 
 to an Infinity of Faults, in not being able to give the Figures their proper Heights proportionate to 
 their Horizons. I ihall therefore here give a fingle Rule, which may prevent their failing, be the Ho- 
 rizon what it will. 
 
 For Figures that have the Eye in the Horizon. 
 
 T N Perfpeaive Draughts placed at the End of a Galjery, Hall, Walk, or the [ike Place, to deceive 
 1 the Eye, the Horizon Jhould always be its natural Height, that is, five Foot, which is that of an or- 
 
 dl A r nd S FTgures intended to appear there as natural muft have the Eye in the Horizon: For having the 
 Eyes in thf fame Horizon whh ourfelves, they will be of our own Height This might be let pafs as 
 fufficient Inftruftion, but to make the Point yet clear and more obvious, I fhall inftance m thefe three 
 Figures, inftead of twenty others which might be brought. . 
 
 The firft Figure A is thenatural Height, and has its Eyes in the Horizon. If a fecond Figure be re- 
 quired in the Place B, from the Point B a Perpendicular muft be raifed to the Horizon, and it will ap- 
 pear of the fame Height with the former. If you require a third at C, let his Eyes likew.fe be » 
 the Horizon, and he will be the fame Height with the reft, in Appearance. In Effeft, thojhere were a 
 Thoufand, there need no other Rule be regarded, when the Horizon is the natural Height. I muft 
 not here be underftood as including Children, which are to be made in Proporuon to the large Figures, 
 according to the Difcretion of the Painter. 
 
 For Figures that have a low Horizon. 
 
 j N Paintings for Halls, which are ufually hung pretty high, the Horizon mtji bt lower, to bring it as 
 
 NZt^eeac^'re its juft Height and Proportion in whatever P,rt of the Painting it be 
 fotne one muft be drawn of any Height at Pleafure, in any Part of the Piece, es the Figure D F, which 
 is here to do the Office of a Line of Elevation. . ' 
 
 And to find the Height of the other Figures in the Painting which are to appear as high as the firft 
 draw Lines from the Head and Feet of this Figure D F, to a Point in the intended Horizon as E and 
 whL thfs Triangle D E F, will be found the Heights of all the reft. Thus e gr if the Height of a 
 Se n the Point G be required, from that Point G I draw a Parallel to thj Bafe G H, till it mter- 
 Stitelii aRarDE inthe Point I, and the Perpendicular HI gives th; Height of the : Figure 
 which is to be takeni the Compaffes, and fet off in the Point G. If anothe; be required in the Point 
 K, the fame Operation is to be Repeated, and we fhall have the Perpendicular vl N for thejuft Height. 
 And fo of the reft. 
 
123 
 
 PERSPECTIVE 
 
 For Figures that have a high Horizon. 
 
 W 
 
 "1X7 HEN the Horizon is high, as we are fdmetimes obliged to make it, in 
 *" order t0 reprefcnt an Objed viewed from fome Eminence, the fame Rule 
 already laid down for a low Horizon muft be obfervcd, all the Figures in the for- 
 mer Cafe being above the firft, and all lefs and lefs ; and in the prefent Cafe all 
 or them likewifc raifed above the firft, and the remoteft always the highefh and 
 at the fame Time the fmalleft in Proportion. 
 
 Having drawn the firft Figure, AB, draw a Line from the Top of its Head 
 and the Bottom of its Feet, to fome Point in the Horizon, as the Point C, then 
 will all the Heights of the other Figures be taken within this Triangle ACB 
 For Example, if you would have the Height of the Figure in the Point D, from 
 D draw a Parallel to the Bafe Line D E, as far as the Line A C, which will give 
 the Point E, from which a Perpendicular is to be raifed as far as the Line B C 
 which will give the Point F. This Perpendicular, E F, will be the Height of I 
 Figure in the Point F. If a Figure be required in the Point G, the fame is to 
 be done as for D, and you will have the Perpendicular H I, for the Height of 
 the Figure G. By the fame Method the Heights of all other Figures in any 
 other Places may be taken. 7 
 
 For Figures that have their Feet in the Horizon. 
 
 IT is but rare that Figures are made above the Horizon, but where there is a 
 Neceffity for if, thofe intended to appear the foremoft muft be made the 
 largeft, that is, they muft be made the natural Height, and all the reft being 
 made lefs, as they are more remote, will appear equal to them. Thus the Fi- 
 gure KL is here the biggeft and the neareft, and MN the remoteft. All the 
 
 on^nl' ? m u thc | a L nters fini(h , in g. the fa™ Figures more than thofe behind,, 
 and ftilL the farther off they are, the feinter and lefs perfedt muft they be. 
 
 1 he Rule for thefe Figures, and for thofe which have their Eyes in the Hori- 
 zon, is no other than their own Height. For in each Way, all you have to re- 
 gard, is to make them lefs, and feinter as they are thrown farther behind. 
 
124 
 
 PERSPECTIVE 
 
 Figures raifed above the Plan. 
 
 THERE are fome who hold, that Obje&s 
 raifed above the Ground are more diminifh'd 
 than if they were on the Plan ; and, of Confe- 
 quence, a Figure mounted four or five Foot fliould 
 be fmaller than if on the Earth. And the Rule 
 is good for Figures a great Height, as (hall be 
 {hewn in its Place : But a Rife, like that juft men- 
 tioned, can only make an infenfible Diminution. 
 For fuppofing fuch an Obje&, or Figure, may be 
 feen at one fingle View, that is, without raifing 
 the Eye, it muft be the fame Height when rais'd, 
 as when on the Ground. Thus, the Figure A 
 muft be the fame Height as B, and the Figure C 
 as D, and F equal to G, and fo of the reft. 
 
 The fame Reafon holds for Figures below the 
 Plan, which are to be reprefented of the fame 
 Height as thofe above it, as is (hewn in Figure E, 
 which is equal in Height with H and I, and as 
 big as K. Thefe two Examples may ferve for all 
 Cafes. 3 
 
PRACTICAL. 
 
*25 
 
 PERSPECTIVE 
 
 "The Poftures of Figures in Perfpe&ive. 
 
 THERE muft be a deal of Choice in the Pojlures, or Attitudes of the Figures, 
 to deceive the Eye. For 'tis not all of them are good, as we have already 
 obferved. This Confideration has determined me to add a few, which may 
 pave the Way for the Invention of numerous others. 
 
 The firft is a Man who reads, (landing •, the fecond is reading an Advertife- 
 ment polled on the Wall ; the third plays on a Lute ; the fourth is afleep •, the 
 fifth is lolling, with his Back turned on the reft, who are ranged two by two ; 
 thofe marked 6, are looking on a Draught on Paper ♦, the remoter, mark'd 7, 
 are in earneft Difcourfe. One might add others, playing, fpeaking, or difcourf- 
 ing at Table, writing, praying, In Effect, you have a Choice of an Infinity 
 
 of Poftures, provided they be fuch as that a Man may continue 'em for a Time. 
 But never ufe fuch as are much in Action for you can never be deceived in fee- 
 ing a Leg or an Arm in the Air, or a Perfon running without ftiifting his Place. 
 
 0% 
 
 JUfct' 
 
 tffkS Cm9 
 
 Beasts and Birds in PerfpeBive. 
 
 TH E fame Rules muft here be obferved as in human Figures, giving each 
 the Height or breadth of the firft, and from the two Ends of this firft 
 Meafure drawing Lines to the Horizon for the Meafures of all the reft. For 
 Example, having intended the firft Horfe, A D, to be the Height of that other, 
 B, from the Line AD draw a Line to the Horizon C, and from B draw a Pa- 
 rallel to the Bafe Line B K, till fuch Time as it cut the Line A C, which will give 
 the. Point K; from which a Perpendicular, K L, being erected, will give the 
 Height of the Horfe in the Point B. 
 
 As to Birds : From the Extremities of their Wings, F F, you are to draw Lines 
 to the Horizon, and between thofe Lines to take the Dimenfions of the reft, which 
 we fuppofe of the fame Size. For Example, to have the Magnitude of a Bird in 
 the Point G, draw a Parallel to the Bafe Line, G H, till fuch Time as it cut the 
 Rays E and F, which will give the Line HI for the Magnitude of the Bird G. 
 
 When Beafts or Birds are required, you muft always make Choice of fuch as 
 are the ftilleft, or leaft a&ive, as a Dog fieeping, or gnawing a Bone, a Cat 
 watching a Mo ufe, a Parrot, f£c. 3 
 
126 PERSPECTIVE 
 
 To find the Height of remote Figures , whereof the 
 firfl is on a Mountain near the Eye. 
 
 IT is a Thing that gives a deal of Satisfa&ian to the Mind, when a Peribn 
 knows what he does : On which account the Reader will be well enough 
 pleafed to have the following Rule, which few Practitioners are acquainted withaL 
 When fuch Figures are to be made determine the Height of the firft, that 
 is, the Space of the Ground you would have it rais'd j and at that diftance put 
 another Figure underneath, of the fame Height as the firft ; and from the Feet 
 and Head thereof draw Lines to the Horizon ; by which you will have the 
 Height of the other Figures in the Champain. To explain myfelf : 
 
 The Figure A, for Example, which is a-top pf a Mountain, is five Foot high, 
 which is the natural Height ; and I fuppofe the Mountain twenty-five Foot high: 
 If now a Man be rais*d twenty Foot, as is the Piece in the Middle, whereon the 
 Spectator is mounted (who himfelf is fuppos'd five Foot high ^ the Horizon will 
 be twenty-five Foot as well as the Mountain and confequently will rafe the Top 
 of the Mountain : As is expreffed in the Figure. 
 
 Now to find the Height of the little People in the Champain make a Fi- 
 gure twenty-five Foot lower, underneath the Figure A, or in fome other Place, 
 as B C •, and from the Feet B, and the Head C, draw Lines to fome Place ir> 
 the Horizon, as the Point O ; and between thofe two Lines, B and C, drawn 
 to O, take the Height of the little Figures, as already taught. Thus, for the 
 Height of the Figure D, draw a Parallel to the Bafe-Line, till it cut the Line B 
 in the Point E ; from which a Perpendicular is to be rais'd, cutting the Line 
 C O in the Point F : And take the Height of this Perpendicular E F, for the 
 Height of the Figure in the Point D. If you likewife require the Height of the 
 Figures in the Point G and H, proceed after the fame manner as in the Figure 
 D, and you will have their Heights between the Lines B and C; to be taken in the 
 CompalTes, and fet off in the Points G and H. The fame you are to do for any 
 other Figures, ftill diminifhing, fill at length you come to a mere Point. 
 
 This is all we have to fay as to the Meafures of Figures in Perfpeftive : But 
 as I have ingag'd myfelf to give all the Meafures of this Kind, the following 
 Rules come in my way, though they have no ftrid Relation to that Art. 
 
127 
 
 PERSPECTIVE 
 
 To give the natural or any other Height to Figures much elevated, 
 
 TO omit nothing relating to the Heights of Figures we add the two following Rules : The firft 
 given by Albert Durer r Serlio, and others, for writing of Letters on eminent PJaces ; fo as they 
 may appear of the fame Size as thofe at Bottom. But for the fame reafon it may be applied to find the 
 Meafures and Magnitude of Figures which fhall appear equal when view'd from a certain Place wherein 
 the Spectator is. 
 
 Thus in B there is a Man five Foot high, and fifty diftant from the Tower A, viewing the firft Figure 
 G, which there appears of the natural Size ; and thirty Foot higher another Figure is to be placed, which 
 ihall appear of the fame Size as the other, when view'd from the fame Place. Now, to find its Di- 
 menfions defcribea Quadrant of a Circle, or a leffer Arch, on a Paper to be placed before the Eye; 
 then looking at the Feet, and the reft of the Figure C, it will give the Diftance or Angle, E F, on the 
 Paper. This done without moving the Quadrant look at the Point D, where the Foot of the Figure 
 D I is to be ; and obferve what Point it gives in the Quadrant, viz. . G. And from this Point G fet off 
 the fame Diftance or Angle, as that of the Figure C, viz. E F, which being remov'd to G gives G H. 
 Then looking through the Point H, note what Part of the Perpendicular rais'd from D is cut thereby* 
 viz. the Point I, then will the Interval D I, be the Height requir'd for the Figure to be placed there' 
 If you would have another ftill higher the fame Operation mult be repeated, and they will all appear of 
 the natural Bignefs to the Spectator, B. 
 
 If you require the Reafon thereof you muft recollect the Principles already laid down, or recur to 
 them again ; and you will find that all Objects view'd under equal Angles appear equal. Now 'tis cer- 
 tain, that the Angle G H is equal to EF ; confequently the Figure D I muft appear equal to the Figure C 
 
 "To find in what Proportion equal Figures grow lefs to the Eye, when placed 
 
 over one another. 
 
 TH E^ Speaator K having a Quadrant, or part of a Circle, like that of the firft Figure B, looks to- 
 wards the firft Figure M of the Tower L ; which there appears of the natural Size. Then 
 taking its Meafure from Head to Foot he marks the Diftance thereof on the Quadrant, vise. N O. 
 After this, without ftirring out of his Place, he directs his Eye to the Head of Figure P, and marks the 
 Angle it. gives on his Quadrant, viz. QR. And if there be others ftill higher, he would take them all 
 after the fame manner, and lay them down on his Quadrant. 
 
 Now to find the Difference between the one and the other take the Angles or Diftances of each in 
 your Compafles, and you will find that the higheft gives the fmalleft Angle ; and of confequence fhew 
 the fmalleft Figures to the Eye ; fo as the Figure P fhall only appear half the Figure M, tho' the one be 
 in reality as big as the other. If you ask the Reafon, we anfwer, that the Angle of Figure P is only 
 half that of the Figure M j as you fee that Q_R is only half of N O, or nearly fo. 
 
 By this Knowledge we may arrive at that above, and by that above we can come at this : For if M 
 and P be the fame Magnitude, and yet P only appear below to be half of M, we may fecurely fay, that 
 to make P appear as big as M, it muft be twice its prelent Magnitude. The fame may be faid of the 
 upper Figure, where D, which is double to C, appears no bigger to a Spectator in B than C does. It 
 might be added, that unlefs D were bigger than C, it would only appear half as big ; fo that one Rule 
 is the reverfe of the other. Both the firft and fecond Rules are beft put in practice by the little Foot, as 
 the Figures hitherto have been ; by which we come at the Difference and Proportion of Figures as fe- 
 curely as if they were taken from the Life by a Quadrant.- a 
 
i28 PERSPECTIVE 
 
 Meafures for elevated Figures. 
 
 FROM what we have been faying of the Diminution of Figures when placed on high ; we are t« 
 take our Meafures in Proportion, for fuch as are to be rais'd in Paintings, whether they be placed 
 on Mountains, Houfes, or above the Clouds in the Air. The two Rules we have now to give, will 
 render the Method extremely eafy. 
 
 m For the firft, I fuppofe the Man A to be fix Foot j which Height I fet off feveral times on a Perpen- 
 dicular B, over the Bafe-Line; and from the feveral Divifions 6, 12, 18, &c. draw Lines to the Head of 
 the Figure A. Then fetting one Point of the Compafies in the Point A, with the other I defcribe the 
 Arch C D, and the Interferons that Arch makes with the Rays, are the Meafures to be given the Fi- 
 gures. Thus, if I would have a Figure appear forty two Foot high ; I take E D, which cuts the two laft 
 Rays, and fet it off to F, which is forty two Fooc above the fame Bafe-Line A B. If another be re- 
 quired thirty Foot high ; the Diftance G H muft be took, which cuts the Rays 30, 36, and gives the 
 Height of the Figure P ; and fo of the reft. The main Point is the approaching or receding of the Line 
 B ; which muft always be the Diftance between the Spectator and the Objeft, <viz. here, thirty Foot, or 
 thereabout. 
 
 For the fecond Rule : Inftead of the Line B, usM in the firft Figure, I here put the Divifion from fix 
 Feet to fix on the Bafe-Line I T. The two firft Points I and 6 are to be drawn to the Point of Sight 
 K. Thus between the two Rays I K, and 6 K, we have the Meafure of fix Foot, which is the Height 
 to be given the Figures. Then from all the other Divifions 12, 18, 24, 30, &c. draw Lines to the 
 Point of Diftance L, and in the Interferons made with the Ray 6 K, draw little Parallels to the Bafe- 
 Line, between the Rays I K, and 6 K. Thefe Parallels will give the Heights of Figures unequally 
 high, but at the fame Diftance. Which may be prov'd by comparing the Meafures of the firft Method 
 with thofe of the fecond. 
 
 If it be ask'd how much each Figure is diminifiYd from the firft, which is fix Foot high, you need 
 only to take the Height of the Figure required in your Compafies, and fet it off on the little Scale M, 
 and the Queftion is IblvM. Thus, having taken the Height of the Figure B,and fet it on the Scale M, it 
 gives four Feet ; which {hews, that a Figure fix Foot high, rais'd thirty Foot, will only appear to be four 
 Foot. The Heights or Diminution of the reft are found by the fame Operation ; provided the Diftance 
 be the fame with that of thefe. If the Diftance be chang'd the Procefs muft be begun anew. 
 
 The Figures V, X, Y, which are in the Clouds in the fecond Figure underneath, are of the fame 
 Height and Proportion as in the firft Figure. They are only here added to ftiew, that tho' the Method 
 be different theEffefts are the fame. 
 
 What has been faid as to the Heights and Diminutions of Figures on the Bafe-Line A B in the firft 
 Method, and I T in the fecond, muft be obferv'd in Proportion as they are funk farther behind ; And 
 the higheft muft have the fame Relation to thofe under Ground which are in the fame Line, as thisF P 
 to that A. Thus, in the fecond Rule, if over-againft the laft Figure N there were another Figure O, 
 placed on a Tower forty-eight or fifty Foot high, and its Magnitude requir'd, it muft be put in the 
 fame Proportion as N has to I. And inafmuch as the laft N only contains two and a half of the fix 
 Parts which I contains, this O upon the Tower muft only have two and a half of the fix Parts in the 
 Figure N. If I would have another Figure, R, on another Tower, forty-eight or fifty Foot before the 
 Figure I take two Parts and a half of the Figure QJbr the Height of the Figure. If another were 
 requir'd in S, which is thirty Foot high, in the fame Tower he muft take four of the fix Parts of the 
 Figure Q, that is, four Foot; as already mentioned in the firft Method between the Rays G andH. 
 
 What renders this Rule the more valuable is, that all the Proportions of Figures may be learnt by 
 heart. For whoever would be at the trouble of making this Meafure, where he might add more Parts, 
 they would ferve him for ever ; and.he would render them fo familiar, that in a little time he would tell 
 you offhand, that if you are thirty five Foot diftant, and the Figure fix Foot, or fix Parts high, when 
 on the Ground, another, that fliall be of the fame Size, will only appear five Foot and a half when rais'd 
 to the Height of twelve Foot ; only five, if rais'd eighteen Foot ; only four and a half, if twenty-four 
 Foot; only four, if thirty ; only three, if thirty-j&x i and only two and a half, if forty- two : And fo 
 on, by fix and fix, to any Number at Pleafure. 4 
 
PRACTICAL. 
 
METHODS 
 
 Of finding the 
 
 NATURAL SHADOWS 
 
 O F 
 
 O B J E C TS 
 
 Both by the 
 
 Sun, Candle, Torch, and Lamp. 
 
129 PERSPECTIVE 
 
 iirfririrwi.f'wiiriri 
 
 Or/po/ Shadows, 
 
 TO define a natural Shadow, we do not call it an abfolute Privation of all 
 Light, for this would be to form a perfect Obfcurity, wherein Objects would 
 be no more feen than their Shadows: But we mean by Shadow, a Diminution of 
 Light, occafioned by the Inter pofition of fome opaque Body, which receiving and 
 intercepting the Light that mould be call on the Plane it is placed on, there gives 
 a Shadow of its own Form. For Light being of a communicative Nature, dif- 
 fufes itfelf on every Thing not hid from it, particularly on every Thing that is 
 plain and fmooth. But where there happens the leaft Elevation, a Shadow is 
 produced, which exhibits the Figure of the illumin'd Part on the Plan. 
 
 The Diverftty of Luminaries occafions a Difference of Shadows ; for if the 
 Body thas; illumines be larger than the Body illumined, the Shadow will be lefs 
 than the Body. If they be equal, the Shadow will be equal to the illumined, 
 and if the lLumina'ry be lefs than the Object, the Shadow will be continually en- 
 larging as it goes farther off. 
 
 The better to comprehend this, we here add three Figures, which may ferve as 
 a Foundation for ail the Rules to be advanced hereafter. 
 
 The firft (hews, that the luminous Body A B, being larger than the illumined 
 C D, enlightens more than half the Object, and gives a pointed or conical Sha- 
 dow' whereof the Luminary is the Bafe. This Truth is evinced in an Eclipfe of 
 the Moon, wh-ich is rarely quite covered by the Shadow of the Earth, tho* the 
 latter be above forty Times the bigger. The Reafon is, that the Sun, which is 
 the Luminary, is one hundred and fixty Times bigger than the Earth, which 
 therefore it illumines more than half, and of Confequence makes its Shadow ter- 
 minate in a Point. 
 
 The fecond having the luminous Body, FG, equal to the illumined H I, half 
 the Object is enlightened, and its Shadow projected parallel, HI KL. 
 
 The third fhews, that the Luminary, or Light, M, being lefs than the "illu- 
 mined N O, the latter is not half enlightened. And of Confequence the Shadow 
 N OPQ^ enlarging as it recedes farther from the Object, makes a Pyramid, 
 whereof the Luminary is the Point, or Vertex. 
 
LI 2 
 
i 3 o PERSPECTIVE 
 
 Of the Difference of Shadows. 
 
 FROM what has been obferved in the preceding Page we draw this 
 Conclufion, That the fame Object may project Shadows of divers 
 Forms, tho' ftill illumined on the fame Side s the Sun giving one Form, 
 the Torch another, and the Day -light no precife Form at all. 
 
 The Sun always makes its Shadow equal to the Obje5i i that is, projects it 
 parallel-wife, as in the firfl Figure. 
 
 How this Method is to be put in Practice, and each Object have its 
 natural Shadow, (hall be (hewn hereafter. 'Tis certainly of Confequence 
 to all Painters, Engravers, &c, to obferve thefe Rules precifely, and not 
 take the Rules for Candles, Lamps, or the like, in Lieu thereof, as is too 
 frequently done, 
 
 The Shadow of a Torch or Flambeau, is not projected in Parallels, but 
 in Rays proceeding from a Centers whence, the Shadow is never 
 equal to the Body, but always bigger, and grows bigger as it recedes the 
 farther, This is (hewn in the fecond Figure, where the Shadow is larger 
 than in the firft, tho' the Cubes of the one and the other be of equal 
 Breadth and Height, It appears, therefore, a grofs Abufe, to represent 
 the Shadow of a Torch like that of the. Sun, and the Shadow of the Sua 
 like that of a Candle, when the Difference is fo confiderable, 
 
 There is a third Kind of Shadow, neither produced by the Sun nor 
 a Torch, but only a fine funny Day, which wanting Strength to finifh and 
 define its Form occafions a Dimnefs near the Object, as in the third 
 Figure, Now for this there is no certain Rule, but every Body condu&s 
 |t at Difcretion, 
 
 All thefe Shadows, both thofe of the Sun, of the Torch, and of the 
 Day-light, mud appear darker than the Parts of Objects not illumined, 
 Thus A is lefs dark than B, by Reafon A receives the Reflexion of the 
 Brightnefs around it, and B has no Reflexion but from A, which Ufelf 
 |s in Obfcurity, It mult be obferved by the Way, that the Part of the 
 Shadow moft remote from the Object is ftill darker than that neareft it j 
 as Q is darker than H> by Reafon A cannot communicate the little ReflexU 
 on it receives, as far as Q 3 tho 5 it does tc?H, 
 
PERSPECTIVE 
 
 To find the Form of the Shadows. 
 
 IT may be remembred, that at the Beginning of this Book, Perfpe&ive 
 was defined, The Art of reprefenting Objects which are on the Ground, 
 or a horizontal Plane, upon a Plane perpendicular to the Horizon. But 
 in the Bufinefs of Shadows it is quite the reverfe, fince we there conceive 
 aBodyraifecl over the Plan, which being illumined, cafts its own Shadow 
 on the Plan j as we find the Body A gives a Shadow B, on the Plan. 
 
 To find a Shadow two Things are fuppofed, viz. Light and a Body. 
 Light, tho' quite contrary to Shadow, is yet what gives it its Being, as 
 the Body, or Obje&, is what gives its Form and Figure. What we have 
 here is to confider the Shadows, the Reader being fuppofed already injlruBed 
 in what relates to putting the Bodies in PerfpeSfive. 
 
 To conceive the Nature of Shadows more clearly, and render the Prac- 
 tice more eafy, it muft be obferved, that there are two Points to be made 
 ufeof. One of them the Foot of the Light, which is always taken on 
 the Plan the Objed is placed upon, the other, the luminous Body : The 
 Rule being common to the Sun, Torch, &c. with this Difference, that 
 the Sun's Shadow is projected in Parallels, and that of the Torch in Rays, 
 from the fame Center. We begin with that of the Torch, as leading 
 to a more eafy Underftanding of that of the Sun, which follows. 
 
 We fay then, for Example, that if "tis defired to have the Shadow of 
 the Cube A, here reprefented in B, Lines muft be drawn from O, the 
 Foot of the Luminary, through all the Angles of the Plan of the Ob- 
 ject, as here O D, O E, OF, O G. Then other Lines are to be drawn 
 from the Point of the Light of the Torch C, through all the fame An- 
 gles, till they interfecl: the Lines from the Point O. Thus, having drawn 
 a Line from O through the Angle D, another muft be drawn through 
 the fame Angle, interfering the former in H, which Point H will be the 
 Shadow of that Angle. And if -from the fame Point C,. the fame be 
 done through all the Angles, the Lines of the Plan will be cut in the 
 Points H, I, K, L, which being conne&ed together by right Lines, you 
 will have the Shadow of ^the Cube, as is (hewn in the Figure above, and 
 more diftin&ly in that below. 
 
i3 2 
 
 PERSPECTIVE 
 
 Shadows from the Sun. 
 
 THE Sun, that magnificent Luminary, being vaftly larger than the 
 whole Globe of the Earth, as has been already intimated, mull give 
 all its Shadows pointed, by Reafon it always illumines more than half of 
 
 In Confequence of this Demonftration we might conclude, that all the 
 Sun's Shadows muft be lefs than the Bodies that project them, and dimi- 
 nifti more and more as they recede farther and farther. Now this would 
 be true, were there any Relation between the illumin'd Body and the 
 Illuminer; but as all Objects on the Earth are fo fmall, in Comparifonof 
 that Star, the Diminution of their Shadows is imperceptible to the Eye, 
 which fees them always equal, i. e. neither broader nor narrower than the 
 Body that forms them. On this Account all the Shadows caufed by the 
 Sun are made in Parallels, as is (hewn in the fecond Figure of this 
 Treatife. 
 
 From the whole it appears, that to find the Shadow of any Body what- 
 ever, oppofed to the Sun, a Line muft be drawn from the Top of the Lu- 
 minary perpendicular to the Place where the Foot of the Luminary is to 
 be taken, and thro' this Place an occult Line to be drawn through one of 
 the Angles of the Plan of the Objed, and another from the Sun to the 
 fame Angle j the Interfe&ion of the two Lines will exprefs how far the 
 Shadow is to go. All the other Lines muft be drawn parallel hereto. 
 
 For an Example, to take the Shadow of the Cube A, the Sun being 
 in B, from the Bottom of the Sun C, which is, as it were, the Foot of 
 the Light, draw a Line thro* one of the Angles of the Plan, as CD. Then 
 from the other Angles E, draw Parallels to this Line. And to find the 
 Extreme of the Shadow draw a Line from the Sun, B, through the An- 
 gle F, cutting the Line C D in G. Then drawing a Parallel to this Line, 
 through the Angle H, it will cut the Line E in the Point I, and give the 
 Shadow of the Cube, D G I. 
 
 If youdefire to have the Shadows caft forward, or any other particular 
 Way, you have only to determine the Place of the Sun, and the Point be- 
 neath it, to draw the Lines of the fame Angle, and the other Lines parallel 
 thereto. The Method is the fame as in the former Cafe, fo that it needs 
 not be lepsated. The Figure (hews the reft. 
 
133 
 
 PERSPECTIVE 
 
 *The Shadows of the Sun are equal in Obje&s of the 
 fame Height , tho' at a Diftance from each other. 
 
 EXPERIENCE teaches us, that feveral Styles, or Elevations of 
 the fame Height, remov'd to a diftance from each other, do yet 
 project equal Shadows at the fame time: We fay in the fame time, for they 
 are lengthening and ftiortning, in proportion as ^ie Sun comes nearer or 
 recedes farther off ; one or other of which he is continully doing. 
 
 For this reafon, when the Shadow of an Object is to be caft any way, 
 you mud determine the Place of the Sun, and the Point underneath, to 
 draw two occult Lines from the fame, for the Extremity of the Shadow ; 
 as here the Pallifade A gives the Extreme of its Shadow in B ; And if 
 from this Point B, you draw a Line to the Point of Sight C, this Line 
 B C will be the Shadow of the Pallifade D, "as well as of that of A, and 
 of all the reft in the fame Line to the very Point of Sight In Effect, 
 it muft be held for a certain Maxim, that Shadows always retain the 
 fame Point of Sight as the Objects. 
 
 On the footing of this Obfervation, that Objects of the fame Height 
 give equal Shadows, if you would give the Shadow of the Pallifades 
 E, F, which are the fame Height as A, D j take in your Compaffes the 
 Diftance A, D, and fet it on the Foot of the Pallifade E, by which you 
 will have E G; then from G draw a Line to the Point of Sight G : 
 And thus you are to proceed, though the Walks were infinite. 
 
 If the Light come from the Middle, or Fore-part, as in the Figure 
 underneath, the Method muft not be alter'd ; but only the Foot, or 
 Bottom of the Sun, to be brought nearer or farther off, and Lines 
 drawn from each thro' an Angle: Thus H and I give the Extreme of 
 the Shadow of the Pallifade K, in the Point L; and from L a Line muft 
 be drawn to the Point of Sight M: Then from all the Angles of the 
 Plan of the Pallifade, Parallels to be drawn to the Line H, as far as 
 the Ray L M; and the natural Shadow of the fame Pallifade will be 
 given. ' 4 
 
PERSPECTIVE 
 
 ^mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm^ 
 
 mOti Wm WW WiWiWf WW$ WWW WW WW Wl WW WWa^ 
 
 O/* Shadows, /lr direBly opposed to 
 
 the Eye. 
 
 AS often as- the Sun is before the Eye, that is, directly over the Point of 
 Sight, the Sides of the Shadow it produces will be Parallels, as all the 
 vifual Rays are. For this Reafon, the Point of Sight is always to ferve for the 
 Foot of the Light ; and the other Ray, that is to determine the Shadow, will be 
 fl&ken from the Centre of the Sun. 
 
 Thus the Shadow of the Cube A being requir'd, draw Lines thro' all the An- 
 gles of its Plan B C, to the Point of Sight D, as the Lines B E and C F. Then, 
 from the Center of the Sun, G, draw two Rays, cutting the former in the Points 
 K and L, and pafTing thro' the Extremes of the Lines rais*d from the Angles B 
 andC; viz. H and I. By this means the Shadow of the Cube will be found 
 BKLC. 
 
 The Shadows of the two other Objects, M and N, are found by the fame 
 Rule, and fo might as many others as mould be feen there. 
 
 But my Mind fuggefts, that there might be fome Difficulty, if, inftead of a 
 Cube, a Pyramid were given \ by reafon the Ray from the Middle of the Pyra- 
 mid, and that from the Sun, pafling thro" its Vertex, or Point, only make 
 one Line-, and, of confequence, cannot terminate any Thing for the Shadow 
 of the Vertex of that Pyramid. 
 
 When this happens, draw a Line from the Point of Sight P, thro' one of the 
 Angles of the Plan j by which means you will have O Then from O erect a 
 Perpendicular O S, and from the Point of the Pyramid T draw a Parallel to the 
 Bafe, till it cut the Perpendicular O S in the Point V. Draw the Ray of the 
 Sun thro' this Point, and continue it till it cut the Ray O Z in the Point X ; 
 from X draw a Parallel to the Bafe, as far as the Ray of the Middle of the Py- 
 ramid, which will be cut thereby in the Point Y, the Extreme of the Shadow, 
 To Y draw Lines from the Angles .Z and O ; and the Triangles Z Y O will be 
 the Shadow of the Pyramid. 
 
 The like you are to do for the oppofite Face, if it be perpendicular to the 
 Plan ; and the fame Rule will ferve in all Cafes. For Example, if the Point, or 
 Apex, correfpond to the Centre of the Plan, draw a Line from the fame°Cen- 
 ter parallel to the Bafe, and of any Length at Difcretion ; and from the End of 
 the Line, as here from O, draw a Line to the Point of Sight, and proceed as be- 
 fore. Which will be a (landing Rule, whether the Pyramid be view'd in front 
 or fide-wife. And hence you will eafily judge what is to be done, if the Point, 
 or Vertex, correfpond to any other Ray of the middle of the Plan. 
 
 The Walls in the Front of each Figure have their Shadows as already taught 
 in that of the Cube A. 
 
*35 
 
 PERSPECTIVE 
 
 ^ Shadows ^ perforated Obje&s. 
 
 WH E N the Object is fquare, or re&ilinear, Lines muft be drawn 
 from the Foot of the Luminary through all the Angles of the 
 Plane j then from the Middle of the Sun B, draw a Line to the remoteft 
 Angle C, which will cut the Line from A, in the Point D ; through 
 which Point a Line muft be drawn from the Point of Sight, till it meet 
 the laft Line from the Plan F. To find the reft of the Shadows ; draw 
 Parallels to the Bafe BCD, through the Angles GHI; and inafmuch 
 as the Sun illuminates two Sides, or Faces, and makes the Shadow 
 broader, as is (hewn in the firft Figure, where GC and HI are the 
 Diagonal of the fquare Pieces; where thefe Lines drawn through GC 
 and H I cut the Line A, a Line muft be drawn to the Point of Sight E; 
 and you will have the whole Projection, or Shadow of the Object. 
 
 Jf it be a round Object:, as reprefented in the fecond Figure, a Cir- 
 cle muft be defcrib'd, according to the Rule given for Arches in Pag. 
 62, 63. by erecting of Perpendiculars, &c. And when the Circle is 
 form'd, and its Thickneffes given, from the Bottom of thofe Perpendi- 
 culars, Parallels to the Bafe muft be drawn; as here K L. Then tak- 
 ing L, which is the Parallel of the Middle of the Circle, for the Foot 
 of the Luminary, from the Middle of the Sun, M, draw a Line paf- 
 fing over the Circle N, and continue it till it cuts the Parallel L in the 
 Point O ; which will be the Extremity of the Shadow. The Vacuity, 
 or Aperture, of the Rotundo, is found by drawing a Parallel to N 6 
 from the Point P, which is the Top of the Object oppofite to the Sun, 
 till it cut the Line I O. The reft of the Rotundo will be found by 
 drawing another little Parallel to N O from the Point R, which will 
 give S. The reft of the round Object is found by drawing Parallels to 
 N O, through all the Points of the Circle of Perpendiculars, which are 
 to be continued till they cut the Parallels to the Bafe-Linej as is here 
 done for that of the Middle, L O. I could eafily mark them all with 
 Points, but lam too great an Enemy to Confufion. 
 
P R A C T I C A L. 
 
 I 3S 
 
136 
 
 PERSPECTIVE 
 
 ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ StV ^ ^ ^ ^ ^ ^ ^ ^ ^ *?? ^ 
 
 Shadows ajfume the Form of the Planes they are 
 
 cafl upon. 
 
 HITHERTO we have confider'd Shadows on an even Plane ; being fecure 
 that a Perfon, who understands fuch, will find no Difficulty in the .Practice 
 of the reft which follow: For the Rule is the fame in all ; and one fingle Inftruc^ 
 tion will fufHce to (hew how Shadows fink and rife according as their Planes are. 
 
 To mew that thefe Shadows are form'd by the fame Rule as the preceding 
 Ones, draw a Line from the Foot of the Luminary A, through the Plan of the 
 Door B •, and another from the Sun C, over the Top of the Door D thefe 
 Lines will interfed each other, tho' without the Limits of our Page, and give the 
 Extremity of the Shadow as already is obferv'd of the others. But the Wall 
 E preventing the Line A B from being continued as it mould be* if the Plane 
 were even, obliges it to rife, as we fee in F G: For this reafon the .Sun's Ray, 
 which mould proceed to meet the Line A B, cuts it on the Wall in the Point G, 
 and there marks the Form or Shadow of the Door •, the Top whereof is drawn 
 to the Point of Sight H. 
 
 The Shadow of the Object K is caft in all its Length K I, and paffes over 
 that other L : And it is to be obferv'd, that the Shadow ftill preferves its 
 Length, though it meets with fomething between the two : and that the Shadow 
 which paffes over any thing aflumes the Figure of the fame thing ; as here the 
 Shadow of M and N, take the Form of the Object L. 
 
 Though I have made the Sun r 0 appear in all my Figures, it muft not be ima- 
 gin'd that he is fo near the Obj cts. My Intention was to fhew that the Rays 
 proceed from him when at fuch a Height, tho' far without the Limits of the Piece. 
 As in this fecond Figure, which yet has the Line for the Foat of the Sun A B* 
 and that of the Rays of the Sun G ; by reafon thofe are always required for finding 
 the Extremities of the Shadow. 
 
 The Shadow of the Object O is found by continuing the Line A B, and 
 making it rife over the Steps, and againft the Wall, till cut by the Ray in the 
 Point S, by the Rays paffing over the Corner of theObje£; and from S draw- 
 ing a Line to the Point of Sight T. 
 
 To find the Shadow of the Object P it muft be remenber'd, which has al- 
 ready been obferv'd, that the Foot of the Light muft always be fuppos'd on the 
 Plan where the Object is placed. Accordingly, the Ray G cutting the little Line 
 \ B, mews how far the Shadow of the little Object, P, muft go, to be thence 
 Irawn to the Point of Sight T. 
 
 The Object V cafts its Shadow all along, tho* in i:s way it defcends into a 
 Ditch. 5 7 
 
 The Shadow of the Wall, R, is found by the fame Rule as the reft 5 as ap- 
 pears from the Lines A B> and the Ray C. 4 
 
137 
 
 PERSPECTIVE 
 
 To find the Shadows of Objects broader at Top than 
 
 at Bottom. 
 
 WHEN the Projection or Shadow of a Figure is required, 
 whofe Top is broader or wider than the Bottom, as in 
 the two adjoining Figures, the ufual Method is, to make a Plan, 
 and draw Perpendiculars, as BA, BA, from the fame. The 
 Plan finifh'd, a Line muft be drawn underneath the Sun, as 
 already mentioned, and Parallels to this Line be drawn from all 
 the Angles of the Plan. Then a Line to be drawn from the 
 SunC, over one of the Angles of the Object, as D, till it cut 
 the Line of the Plan of the fame Angle A, fo as to form the 
 Line DF. Another Line is to be drawn over the Angle A, 
 till it interfe&s the Line B A in the Point F. Then drawing 
 Lines from E and F to the Point of Sight, you will have the 
 Shadow of the Square of the ^p of the Object. Laftly, 
 drawing Lines from the Point of the Figure H, to the Points 
 F and L, you will have the Shadow of the whole Figure, 
 which is a Pyramid inverted. 
 
 'Tis evident that the Projection or Shadow of the Crofs un- 
 derneath is performed after the fame Manner, which it would 
 be unneeeflary to repeat. 3 
 
1 N t\ <z , 137 
 
To find the Shadows of Object r s fufpended from the 
 
 Ground. 
 
 THE Method is rendered very eafy by that juft laid down, all you have to 
 do in each being to find the Plan, and from that Plan to draw Parallels to 
 the Line from under the San, through all the Angles, and then, from the fame 
 Angles of the Objects fufpended in the Air, to draw other Lines, cutting thofe 
 drawn from the Plan by which Means you will find the Extremes of the Sha- 
 dows, as already mentioned under the preceding Figures. 
 
 Iam clearly perfuaded, therefore, that my Reader would eafily conceive any 
 Thing that I can do as to Shadows made by the Sun, without any farther Expla- 
 nation of the Figures here annexed, as being all intelligible, and performed by 
 the Rules already taught. 
 
 However, as every Thing has fomething particular in it, it may not be im- 
 proper to take Notice thereof, that there may be nothing but what is eafily under- 
 flood. 
 
 I obferve then, that in the firft Figure the Plan A BCD is alone made ufe of, 
 to find the Shadows of the Objects EF, by Reafon they are both on the fame 
 Line, and of the fame Height. 
 
 In the fecond, it muft be obferved, that the Piece of Wood G calling its Sha- 
 dow on the "Wall H, that Shadow makes the fame Figure at the Cornice I under- 
 neath. And the fame is bbfervable of the Stick K, raifed againft the Wall H. 
 
 To find the Shadow of the Board L, the Rule already delivered for Objects 
 broader at Top than at Bottom, muft be remembered for having drawn the 
 Perpendicular M, where it cuts the Ray NO, you muft draw the Line from 
 underneath the Sun MP. Then from the Board L, drawing a Line to cut the 
 Line MP, the Point of Interferon will be the Extremity of the Shadow. 
 
 The Shadow of the Globe or Ball Qjs likewife found by letting fall two 
 Perpendiculars, of which the Plan is to be formed, then through the Center of 
 this Plan drawing a Line from beneath the Sun, R, and a Tangent from the 
 Sun, as QS, till it cut the Line R in the Point T, and laftly, another, as V, 
 cutting the fame Line R : This Interval T V will give the Extent of the Shadow 
 of the Ball. 2 
 
*39 
 
 PERSPECTIVE 
 
 To find the Sun's Shadow for human Figures. 
 
 THE Shadow of thefe Figures is found by the fame Methods as thofe of 
 other Bodies, that is, by Parallels both from underneath the Figure, and 
 from the Sun •, with this Difference only, that the Shadow of other Bodies, or 
 Objects, is found by Means of their Plan, whereas Figures have none. But in 
 Lieu of fuch Plans, a Line muft be drawn underneath the Figure, and on this 
 Line, the feveral remarkable Points of the Figure to be let fall perpendicularly, 
 which Line is to ferve as a Plan. 
 
 For an Example, in a Figure naked, or drejfed without a Cloak or Gown, as the 
 firft Figure hereto adjoining, with its Back towards us i from under its Feet, 
 as A, draw a Line to the Point of Sight B, and to this Line A B draw occult 
 Lines from all the Points that may contribute to the true Shadow 5 thus from the 
 Hand C, let fall a Perpendicular, cutting the Line A B in the Point D, and 
 from the Elbow E let fall another to the Point F, and a third from the 
 Head G to the Point H, and from all thefe Points DFH, as alfo from the 
 End of the Staff I, draw Parallels to the Bafe Line. 
 
 Then, having determined the Height of the Sun, a Line muft be drawn from 
 the fame, as K, paffing over the Edge of the Hat G, and continued till it cut 
 the Line H in the Point L, which will be the Extreme of the Shadow. And 
 again, from the hind Edge of the Hat M, draw a Parallel to KGL, till it like- 
 wife cut the Line H in the Point N, thefe two Points N and L, will be the Sha- 
 dow of the Hat. A third Parallel muft be drawn thro' the Point C, till it cut 
 the Line D in the Point O, this Point O will be the Shadow of the Hand that 
 holds the Staff; drawing therefore a Line from the Point O, to the Point I, 
 the Line O I will be the Shadow of the Staff. A fourth Parallel to be drawn 
 thro' the Point E, which cutting Fin P, will be the Shadow of the Elbow. The 
 fame do from all the other Parts, as the Knees, the Feet, &c. Thefe feveral 
 Points connected together, give the Shadow of the whole Figure. The Shadow 
 of the little Figure Q^is done by the fame Method. I have not expreffed all 
 the Points and Parallels therein, in order to avoid Confufion. 
 
 To find the Shadows of Figures clothed in long Garments ; draw a Line from un- 
 der their Feet to the Point of Sight, as here the Line S R, and thro' the Bot- 
 tom of the Robe draw two Parallels to the Bafe Line, each Way, as the Lines T 
 and V, and between the two, another Line X for the Middle of the Figure. Then 
 from the Top of the Head draw a Line Y, for the Ray of the Sun, to be con- 
 tinued till it cut the Line X in the Point Z ; which Point Z will be the Extreme 
 where the Shadow is to terminate. The reft of the Shadow will be drawn be- 
 tween the two Parallels T and V. If any Thing comes over them, as the two 
 Plaits, or Folds, -f* and *, they muft be drawn by Parallels to Y Z, till they cut 
 the Ray V. And thus f gives the Shadow of. the Elbow, and * that of the Folds 
 of the Gown. 
 
140 
 
 PERSPECTIVE 
 
 An eafy Method of finding the Shadow of the Sun. 
 
 WE R E I here to add the Shadows of all the Objects that might be given, 
 it would be a Work without End, Objects being multipliable to Infinity ; 
 In Effect, befides the Greatnefs of their Number, each particular one might 
 furnifh out a whole Book, as being capable to be turned, inclined, and difpofed 
 in various Manners, each of which has its feveral Shadows. But the Labour 
 would be ufelefs, inafmuch as every Body will be prepared to make any at Plea- 
 fure, provided he be Matter of two or three Rules already laid down for the Sha- 
 dows of Objects taken from the Sun, two Kinds of Lines being fhewn to contain 
 the Means for finding all Shadows imaginable •, one of the Lines coming from 
 under the Sun, and paffing over the Plan, and the other proceeding from the Sun 
 kfelf, and paffing over the Object, and cutting the former Line in the Place where 
 the Shadow is to terminate. But as thefe Lines are to be all Parallels, that is, 
 thofe from under the Sun parallel to each other, and thofe from the Sun likewife 
 parallel among themfelves, it may be necefiary to give a Method of drawing 
 them with Expedition and Advantage. 
 
 I have already fhewn how to draw Parallels to the Bafe by Means of a fquare 
 Board, as A, and a Ruler B, which fame may ferve to draw the Lines from un- 
 der the Sun, when found directly over the Face of the Object, as the Line C D. 
 But where he illuminates the Object from an Angle, another Inftrument muft be 
 ufed, as that here reprefented E, which is a Rule fattened to the End of ano- 
 ther Piece of Wood, well fquared, and grooved quite through, fo as the Rule 
 F G may be moveable therein with fome Force, and that having taken an in- 
 clined Line, as HD, another Parallel thereto I K, may be taken by Means of this 
 Bevel, which is the Name the Workmen give this moveable Square E FG. This 
 Inftrument fhortens the Work exceedingly, when Shadows are to be made by the 
 Sun, on which Occafion there is no Line of any Inclination whatever, but Paral- 
 lels will be required thereto. The Application will evince its Ufefulnefs. For 
 Shadows by the Candle or Torch, it is of no Importance, by Reafon all the 
 Lines are there drawn from a Center. 
 
141 
 
 PERSPECTIVE 
 
 Shadows from a Torch, Flambeau, Candle, 
 
 and Lamp. 
 
 IT has been already obferved, that there are two Points requir'd for the find- 
 ing of Shadows ; the one the Foot of the Flambeau, Candle, Lamp, &c. 
 which is always found on the Plane where the Object is placed, the other in the 
 Fire, or Flame of thofe Luminaries. 
 
 From the firft Point, which is the Foot of the Flambeau, or beneath the Lamp, 
 &c. Lines muft be drawn through all the Angles of the Plan of the Object, 
 whofe Shadow is required •, and the fecond Point gives other Rays, which paf- 
 fing through the Angles of thofe Objects, interfect the former Lines, and mew 
 where the Shadow is to terminate. I mail illuftrate this by an Example, wherein 
 the fame Letters fhall be ufed for all the three Luminaries, from which it will 
 readily appear, that the Practice is the fame in all. With this only Difference, 
 that the Foot of the Flambeau or Torch actually ftands on the Plane, and that 
 the others are only conceived to do fo. 
 
 I add then, that if the Shadows B, of the Cubes A be required, Lines muft 
 be drawn from the Point O, which is the Foot of the Luminary, thro* all the 
 Angles of the Plans of thofe Cubes, asOD, OE, OF, OG, and then from 
 the Point C, which is the Light or Fire of the Luminaries, other Lines muft be 
 drawn through the Angles of the Objects, and continued till they interfect the 
 former Lines from O. 
 
 Thus, having drawn aLinefrom the Point O, through the Angle of the Plan 
 D, drawing another Line from C, through the correfpondent Angle of the Ob- 
 ject P, this latter Line being continued, will cut the firft from the Angle D in 
 the Point H, which Point will be the Shadow of that Angle D P. From the fame 
 Point C, do the fame for all the other Angles of the Plan in the Points HIKL, 
 which Points being connected by right Lines, give the Shadow of the Cubes, 
 as in the three Figures. From this Inftance it readily appears, that the Method 
 is the fame in one as another. 
 
 In the following Page we (hall (hew how to find the Bottoms or Feet of Candles 
 and Lamps. 2 
 
142 
 
 PERSPECTIVE 
 
 Of the Foot of the Luminary, 
 
 SI N C "E the Method of finding Shadows by the Torch, Candle, and Lamp is 
 the fame in all, as already obferved, there is no Occafion for diftinguifhing 
 between them in any of the following Rules. For when I put a Candle, a Torch 
 or a Lamp might as well be put in its Place, the Light of one having the fame 
 Effect as that of any of the reft. So that for the future, we mall ufe the Word 
 Light indifferently for all three. 
 
 As to the Foot of thefe Luminaries, which muft (land on the Plans where the 
 Objects are placed, it is found after the following Method. 
 
 A lighted Torch being in a Chamber, whether in a Corner, at a Side, or in 
 the Middle thereof (Inftances of each hereof we have in the erected Figure) we 
 muft confider all the Parts of the Room, viz. the Cieling, Floor, Sides, as 
 having Points wherein the Foot of the Luminary may be placed,, and that from 
 thefe Points Lines may be drawn thro* all the Angles of the Plan of the Object 
 whofe Shadow is required, as fhall be expreffed more at large in the following 
 Page, my chief Defign in this being to fhew how that Point is to be found. 
 The Torch then being placed in A, this Point A is the Foot of the Light, and 
 B the Light or Fire of the Torch, which Fire is there fuppofed immoveable, 
 tho' the Foot may be found on all Sides. 
 
 To find the Foot of the Luminary on the Side of the Wall C, draw a Parallel 
 to the Bafe Line, from the Point A, till it cut the Ray D E in the Point F, from 
 which' Point erect a Perpendicular F G. Then from the Point B r which is the 
 Fire, draw another Parallel to the Bife Line, till it cut F G in the Point PL 
 which H will be the Foot of the Luminary ; as if the Torch were laid all along 
 its Fire ftill remaining in the Point B. 
 
 To find the Foot of the fame Luminary on the Cieling, from the Point G 
 draw a Parallel to the Bafe Line, as GI, and from the Point B erect a Perpen- 
 dicular to the fame GI ; this gives the Point K for the Foot of the Luminary, 
 as if the Torch were turned upfidedown. 
 
 To find it on the other Side of the Room, the fame Method muft be obferv'd 
 as for the Side C, and you will have the Point L. 
 
 To find the Foot of the Luminary in the Middle of the Room, draw a Line 
 from the Point H, to the Point of Sight, till it cut the Perpendicular E in the 
 Point M. Then from M draw a Parallel to the Bafe Line, interfering the Torch 
 in the Point N ; this Point will be the Foot of the Luminary for the Middle of 
 the Room. 
 
 The Foot of a Candle is found after the fame Manner as that of a Torch, ta- 
 king the Middle of the Foot of the Candleftick for the Foot of the Luminary 
 but when it is a Plate, or an Arm fixed in the Wall, 'tis this Arm or Branch, 
 that determines the Line where the Foot of the Luminary mall be. For In- 
 ftance, in the Plate P, through the Arm draw a Perpendicular to the Bale 
 Line as RS. Then from the Fire T, draw a little Parallel to the Bafe Line, 
 which cutting RS in the Point V, gives the Foot of the Luminary for that Side. 
 The Point X will be the Foot for the Floor j the Point Y for the Cieling, and 
 Z for the front Wall of the Room. 
 
 As to Lamps, 'tis the Place they are hung in that determines the Foot, as 
 here the Character*; from which Place a Parallel to the Bafe Line is drawn as 
 far as the firft Ray, &c. The reft the fame as in the Torch or Candle, 
 
143 PERSPECTIVE 
 
 7* ) find the Shadows of a Torch on ail the Sides of a Room. 
 
 THE Shadows taken from the Sun always tend towards the Earth, by Rea- 
 fon that Star never gives us any of its Light, but when above our Hori- 
 zon, and of Confequence raifed above our ordinary Objects, and fo occafioning 
 their Shadows to defcend. But the Cafe is different in Torches, Candles, and 
 Lamps, which may be placed either above, below, or afide of Objects, and 
 therefore may yield Shadows on all Sider, as we are now to (hew. 
 
 The preceding Figure will help to find the Shadows of Objects difpofed on 
 all Sides of the Room, for having found the Foot of the Luminary as already 
 directed, there is nothing difficult behind, the Method throughout being the 
 fame with that for the Cube in Pag. 141, to which Recourfe may be had. How- 
 ever, to fave you the Trouble of going fo far back, I (hall here obferve, that to 
 find the Shadow of the Table the Torch is placed in, you muft draw Lines from 
 the Foot of the Torch A, thro' all the Feet of the Table C. Then from the 
 Point of Light B, draw Lines over all the Points of the Table I, I, I, &c. till 
 they interfect the Rays C, C, fcfr. in the Points O, O, which will give the 
 Bounds of the Shadow of the Table. 
 
 The Shadow of the Object D is found by drawing Lines from the Point A, 
 through all the Angles of the Plan, as far as the Angle of the Wall D, and from 
 that Angle raifing them perpendicularly. Then from the Point of the Light 
 B, drawing Lines over the Object D, and obferving the Angles correfponding 
 to the Lines of the Plan, you will have the Shadow F of the Object D. 
 
 The Shadows of all the other Pieces are found after the fame Manner : So that 
 all we fhall here note, is the Foot of the Luminary, the Fire itfelf being fup- 
 pofed to be fixed in the Point B. 
 
 For finding the Shadow of Figure G, the Point L is the Foot of the Luminary. 
 To find the Shadow of Figure N, the Point H is the Foot of the Luminary. 
 To find the Shadows of the Figures I and M, the Point K is the Foot of the 
 Luminary. 
 
 For the fecond Figure^ having found the Foot of the Luminary on all the Sides 
 of a Room, as directed in the preceding Page, the Shadows of Objects are found 
 in any Place at Pleafure by the Rule now delivered. For Example, having found 
 the Foot of the Luminary Q» and its Fire P, if you would have the Shadow of 
 the Object R, draw Rays from -the Point Q, over the Plan of Object, continuing 
 them indefinitely. But inafmuch as they meet with the Wall, or Side of the 
 Room T, in the Places S and S, where they meet the fame, they muft all be 
 raifed then drawing other Lines from P, over the fame Object R, they will 
 cut thofe of the Plan, and mark the Place of the Shadow upon each, obferving 
 that the Angles refer to the Lines drawn from the Plan. 
 
 This Method is fo univerfal, that a Man who only knows how to take the 
 Shadow of a Cube, will make no Difficulty of finding the Shadow of any other 
 Object whatever. For this Reafon, having defcribed that Method for [the Cube 
 in Pag. 141. and added this above, which in Effect is the fame I imagine I have 
 given abundant Inftruction for the managing of all Shadows, and may be excufed 
 from repeating the fame in the feveral Figures following. Wherein all I (hall 
 note, is the Point for the Foot of the Luminary. 
 
 To find the Shadow of the Figure V, the Point X is the Foot of the Luminary. 
 
 To find the Shadow of Figure Y, the Point Z is the Foot of the Luminary. 
 
 To find the Shadow of the Figure +, the Point C5? is the Foot of the Lumi- 
 nary. P is the Fire, or Light itfelf, for all the Objects in the fecond Figure. 
 
144 
 
 PERSPECTIVE 
 
 The Shadow of an ereB and inverted Pyramid 
 
 by Torch-light. 
 
 npHE Shadow of an erect Pyramid by Torch-light, falls as it .would 
 JL by the Light of the Sun, and in both Cafes there is but one Line, 
 wherein the vertical Point of the Pyramid will be found. Upon the 
 Plane BCDEdraw the Diagonals E B, and DC, through the central 
 Point F, raife the Perpendicular FA, and from the four Points BCDE, 
 draw Lines to the Point A, and the Pyramid will be erected. Then, to 
 find its Shadow, draw an indefinite Line from the Bafis G, of the illumi- 
 nating Body, pafling through F, and from the central Flame of the 
 Torch H draw another Line over the Vertex of the Pyramid in the Line 
 G F, till it cut the Point I, which Point will limit the Shadow of the 
 Pyramid. Laftly, draw a Line from C to I, and another from E to I, 
 and the Triangle C IE will be the Shadow of the Pyramid. 
 
 To gain the Shadow of an inverted Pyramid, draw perpendicular Lines 
 from the angular Points of its Bafe, and form the fubjacent Plane by 
 Means thereof, after the Manner directed for the Sun, Pag. 138. And 
 from all the Angle of this Plane, draw Lines to the Bafe of the Torch 
 G, then from H, the central Point of the Flame draw other Lines, touch- 
 ing all the Angles of the Bafe of the inverted Pyramid, and dividing thofe 
 of the Plane, whereby the Shadow will be defined ; as we before obferved, 
 in other Inftru&ions relating to the Torch, 
 
 M & te. & ft ^ 4fc ft ?\tX ft ^ 4£ ft .ft ft ft ft ft ft 
 
 The Shadow of a Crofs. 
 
 WE before considered the Shadow of a Crofs by the Sun, let us now 
 fuppofe the fame Obje6t placed in the Light of a Torch, that we 
 may find the Difference between the two Cafes. The Construction of 
 the latter is obvious enough, particularly if compared with the Method of 
 finding the Plane, delivered in Pag. 137. and the other Directions laid 
 down for Shadows by Torch-light. 2 
 
PRACTICAL. 
 
 144 
 
 '*4 
 
145 
 
 PERSPECTIVE 
 
 To find the Shadows of round Obje&s by Torch-light. 
 
 THERE may feem to be more Difficulty in reprefen ting the Shadows of 
 Globes, Bottles, Drinking- Veflels, and other bellied Objects, by Torch- 
 light, than in thofe of fquare ones, but the Direaions already given will ferve 
 for thefe alfo; for there is nothing more required here, but to reduce Squares 
 to Rounds, as we taught in Pag. 19, 20, 28, 29, and 86. which contain all the 
 neceffary Inflections for giving the Plans of round Objects in Perfpective, 
 whence all other Cafes of that Kind may be eafily underftood. 
 
 We gave in Pag. 138. the Method for finding the Plan of a Ball, and by 
 Means of that Plan, the precife Magnitude of the Shadow by the Sun. But as 
 the Cafe of the Torch differs from that, we mail be a little more particular upon 
 the Ball, becaufe it will facilitate all the other Dire&ions relating to Rounds. 
 
 Having by Means of a Pair of Compaffes, marked out the great Circle of the 
 Ball A, draw its Diameter BC, and below this Circle draw a Line parallel to 0 
 BC, touching the Circle in the Point H. Then from the Extremes of the Dia- 
 meter BC, let fall Perpendiculars upon the Line below, asBD, andCE, and 
 with thefe Points D and E, make a Plan, DEFG, in the ufual Manner, the 
 Diameter whereof, FG, will divide D E at the Point H. And this Plan will 
 ferve to find the Shadow of the Ball A. Now, having drawn from the Bafis of 
 the illuminating Body I, Lines touching this Plane on both Sides, as I K and 
 IL> and another IHM, through the Center of the Plane H, as alfo Lines 
 from the Center of the Flame N, which touching the Ball between A and B, 
 lhall divide the Line IH at the Point M : This Point muft terminate the Sha- 
 dow. To gain the firft Part of this Shadow, draw from the fame Point N, 
 another Line, touching the Fore-part of the Ball, and dividing alfo the Line 
 IH at the Point then the Diftances between Q^and M will be the Length 
 of the Shadow. And for its Breadth, draw from the fame Point N, two Lines 
 touching the Extremes of the Diameter of the Ball Z Z, and dividing the Lines 
 IK at the Point R, and I L at the Point S. Now then, as RS is the Breadth 
 of the Shadow, and QM the Length of it, if the four Points R, S, M, 
 be joined with curve Lines, there will be an Oval formed for the Shadow of the 
 Ball A. 
 
 I have been the larger upon this Shadow, becaufe I judge the Dire&ion given 
 about it alone fufficient for finding the other Shadows of Rounds, as of the Ob- 
 ject V, for Example, which having two unequal Breadths, ought to have a Plan 
 of two Circles. And the Figure X having three, mould have its Plans corre- 
 spond ing^hereto, one for the Neck of the Bottle, another for its Belly, and a 
 third for its Foot ; all which are to be made as thofe for the Ball. 
 
 An Infpection of the Figures will render any farther Explanation of them, 
 unnecefiary. 3, 
 
Pp 2 
 
146 PERSPECTIVE 
 
 Shadows 0/2 fever al parallel Planes. 
 
 THE firft Plane here is the Floor whereon the Chair A ftands; the fecond 
 Plane is the upper Part of the Table, parallel to the firft, and may be 
 either above or below it. There might alfo be more of thefe Planes wherein to 
 find the Foot of the illuminating Body, in order to come at the Shadow of the 
 Object. Suppofe rhe Foot of the illuminating Body to be C, and the Flame B ; 
 from thefe Points C and Bdraw Lines through the upper and under Part of the 
 Object D; which will give the Shadow E upon the Table. 
 
 To find the Shadow of the Chair A, which is placed on the Ground ; determine 
 the Foot of the Luminary on the Table in C, on the Ground : This is clear'd 
 by the Inftructions following. 
 
 From the Point of Diftance, which is here fuppos*d without the Limits of the 
 Paper, draw a Line thro' the Foot of the Table F ; then from the Angle G upon 
 the Table, let fall a Perpendicular, cutting the Line F in the Point H j and from 
 H draw a Parallel to the Bafe H I, which is equal to the upper Part of the Ta- 
 ble, and will direct us to the thing requir'd. For, drawing a Line from the Point 
 of Sight K, through the Foot of the Luminary C, to the Extremity of the Table 
 L ; from the fame Point L, let fall a Perpendicular to H I, which will give the 
 Point M. Then from M draw a Line to the Point of Sight K ; in which Line 
 M K will the Foot of the Luminary be found. To determine the precife Point 
 let fall a Perpendicular from the Point C, which, cutting the Line M K, will give 
 the Point N for the Foot of the Luminary. This Point N thus found, there 
 will be no Difficulty in finding the Shadow of the Chair A the Method being 
 the fame as for the other Objects taught in the preceding Pages : That is, from 
 the Foot of the Luminary N draw Lines through all the Angles of the Plan 
 of the Chair, and other Lines through the upper Part of the Chair, from the 
 Luminary B •, thefe latter by interfering the former exprefs the Bounds of, 
 the Shadow. For the reft the Figure gives fuffieient Directions. 
 
 The fecond Figure is not here added as if there were any particular Circum- 
 fiances different from thofe of the Figure above, but only to put you upon re- 
 collecting what has been already taught, viz. That Objects caft their Shadows 
 differently, according to their different Difpofitions about the Luminary. Thus* 
 the little Objects on the Table project their Shadows this or that way, as the 
 Luminary is on this or that Side •, as is found from the common Rules relating 
 to the Foot of the Luminary, and the Light itfelf. Moft of the Objects here 
 reprefented are broader at the Top than Bottoms; fothat it wiil be neceffaiy. to. 
 make Plans thereof, after the manner already (hewn.. 
 
PERSPECTIVE 
 
 Shadows of Cielings by 'Torch-light. 
 
 **p H ESE Figures are not placed in the Sun's Light, becaufe that Luminary 
 JL is high above all the Objects of the Earth, and confequently can give no 
 Shadow where the illuminating Body is fuppofed to be under the Object. If it 
 be faid, tho' the Sun's Rays enter a Room, yet the Shadows of Bodies continue 
 to appear ; I anfwer, that fuch Shadows are not immediately caufed by the Sun, 
 but the Brightnefs thereof, and that they cannot be reprefented by parallel 
 Lines, as thofe of the Sun, but by Rays iffuing from the fame Center, as thofe 
 of a Torch, taking the reflecting Body for the illuminating Point, and proceed- 
 ing in drawing fuch a Shadow as in the Cafe of a Torch. 
 
 The Directions hitherto given, which turn upon the forming of Plans, and 
 drawing of Lines from the Angles of Objects, to find the Bounds of the Sha- 
 dow, would be too tedious here, and the great Number of Lines necefiary to be 
 drawn, would render the Figure exceeding intricate, on Account of the feveral 
 Beams, Supporters, and Rafters that would occur. This Inconvenience drove 
 me to invent a fhort, eafy, practical Method for the fame Purpofe, without 
 departing from the Rules of Art. 
 
 The Floor being put in Perfpective, as was taught in Pag. 55, and 57. and the 
 illuminating Body fixed, we muft inquire by Means of the Bafis of that Body 
 where the illuminating Point ought to be. To find this Point, when the illumi- 
 nating Body is at B, draw from the Foot of it C, a Parallel to the Bafe DE, 
 till it cut the Ray EFin the Point G, from this Point G, raife a Perpendicu- 
 lar G L, and from the Flame of the Torch B draw a Parallel to DE, dividing 
 the Perpendicular G L at the Point L, and this Point L will give the Place and 
 Length of the Shadow. 
 
 For Example, to find the Shadow of the Band A, from the Point L draw a 
 Line, touching the Vertex of the Angle H, and obferve where this Line L di- 
 vides the firft Rib, as at the Point I, which is the Place of the Shadow's Ending. 
 From this Point draw a Parallel I K, and mark upon the Ribs the Place of the 
 Shadow O. And to find the Shadow of the Space betwixt them, draw another 
 Line from the Point L, touching the Vertex of the Angle of the firft Rib M, which 
 will divide the Angle of the Interval at the Point N. Now then, from the Point 
 N draw a Parallel NP, and you will thence have all the Shadow QJbr the Beam A. 
 
 To find the Shadow of the Joifts, draw a Line from the illuminating Point B, 
 touching the Angle S, and dividing the Bottom of the Entablature at the Point 
 T. Proceed thus with all the other Ribs, and the Shadow will appear to be 
 longer the farther 'tis removed from the luminous Body. Then mark upon one 
 Beam all the Points T, and from the Point of Sight R, draw Lines through each 
 of thefe Points, and then the Shadows of all the other Ribs will fall exactly be- 
 tween the Bands, as we fee in the Points V V. 
 
 The fecond Figure is the fame with the former, and differs from it only in 
 being fhadowed, which would have obfcured the Letters and the fine Lines necef- 
 fary in the other: Only here the Shadow of the Jaumbs of the Gate muft be 
 taken frojn the Foot of the illuminating Body, as in X and Y. 
 
PRACTICAL. 
 
 i47 
 
4 8 
 
 PERSPECTIVE 
 
 "To find the Shadow by the Foot of the Luminary. 
 
 ■j F the Objects be perpendicular to the Bafe Line, and higher than the Flame of 
 the Candle A, we need only draw Lines from the Foot of the Luminary 
 B, thro* the moft advanced Angles of the Objects, e.g. C and D of the Skreen, 
 Fig. I. and others from the Angle of the Wall E. Thefe Lines BC, BD, and 
 BE, give the Place of the Shadow in the Points where the Angles made by the 
 Leaves of the Skreen, meet the Floor as alfo the Return of the Wall in the 
 Point G, from whence Perpendiculars muft be railed, as GR, which will termi- 
 nate the Shadows given by the Candle A. 
 
 The Reafon hereof is, that the Line A B being parallel to the Line CH, D I, 
 K and E L, occafions the Flame, |n what Part foever of the Line A B it be found, 
 whether on high, in the Middle, or below, to give a like Shadow. 
 
 It muft here be obferved, that this Rule only holds good of Objects raifed 
 above the Flame, as thefe are in the prefent Figure. For fuch as (hew their up- 
 per Part, as here the Object M, the preceding Rules take Place s that is, Lines 
 muft be drawn from the Foot and Flame of the Luminary. 
 
 The Shadow doubled. 
 
 WHEN two Luminaries mine on the fame Object, two Shadows muft be pro- 
 duced, each of the Luminaries occafioning its refpective Shadow, and that 
 in Proportion to the Circumftances of the Luminary. If fuch Luminaries, when at 
 equal Diftances be equal, the Shadows themfelves muft be equal ; but if there be 
 any Difproportion, that is, if one of them be a little bigger than the other, or one 
 of them a little nearer the Objeft than the other, the Shadows will be unequal. 
 Thus the Object O being illumined by two Candles, the one near at Hand in 
 P, the other farther off in it is evident, the Shadow of the Candle P will 
 be deeper than that of the Candle Q, as is expreffed in the Figure. 
 
 The Rules for fuch Shadows are the fame with thofe already given both for 
 the Sun and the Torch. 3 
 
149 
 
 PERSPECTIVE 
 
 The Shadows of human Figures of Torch-light. 
 
 IH A V E reafon to hope that the Advice given long ago, 
 not to turn over the Page to a new Figure, before the prece- 
 ding one be well underftood, has been carefully obferv'd. Sup- 
 poling therefore my Reader to have mafter'd what was directed 
 in Pag. 139. for rinding the Shadows of human Figures by 
 the Sun; I have little to add as to thofe in the prefent Plate; 
 the Line drawn under them, which I ufe as a Plan, ferving 
 indifferently in either Cafe. But inafmuch, as the Shadow 
 projected from a Torch is not equal to the Body, as is the Sha- 
 dow projected by the Sun, a farther Confideration muft here 
 be added, viz* that inftead of drawing the Lines parallel to 
 one another, they muft here be all drafon from a Center ; 
 that is, all the Lines drawn over the Plan muft proceed from 
 the Foot of the Luminary A, and thofe over and about the Fi- 
 gure, from the Point of the Flame ; in like manner as for the 
 other Shadows of the Torch; which it would be needlefs here 
 to repeat, the Figure itfelf giving abundant Satisfaction. 
 
PERSPECTIVE 
 
 § efe^? e)6ate ?fe .K? e^.j^s ^.'uQ ?)t.jj3 5$ ^ 
 
 7$^ different Difpofttions and Heights of Shadows 
 
 by Torch-light. 
 
 CHADOWS from the Sun are all caft the fame Way, and have the 
 ^ fame Difpofition ; it being impoffible the Sun mould occafion one 
 Shadow to tend towards the Eaft, and another towards the Weft, at the 
 fame time. True, in different times of the Day it makes this Diffe- 
 rence : but never in one and the fame Hour. 
 
 But the Torch, Candle, and Lamp, have always this Effect j for in 
 what Place foever one of thefe Luminaries be found, provided there be 
 a number of Objects about them, the Shadows will be caft various ways; 
 fome to the Eaft, fome to the Weft, fome to the North, and others to 
 the South, according to the Situation of the Objects around the Lumi- 
 nary; the Foot of which, here reprefented by A, ferves as a common 
 Centre, from which they all proceed ; and the Flame here reprefented 
 by B, fhews where they are to terminate, tho' at different Diftances ; as 
 " the neareft produce the (horteft Shadows, and the remoteft the longeft, 
 
 Tho' in the fecpnd Figure the Luminary be not placed in the Mid- 
 dle, yet the fame Rule obtains, with refpect to the Shadows, as in the 
 former Figure ; being all drawn from the Foot of the Luminary C, and 
 terminated by Lines from the Flame D. 
 
 FINIS. 
 
THE GEfiy CENTER 
 
 I IRRARv