The Practice of Perspective : 
 
 OR, AN EASY 
 
 METHOD 
 
 OF REPRESENTING 
 
 NATURAL OBJECTS 
 
 According to the Ru lb s of A R T. 
 
 Applied and exemplified in all the Variety of Cafes j as Land- 
 skapes, Gardens, Buildings of divers Kinds, their Appendages^ 
 
 PavtSy and Furniture. 
 
 With RULES for the Proportion and Pofition of FIGURES, 
 both in Draught and Relievo* 
 
 Alfo the Manner of conducing the Shadows, produced either by natural or arti- 
 ficial Luminaries ; and Practical Methods of Drawing after Nature, when the 
 Procefs of Rules are not underftood. 
 
 A WORK highly neceflary for 
 
 PAINTERS, 
 
 Engravers, 
 
 Architects, 
 
 Embroiderers, 
 
 Statuaries, 
 Jewellers, 
 
 TaPESTR Y-W ORDERS, 
 
 And others concerned in Designing. 
 
 The Whole illuftrated with One Hundred and Fifty Copper-Plates.. 
 Written in French by a Jesuit of Paris, Tranflated by E. Chambers, 
 Author of Cyclopaedia, or> An Universal Dictionary of Arts and Sciences. 
 
 The FOURTH EDITION. ' 
 
 If you would proceed immediately to the Practice of Perfpective, without, engaging in 
 the intricacies of the Theory ; the Jesuit's Perspective will anfwer your purpofe. 
 
 Wolfius in Element. Mathef. Tom. II. P. 1048. 
 
 LONDON? 
 
 Printed for John Bowles, at the Black Horfe in CornhilU and 
 Carington Bowles, in Paul y s Church-Xara\ 
 [ Price bound Twelve Shillings. ] 
 M DCC LXV, 
 
THE 
 
 PREFACE. 
 
 THE Art of Perspective is moll elegant and agreeable: 
 It affords great entertainment to men of leifure, and is 
 the very foul of painting ; without which a P a i n t e r can 
 never be a matter in his profeflion. It is this muft conduct 
 him in the difpoiitions, heights, and proportions of his fi- 
 gures, buildings, and other objects. It is this muft fhew 
 him what colours are to be deep or faint, vivid or dull ; 
 where each is to be applied 5 what parts to be highly finifhed, 
 and what flightly touched ; where light is to be bellowed, and 
 where diminifhed. In a word, it is this begins and compleats 
 the painting. Without the afliftance of Perspective, the beft 
 matter muft make as many faults as ftrokes ; efpecially in 
 buildings with their enrichments. In which particulars I 
 find fome reputable painters fo greatly defective, that this has 
 been one confiderable motive to my undertaking the following 
 work: Wherein their errors will be fhewn, without naming the 
 authors ; and novices inftru(5led how to avoid the like. The 
 moft confummate matter is tied to the ftri<5t obfervation of 
 thefe rules, on pain of pleafing none but the ignorant: And an 
 indifferent painter may be told this to his comfort, that if he 
 make himfelf a thorough matter of them, he will be able to do 
 wonders. 
 
 The Engraver jn copper can no more excel without Per spec- 
 t iv e, than the painter ; as having every thing to exprefs with 
 the graver that the other performs with his pencil. From Per- 
 spective he muft learn where to lean heavily, and where lightly 
 
 A 2 oa 
 
iv PREFACE, 
 
 on his graver; what ftrokes muft be funk deep, and what foften- 
 ed. And his occafion for this art is more important, as his pieces 
 multiply to a much greater degree than thofe of the painter ; 
 and, if artfully performed, will fpread his praife more : But, if 
 otherwife, his failing will be the more notorious, and each print 
 be a monument of the author's ignorance. 
 
 The Sculptor and Statuary muft here learn the heights 
 both for the high, low, and middle fight j the flopes and incli- 
 nations of buildings, and other bodies ; the angle for the point 
 of fight ; and the proportions and dimenfions of all objects, near 
 and remote. 
 
 By the fame art the Architect muft learn how to make 
 his defigns intelligible in a little compafs : How to raife 
 one part, and leave the other in its plan, to mew the whole 
 conduct and effect of his work. By the way, having mentioned 
 architecture, I muft obferve of how much confequence it is, for 
 fuch as practife Perspective, to underftand the fundamental 
 rules of that fcience ; the fineft pieces of Perspective being 
 thofe of great and magnificent buildings, raifed according to 
 the order of columns ; the beauty whereof depends on their 
 juft meafures and proportions, which muft be reprefented with 
 the greatcft exactnefs, otherwife they will fhock and offend the 
 eye. Ignorance in thefe things is not excufable, conlidering with 
 how much eafe they may be learned in Vitruvius, Vignola, Scamozzi, 
 and fome others. 
 
 To know the orders of columns and their characters, is not 
 enough : A draughts-man mould likewife underftand all the 
 ufual dimenfions of buildings, and the feveral parts ; as doors, 
 windows *, chimneys, &c. how to difpofe them to receive the 
 light to advantage, and that no part may appear maimed, 
 ufelefs, or ill fupported, and that there be a fymmetry and pro- 
 
 * Halfpenny's Practical Architecture, in nmo, price 4 s. illuftrates, by various ufeful 
 tables, the exact meafures and proportions of the five orders of columns, with doors and 
 windows adj ufted to them. 
 
 portion 
 
PREFACE, v 
 
 portion running throughout the whole. Without fuch regu- 
 lation, a piece of Perspective, in which noble flruclures have 
 a place, inftead of pleafing the eye, will offend it. 
 
 Goldsmiths, Embroiderers, Tapestry-makers, Enamel- 
 lers, and even Joiners, and others who have occafion to make 
 defigns, are under the ftridteft obligations to attain the know- 
 ledge of Perspective, if they would be eminent in their pro- 
 feflions. 
 
 Many who defired to improve themfelves by the ftudy of 
 this art, have affured me, that they were difcouraged by the 
 great number of lines which moll authors make ufe of to form, 
 and find the places of their objects. Others have been deterred 
 by numberlefs obfcurities in the rules and operations, and of- 
 ten perplexed from the inftructions not being immediately 
 annexed to the figures. Now thefe complaints have warned 
 me to be more clear and methodical in my initructions, and 
 to place them fronting the copper-plates, fo that the Reader 
 may have both the rule and the example in his eye at 
 once. Through the whole I have accommodated myfelf to 
 the capacity of learners ; not perplexing them with too many 
 demonftrations, nor ufing any words but fuch as may be readily 
 underftood, at leaft in the definitions. With the fame view I 
 have followed the common cuftom of attributing qualities to 
 certain things which really have them not. Thus, in confider- 
 ing diftance, or removal, I have been forced to fay, contrary to 
 my own fentiment, that it is the Pupil which receives the rays 
 from objects, as if they terminate therein ; whereas it is pafl 
 difpute, that vifion is performed on the Retina at the bottom of 
 the eye ; and that the rays only pafs through the pupil in the 
 way thither: Which, to fome people, will appear a new lan- 
 guage, and not eafily to be conceived. However, being affured 
 that fuch a piece of knowledge imported but little to the prac- 
 tice of Perspective, I have attributed to the pupil what really 
 belongs to the bottom of the eye, the proper place of vifion, 
 
 where 
 
vi PREFACE. 
 
 where the images of all objects are formed ; though there are 
 others who refer this to the cryftalline. The Reader who re- 
 quires farther fatisfaction in this point, may confult Aquilfo 
 Scheiner, and Des Cartes, 
 
 Though I have ftrained every nerve to render the fcience 
 eafy, I do not doubt but there are feveral will find fome diffi- 
 culty at the beginning. But whoever can furmount the firft 
 difficulties, may reft allured he will eafily underftand and 
 pracKfe the remaining rules, provided he takes care to matter 
 one rule well before he turn over the leaf to another. The 
 rules, in fome meafure, depend on each other: And a little 
 trouble, at firft, will be abundantly recompensed by the future 
 eafe accruing from it. 
 
 It will appear from the following table, that this work alone 
 fuffices to carry you through all the ftages and degrees of Per- 
 spective, and to perform every kind of draught; having recourfe 
 to the feveral rules, and collating them together, to furnifh out 
 the performance required. No doubt it muft be agreeable to any 
 one, who defires to produce a compofition of his own, to find imme- 
 diately rules that will anfwer his purpofe : His fatisfaction, afiur- 
 edly, muft far tranfcend that of barely copying the defigns of o- 
 thers ; and, in cafe he be obliged to copy any other, he will do it 
 with much more eafe and pleafure, when mafter of thefe 
 rules, in which inftructions are given for every thing that can 
 occur. I take great pleafure in making new defigns, and in- 
 venting new figures ; which I mould have made public, as 
 my predeceftbrs have done, but that I was willing every per- 
 fon mould participate in the pleafure of compofing from his 
 own fancy ; having furnifhed him with all the means requi- 
 fite thereto. Such as chufe to decline that trouble, will meet 
 with defigns enough ready to their hand in Marolois, Vredeman^ 
 UrieJJe, and others, who have fliewn the politenefs of their 
 genius in this way. 
 
PREFACE. vii 
 
 So many fine performances, I doubt, have helped to render 
 many of our painters too lazy to learn to do what they find 
 ready done. All they afpire at is to copy them as well as they 
 can ; which were excufable, did they know how to do it with 
 judgment : But their way is to copy without underftanding the 
 rules of proportion and beauty, or, in other words, the rules of 
 Perspective. And hence it is, that we have often as many 
 different points in a painting, as there are objects, lines, and 
 returns. Some of them will let you fee the bottom of an ob- 
 ject that fliould only ftiew the top ; and others, rather than be 
 defective, will ftiew both. Others again, having feveral figures 
 to ftiew in a painting, will make them all of the fame height : 
 Though fometimes they vouchfafe to difpenfe with that rule, 
 and make thofe in the fore-part lefs than thofe behind, to give 
 room, as they tell us, for the hind figures to be feen : Which is 
 to overturn both art and nature at once. 
 
 As to the order of this work, I have divided it into five parts* 
 In the First are delivered a few definitions, demonftrations, 
 and reafons, which need no great flock of mathematics to be 
 underftood, and yet give a deal of light into the fubject. Thence 
 I proceed to ftiew the nature of the point of fight, points of 
 diftance, accidental points, front point, and fide point; vifual 
 rays, diagonals, parallels, perpendiculars, and bafe line. The 
 previous knowledge of which things is very neceffary to the 
 eafy underftanding the inftructions that follow. In the Second 
 Part * I give the methods of ftiortening and diminifhing plans 
 divers ways ; with feveral forms of pavements, which ordinarily 
 ferve for the foundations of Perfpective Draughts. Having 
 given fufficient inftructions for puking all forts of planes in 
 Perspective, I proceed, in the Third Part "j", to the elevation of 
 divers objects, beginning with the eafieft, which are cubes, and 
 other bodies of feveral fides or faces. Thefe are followed by 
 
 * See Page 19. 
 
 f See Page 42. 
 
 walls, 
 
PREFACE. 
 
 walls, doors, windows, cielings, vaults, and Hair-cafes of divers 
 forms ; all without ornaments, or mouldings, that the rules 
 might be lefs perplexed with a number of lines which fuch 
 enrichments would have rendered neceflary. After mewing 
 all the buildings in their fimplicity and nakednefs, I go on to 
 furnifh them with columns, cornices, and other ornaments, 
 which add a majefty and grace. The houfes all built to the 
 roof, I fhew how to put them in Perspective with variety 
 of coverings : Then proceed to the infides, and give rules for the 
 furniture, moveables, <&c. Thefe are followed by inflructions 
 relating to ftreets, gardens, trees, walks; which are plealing 
 objects, and render the draughts very entertaining. This part is 
 clofed with two or three contrivances for drawing after nature, 
 when the rules of Perspective are not underftood. In the 
 Fourth Part * is given the meafures and proportions of figures, 
 their poftures, fituation, and horizons, both for flat paintings 
 and relievo's. The Fifth and Last Part f confiders natural 
 fhadows, whether projected by the fun, torch, candle, or lamp. 
 
 When the Perspective of a building, garden, range of trees, 
 palifade, or the like intermixed with figures, is intended, I 
 would recommend it to you, to fketch out what relates to the 
 Perspective with a pencil in the firft place; which done, you 
 will proceed with more afiurance to fix the heights of figures, 
 and other circumftances. 
 
 One thing fome people will find to cenfure in this work, 
 namely, That the points of diftance in all my figures are too near 
 the point of fight. But if this be a fault, it is a voluntary one. 
 For my defign being to teach, it was necefiary every thing fhould 
 be fhewn, and the reader led to fee where fb many lines were to 
 terminate ; otherwife he would have been left to his own con- 
 jectures. It is fufficient that I direct the learner to place them 
 farther off ; and even fhew the laws and occafions thereof. Nor 
 can it be fuppofed I mould have fcrupled making them more 
 remote, had not other confiderations prevailed with me : One of 
 
 See Page 122. 
 
 f See Page 129* 
 
 which 
 
PREFACE. ix 
 
 which was, to render the book as fmall, convenient, and cheap 
 as pomble. Had I followed the advice of fome of my friends, I 
 Ihould only have given a fingle inftnj&^n in each leaf ; which 
 would have fwelled the book to about thrice its bulk, without 
 rendering it a whit the more intelligible. 
 
 Some people affedt to conceal the names of the authors they 
 have followed ; and, as has been well obferved of a certain one, 
 pilfer from private perfons what they give to the public. For 
 my own ftiare, I confefs, that having propofed to write a little 
 treatife of Perspective, I was willing to fee as many authors as 
 I could on the fame fubjed ; nor made any fcruple of borrow- 
 ing from any of them what I found to my purpofe, with an 
 intention of making an open reftitution of all my private thefts 
 to the public. The firft writer of any account is George Reich, 
 in the Tenth Chapter of his works. The next, Viclor, a canon of 
 Toul, who gives us a number of good figures, but is too fparing 
 in his inftruaions. After him comes Albert Durer, who has left 
 us fome rules and principles, in the Fourth Book of his Geometry, 
 Then J. Coufin, who has an exprefs Treatife on the Art of Per- 
 spective, wherein are many valuable things. After thefe come 
 Dan Barbaro, Vignola, Serlio, Du Cerceau, Sirigaty, Solomon de Cans, Ma- 
 rolois, Vredement, Urieffe, Guidus Ubaldus, Pietro, Acolty, the Sieur de 
 Vaulizard, the Sieur Def argues, and lately Father Niceron, a Minim: 
 All whom I have read, one after another, and not without ad- 
 miring their great and happy induftry in the fervice of the 
 public ; efteeming it fufficient honour for me to imitate what 
 they have done, and to be the unknown copift of their works. 
 Befides thofe already recited, there are many others whom I 
 have never feen ; which multitude of authors muft 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 ; efpecially as it brings along with it feve- 
 ral new rules and inftruaions, for putting in Perspective any 
 of the objeas our fenfes are ordinarily converfant about ; and, 
 bvconfequence, of truly performing whatever relates to that Art. 
 
 7 ^ a A TABLE 
 
A 
 
 T A B L E 
 
 DIRECTING TO 
 
 The feveral Parts and Members whereof any Perspective 
 Draught is to confift. 
 
 Perspective muft begin with plans, and, of courfe, with 
 fuch as are the moll fimple and eafy; among which is the 
 fquare, or cube. The method of making the plan is Ihewn in 
 page 19, and that of its elevation in page 44, 49. If an angular 
 view be required, its plan is given in page 20, and its elevation 
 in page 50. 
 
 To raife the walls of a houfe, or the palifades of a garden, &c. 
 fee the plans and elevations, page 51, 52. 
 
 Such as require the infide of a hall, or chamber, in a front 
 view, muft take the fame page 52 for the walls ; the following 
 page for the doors ; page 54 for the windows ; and page 77 for 
 the chimney. The pavement they will find in page 31, 32, 33, 
 and 34. The ceiling is Ihewn in page 55, 5$, 5/> and 58. If a 
 door is to be open, you have your inftrucldons in page 53, and 
 the page following gives a window or cafement open. The 
 fame rules are to be obferved when there are two or three ftories 
 over each other, as in page 76. To afcend to thefe ftories, ftair- 
 cafes are furnifhed in page 82, 83, and 84. 
 
 Houfes viewed on the infide are ufually feen furnhhed with 
 moveables ; moft kinds whereof are Ihewn in page 96-103. The 
 proportions of figures to be placed therein are found in page 122, 
 123, 124, 125. 
 
 To fhew the infide of a church, the plan muft be put in per- 
 fpective, according to the inftruclions in page 37, or 41. The 
 walls to be raifed, from page 51. The windows are conftrucled 
 by the fame rules as the arches of page 62, or 54. Pillars and pi- 
 lafters are to be taken from page 48. Columns from 87. A vault, 
 or vaults, from page 68—72. And a dome, or cupola, from 
 page 74, 75*. To enrich it with cornices, mouldings, and other or- 
 naments, have recourfe to page 88 — 92. For altars, to page 104. 
 
 For outfides of buildings ; The doors and windows are per- 
 formed as in the infides, fee page 53, 5-4, and 106. When raifed 
 
 a 2 to 
 
 A Cube <view*d 
 in Front, and 
 Angle-wife, 
 
 Walls and Pa* 
 lifades. 
 
 Infide of a Room, 
 The Walls. 
 Doors. Windows, 
 Chimney. Pavemen 
 Ceiling, 
 
 Stair-cafe, 
 Moveables. 
 
 Infide of a 
 Church, 
 
 Windows. 
 
 Filajlcrs. 
 
 Columns* 
 
 Vault. 
 
 Dutne. 
 
 Cornices and 
 
 Mouldings. 
 
 Altars. 
 
 Outfides of 
 
 Bundins. 
 
Xll 
 
 A 
 
 B L E, &c. 
 
 Cbrnke. 
 Galleries. 
 
 Street, 
 
 Houfes far off '< 
 Pyramid, 
 
 Buildings 
 viewed by the 
 Angle. 
 
 Gardens. 
 
 Arbour.-. 
 
 Pahfades. 
 
 Alleys of Trees, 
 fountains. 
 
 Steps. 
 
 Shops. 
 
 tinxes. 
 
 i theatres. 
 
 fe tifuatians. 
 
 Shadows. 
 
 to the proper height, the method of roofing and covering them 
 will be found in page 107, 108. And if a cornice or other orna- 
 ments be required, you have them in page 88 — 92. Arched gal- 
 leries, both within and without fide, are fliewn in page 63, 66, 
 and 67. 
 
 If a whole ftreet be required, you mull multiply the houfes 
 on either fide, as in page 10^. When houfes are made pretty 
 deep within the draught, fee page no. In large fquares, &c. 
 a pyramid may be erected, as in page 144. Or fome ftatue, fi- 
 gure, or a pedeftal, as in page 91, and 124. 
 
 When a building is to be viewed by the angle, you may take 
 its plan from page 19, 30, and nr. and manage the elevation as 
 taught in page 50, and i i i. which give rules for doors and win- 
 dows therein. 
 
 Gardens in perfpective are exceeding agreeable. Their plans are 
 to be made as in page 35, 38, or 113. If arbours be required, you 
 are fupplied from page 60, or 61, If palifades, look to page 51, 
 and 52. And if you prefer a grove, thicket, or walk planted with 
 trees, page 1 12 furnimes variety of each. If fountains, or jets d'eau 
 be wanted, page 29 gives a bafon, and its elevation is perform- 
 ed as in page 73. For fquares, or beds, fee page 35, or 38. For 
 polygons, 45, or 46. For placing ftatues, or figures in a garden, 
 take the meafures from page 122, or 125. For grotto's, or 
 niches, fee page 74. For an afcent out of one garden into an- 
 other, you have divers forms of fteps in page 78, 79, 80, 81. In 
 fine, you are at liberty to chufe whatever pleafes your fancy, 
 and may range them all in the fame piece, provided you avoid 
 confufion, and obferve the due fymmetry and proportions. 
 
 If you would have open fhops, without any fixtures, you are 
 furniftied in page 55. If you require them fitted up with draw- 
 ers, boxes, &c. look to page 95, and 105. 
 
 Amphitheatres were antiently of more ufe in paintings than 
 at prefen t, for which reafon I have chofe to omit them : And 
 yet lhift might be made, by taking the plan in page 29, and add- 
 ing more circles, according to the number of ftories intended. 
 To raife the ftories, you are to ufe the line of elevation in page 75. 
 
 For fortifications, you have the method of diminifhing their 
 plans in page 39, and the method of railing- them in page 1 14. 
 
 To give the lhadows to bodies of all kinds, both thofe occa- 
 sioned by the fun, candle, and torch, is fhewn from page 129, 
 to the end of the book. 
 
 See particulars in the following Table of Contents. 
 
 THE 
 
THE 
 
 CO N TENTS. 
 
 M 
 
 R. Hodg fin's Theory of Perfpeclive, 
 
 Page i 
 
 PARTI. 
 
 Shewing the Definitions and Principles 
 of Perfpective. 
 
 DEfinitions, names, and terms of the 
 points, lines, and figures ufed in the 
 following work i 
 Sequel of the definitions, names and terms 2 
 Methods of defer ibing the lines and figures 3 
 Methods of defcribing the figures 4 
 Of circular polygons ^ which are figures of 
 fever al angles infer ibed in circles ib. 
 Of the vifuat rays 5 
 Why a piece of perfpetlive is feen better 
 with one eye than with two ib. 
 Firjl definition 6 
 Second^ third, and fourth definitions 7 
 Why objecls appear the nearer each other, 
 as they are more remote from the eye 8 
 Why objecls appear the fmaller as they are 
 at the greater aifiance 9 
 The obfevvation of the former page applied 
 to praclice 1 o 
 
 Of the horizon 1 1 
 
 Of the t err eft rial line 1 2 
 
 Of the point of fight ib. 
 Of the points of diftance ib. 
 Of the accidental points ib. 
 Of the point of the front, and fide point 13 
 Of the vifual rays 1 4 
 
 Of the diagonals and their feUicns ib. 
 Of the diftance) or removal 1 5 
 
 Obfervation I. Relating to the fide-point 16 
 
 Obfervat.'ll. Of the depths or hollowings ib. 
 
 Obfervat. III. Of the meafures upon the 
 bafe 1 7 
 
 Obfervat. IV. Of the bafe-line, and a Jingle 
 point of di fiance ib. 
 
 Obfervat. V. Not to deceive one's f elf in 
 the meafures ib. 
 
 Obfervat. VI. Of a Jingle point of dif- 
 tance 1 8 
 
 Obfervat. VII. How to perform without 
 making life of the diagonal ib. 
 
 Obfervat. VIII. Other methods of Jhorten- 
 ing and diminifioing ib, 
 
 PART II. 
 
 Shewing the Method of putting Planes 
 in Perfpeftive. 
 
 OF planes viewed direclly, or in front 19 
 Planes viewed obliquely, or fide -wife 20 
 To find the perfpetlive appearance of a 
 
 21 
 22 
 
 2 3 
 24 
 
 25 
 26 
 
 ib. 
 
 27 
 
 ib. 
 
 28 
 29 
 
 triangle 
 — a pentagon, or five-angle 
 
 an hexagon, or Jix-angle 
 
 an heptagon, or fept-angle 
 
 an oclagon, or eight- angle 
 
 Another method, for the oclagon 
 Another method for 'the hexagon 
 Of the double oclagon 
 Of the double hexagon 
 T 0 exhibit the perfpetlive of a circle 
 a double circle 
 
 The plan of a.fquare viewed angle-wife 30 
 A pavement of ft ones viewed by the angle 31 
 1 A pavt- 
 
xiv CONTENTS, 
 
 A p/zvetnent of fquares encompajjed with a 
 lift* or fillet page 31 
 
 Pavements viewed angle-wife encompajfed 
 with a band) or fillet . 32 
 
 Pavements of fquares viewed in front en- 
 compajfed with bands, or fillets, whofe 
 fquares are divided by the angle ib. 
 Pavement of fquares viewed angle-wife, 
 with chains of fquares in front 3 3 
 Pavement of fquares. in front, with chains 
 of fquares angle- wife . ib. 
 
 Pavement of oclagons, intermixed with 
 fquares 34 
 A pavement of Jingle fquares viewed in 
 front y ib. 
 
 Plan of a garden in perfpeclive 3 5 
 
 Plan of a building in perfpeclive 36 
 Plan of a church in perfpeclive 37 
 Plan of a houfe with a garden 3 8 
 
 Plan of a fortification in perfpeclive 39 
 An irregular plan in perfpeclive 40 
 The plan of a church in perfpeclive 41 
 
 PART III. 
 
 Rules for Elevations. 
 
 TIReliminary inftruclions neceffary to the 
 *• following methods 42 
 Qf the line of elevation, ferving to give 
 the heights of all kinds of objetls in all 
 parts of the plan 43 
 $0 exhibit the elevation of a cube in per- 
 fpeclive 44 
 To find the elevation of a triangle 45 
 ' of a pentagon ib. 
 
 ■ of the hexagon ib. 
 
 ~= of the heptagon 46 
 
 n of the otlagon ib. 
 
 A double crojs in ptrfpetlive 47 
 d ft one fluted, or channeled ft ar- wife, in 
 perfpeclive ib. 
 To exhibit pilafters in perfpeclive 4 8 
 
 To exhibit pilafters viewed by the angle ib. 
 Effecl of the difference of horizons 40 
 fi!evation of objetls viewed by the angle 50 
 To raife objetls to any height, and remove 
 them to any diftance at pleafure 5 1 
 
 Walls viewed in front page 52 
 
 Walls viewed by the angle ib. 
 To place a door in any part of a wall at 
 
 pleafure ■ £3 
 To dra w windows, in perfpeclive 54 
 Of cielings 55 
 The cielings of two ftories Jhewn in per- 
 fpeclive 56 
 Other dijpofitions of cielings in perfpec- 
 
 tive '■ £j 
 
 Circular gates and arches viewed direclly 
 
 in the front, or partly on the fide * 59 
 To defcribe circular arches over pilafters 60 
 The Gothic-arch, or afch'in the third 
 
 point ib. 
 Sequel of the former figure . 61 
 To defcribe and put in perfpeclive femicir- 
 
 cular arches and doors . 62 
 To defcribe and put in perfpeclive double 
 
 arches and gates, that is, fuch as Jhew 
 
 their thickneffes 63 
 Another method for defcribing circular 
 
 arches 64 
 Arches viewed obliquely in perfpeclive ib. 
 T 0 exhibit elliptical arches 65 
 To raife arches upon pilafters or columns 6y 
 Gothic arches ib. 
 To find crofs vaults in perfpeclive 68 
 To draw the fame vault more accurately 69 
 To form narrow vaults 70 
 A vault on the principles of the preceding 
 
 rules 7 1 
 
 To exhibit arches with three fides 72 
 To exhibit an arch with five fides ib. 
 To exhibit the elevation of round objetls 73 
 For the elevation of pilafters ib. 
 A vault in form of a /hell in perfpeclive 74 
 Open domes, or vaults in perfpeclive 75 
 That a number of objetls, and plurality of 
 ft cries, only admit of one point of fight y6 
 To put chimneys in perfpeclive yy 
 To exhibit fleps or flairs in perfpeElive 78 
 Stairs open, or perforated underneath 79 
 Steps or flairs viewed in front ib. 
 To exhibit fteps that JJoew four fides 80 
 Steps viewed fide-wife in perfpeclive 8 1 
 Stairs in a wall in perfpeclive ib. 
 
 A fair- 
 
CONTENTS. xv 
 
 To exhibit a flair-cafe with landing-places 
 in perfpetlive P a S e 8 2 
 
 Winding or fpiral Jlairs in perfpetlive 8 3 
 Winding Stairs 8 4 
 
 Round flairs, or fteps, in perfpetlive 85 
 Round fleps viewed fide-wife ib. 
 To exhibit fquares with circles therein in 
 perfpetlive' 86 
 Columns in perfpetlive 8 7 
 
 Cornices and -'mouldings in perfpetlive 8 8 
 A large cornice above the horizon in per- 
 fpetlive - #9 
 To find the bottom of large projetlures 90 
 Cornices and mouldings below the horizon 91 
 Cornices with fever als returns 92 
 The apertures of doors in perfpetlive 93 
 Apertures of cafements in perfpetlive 94 
 Apertures of cafements with embrafures ib. 
 Divers other apertures 95 
 Plans and firfl elevations of moveables 96 
 Elevations of moveables 97 
 To exhibit the upper part of tables 98 
 Elevation of buffets, preffes, and cup- 
 boards 99 
 Elevations of chairs, Sec, 100 
 Another method of putting moveables in 
 perfpetlive *oi 
 Moveables placed without any order 102 
 Moveables laid or tumbled on the ground 103 
 Altars in perfpetlive * 04 
 The fixtures of Jhops in perfpetlive 105 
 Buildings viewed on the outfide 106 
 Roofs of houfes in perfpetlive 10 7 
 Sequel of the roofs in perfpetlive 108 
 To exhibit a ftreet in perfpetlive ^ 109 
 A demonftration that remote objects do not 
 Jhew their thicknefs 1 10 
 Buildings viewed by the angle 1 il 
 To exhibit walks, with rows of trees, in 
 perfpetlive 112 
 T 0 put gardens in perfpetlive 113 
 To exhibit beds with borders, groves, &c.ib. 
 To put fortifications in perfpetlive 1 1 4 
 T 0 make dfigns in perfpetlive 1 1 5 
 The method of enlarging and of reducing 
 perfpetlive draughts 1 1 6 
 
 Apparatus to the univerfal method of the 
 Sieur G. D. L. 117 
 
 An univerfal method of performing perfpec- 
 the, without having the point of diflance 
 out of the painting, or ground of the work, 
 made public by the Sieur G. D. L. 118 
 
 To give any precife diflance required, with- 
 out removing the point of fight out of 
 the piece 119 
 
 A very curious method of drawing per- 
 fpetlives after nature, without obferv- 
 ing the rules 1 20 
 
 Another curious manner of pratlifing per- 
 fpetlive, without under ft anding the rules 
 
 121 
 
 * PART IV. 
 Meafures and Proportions of Figures. 
 
 Figures in perfpetlive 1 2 2 
 
 Figures that have the eye in the horizon 
 
 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 poftures of figures in perfpetlive 125 
 Beajts and birds in perfpetlive ib. 
 To find the height of remote figures, where- 
 of the firfl is on a mountain near the eye 
 
 1 26 
 
 To give the natural or any other height to 
 figures much elevated 127 
 
 To find in what proportion equal figures 
 grow lefs to the eye when placed over 
 another *b. 
 
 Meafures for elevated figures 1 2 8 
 
 PART V. 
 Methods of finding the natural Shadows 
 of Obje&s, projeaed either by the 
 fun, candle, torch, or lamp. 
 
 \Rigin of Jhadows, or laws of their 
 projetlion * l2 9 
 
 Of the difference of Jhadoivs 130 
 To find the form of the Jhadows £$* 
 g Shadow* 
 
XVI 
 
 O N T E N T S, 
 
 Shadows from the fun Page 132 
 
 The fhadows produced by the fun are equal 
 
 in all objetls of the fame height, though 
 
 at a diftance from each other 133 
 Of fhadows, when the fun is direflly op- 
 
 pofedto the eye 134 
 For the fhadows of perforated obj eels 135 
 Shadows affume the form of the planes they 
 
 are cafi upon 136 
 T 0 find the fhadows of objects broader at 
 
 top than at bottom 137 
 To find the fhadows of objetls fufpended from 
 
 the ground 138 
 To find the fhadows of human figures 
 
 caufed by the light of the fun 139 
 An eafy method of finding the fhadow of a 
 
 body from the fun 140 
 Shadows from a torch, flambeau, candle, 
 
 and lamp, Page 141 
 
 Of the foot of the luminary 142 
 To find the fhadows of a torch on all the 
 fides of a room 143 
 The fhadow of an ere St and inverted pyra- 
 mid by torch-light 1 44 
 The fhadow of a crofs ib. 
 To find the fhadows of round objetls pro- 
 duced by torch-light 145 
 S hadows on fever al parallel planes 146 
 Shadows of cielings by torch -light 147 
 To find the fhadow by the foot of the lumi- 
 nary 148 
 The fhadow doubled by two luminaries ib. 
 The fhadows of human figures by torch- 
 light 149 
 The different difpofitions .and heights of 
 Shadows by torch-light 1 50 
 
 SOME 
 
Fiff. the 8^ 
 
 F%. the 9? 
 
 Fig. the lot 
 
 Fig", the lit 
 
 Fi^. the 
 
 K Fig. the 14^ 
 
 JE „y 
 
 Fig. the 15^ 
 
 2 
 
 A 
 
THE 
 
 THEORY 
 
 O F 
 
 P E RSP ECT IVE. 
 
 By James Hodgfoti, F. R. S. - 
 
 p 
 
 DEFINITIONS. 
 
 ERSPECTIVE is the art of defcribing on a plain furface 
 the true reprefentation or appearance of any given object, as feen 
 from one determinate point for any given dittance and height of 
 the eye. 
 
 2. The perfpective table, or plane, is that furface whereon the picture ot the 
 object is formed, according to the rules of perfpective, as ABC F. See Fig. i. 
 
 3. The geometrical or ground plane is that furface whereon the perfpective 
 table is fuppofed to ftand, as G I K L. • 
 
 4. The height of the eye is equal to the length of a perpendicular let tall 
 from it to the ground plane, as E H. ' 
 
 5. The diftance of the eye from the picture is equal to the length ot a per- 
 pendicular drawn from the eye to the perfpective table, as E D. 
 
 6. The common fedion of the perfpective* table with the grou.id plane is 
 called the ground line or feclion, as A B. _ 
 
 7. The horizontal line is a line in the perfpective table or pidure, paraHel to 
 the lection 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 table, as E D. 
 
 c 9,1 he 
 
11 
 
 'The THEORY 
 
 9. The diftance of any point in the ground plane from the table is a perpen- 
 dicular drawn from that point to the ground line or fection, as QJI\ 
 
 10. Direct parallel lines are fuch as cut the ground line or fection at right 
 angles, as QT and S O. 
 
 1 1. Oblique parallel lines are fuch as cut the ground line or fection at oblique 
 angles, as XT and YZ. 
 
 12. Tranfverfe parallel lines are thofe lines which cut the direct parallel lines 
 at right angles, as P R and QS. 
 
 13. Radial lines, or vifual rays, are fuch as run up from po ; nts on the ground 
 line, and unite in fome certain point in the horizontal line, namely, either in the 
 point of fight or in an accidental point, as D T, D Z, D O. 
 
 14. The point of fight 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 direfl 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 fection, but parallel amongft themfelves, unite 
 or concur as the direct rays do in the vifua! point, as the point E. See Fig. 2. 
 
 16. The point of diftance E is a point in the horizontal line of the table 
 or picture removed as far diftant from the vifual point D in the ?.d figure, as the 
 eye at E in the firft figure is diftant from the table or picture A B C F, namely, 
 D E. 
 
 17. The point of incidence is a point in the ground line or fection, 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 ihe geometrical or ground 
 plane, interfecls the picture or table, as the point p. 
 
 19. The perfpective of a line is the common fection of the table or picture, 
 and the imaginary plane formed by an infinite number of rays flowing from the 
 ^ye at E, and falling upon every point of the line R S to be reprefemed, as the 
 line r s. 
 
 20. The perfpective of any plane figure is the fection of the cone or pyramid 
 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 folid upon the table or picture is the aggregate of 
 the perfpective of all the planes whereof the folid is compofed. 
 
 22. The optic 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 Extre- 
 mities 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 largtft 
 dimenfion, for in this fituation 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 
 
 bg 
 
PERSPECTIVE. 
 
 in 
 
 be made lefs than 45 degrees, the objed will be too much contraded, and the 
 vifual angle will be fo (mail that the returns in buildings would not be diftinguifhed, 
 and the whole would appear confuted, and therefore when the vifual angle is about 
 60 decrees, which agrees with the above mentioned limitation, then the object 
 is feen°with the utmoft advantage, and confequently in all perfpedive defigns 
 they ought to come as near this fituation as poffible. 
 
 23. When the projedion of any objed is made on a plane parallel to the 
 horizon by rays parallel and perpendicular to the fame plane, the reprefentation 
 of the objed in this cafe is called the tonography of the figure propofed, whence 
 the bafe, bottom or platform, whereon a body or building is ereded, is called the 
 ichnography of that building, fo that to project the ichnographic reprefentation 
 of any building is to draw the exad ground plot of the fame building; thus the 
 geometric ichnography of a column is a circle, of a pedeftal is a fquare, &c. 
 
 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 pro- 
 pofed ; thus the upright front of any building or objed is called the orthography 
 of that objed or building, fo that to draw the orthographic reprefentation of any 
 objed or building, is to draw the exad front of the objed or building as it really 
 is and appears to be. . . 
 
 25. But when the reprefentation or projeaion of any objed is made by rays 
 flowing from the feveral parts of the objed, as the front, top or bottom, fide or 
 fides, and uniting in one point where the eye is fuppofed to be placed, the Re- 
 prefentation of this objed (upon a plane placed before the eye (landing at right 
 angles to the line drawn from the eye perpendicular to the objed, and) formed 
 by the interfeaion of the feveral rays with this plane, is called the Schewgraphy 
 of that objed, fo that to draw the fchenographic projedion or reprefentation 
 of any objed, is to draw the projedion or reprefentation of the feveral parts or 
 that objed, as'they will appear to the eye fituated at a convenient diftance from 
 the objed upon a plane placed perpendicular to the horizon, and in a proper 
 fituation to receive the objed j and how this is to be done, is the proper bufinefs 
 of Perspective. 
 
 axioms. 
 
 I . The common interfection 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 m 
 the fame plane •, that is, if a plane pafs through any two of thefe, it wi.l pais 
 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 interfeded by another plane, their interfedions will 
 
 be parallel to each other. ^ Lines 
 
 C 2 * 
 
iv 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 fpace feen under a iefs angle appears lefs, and the fame fpace feen un- 
 der a bigger angle appears bigger, and confequently fpaces feen under equal angles 
 are equal amongft themfelves. 
 
 Note, In this Axiom we fuppofe the fpaces viewed (land at right angles to the 
 axis or principal ray iffuing 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 h 
 
 If the eye be placed any where between two parallel right lines > the farther 
 thefe lines are produced from the fight , the nearer they will feem to approach each 
 other. See Fig. 3. 
 
 Let S reprefent the feat 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 fight, 
 let the rays S A-, SB, S C, S D, S M, S N, be drawn. 
 
 Demonjir. Becaufe the right angled triangles SQB, S QJ>, have the perpendi- 
 cular S Qjrommon to them both, but have the bafe QJD of the triangle S QJD, 
 greater than the bafe QJB of the triangle S QJ3, therefore the angle SDQ^ 
 of the triangle S Q^D, will, be lefs than the angle S BQof the triangle SQ^B ; 
 confequently the angle PSD, which is equal to S D Q, will be lefs than the 
 angle USB, which is equal to S B Q, and confequently the double of the angle 
 PSD, or the angle CS D, will be leffer than the double of the angle O S B, 
 or 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 QJNT, will 
 appear to the eye placed at S, nearer than the points A and B of the fame parallels 
 JEM, and Q_N. After the fame manner it maybe proved that the line MN, 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 fight, will 
 appear leffer, and confequently the points M, andN, in the laft Situation will feem 
 to approach nearer to each other than in the prefent fituation, and thus fuccefllvely,. 
 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 paffinty 
 through the given parallels, and let E M and QJM be the parallels themfclves. & 
 From H, the middle point of the line E CV, erect the perpendicular H S, equal 
 to the height of the eye above the plane, then will S be the place of the eye 
 
 1 from 
 
of PERSPECTIVE. f 
 
 from the point S draw the rays SE, S Q, S A, S B } Now becaufe the 
 ancrles SEA, and S QB are right angle.,, the hypothenufes, or rays S A, and 
 S B will be longer than the perpendiculars.SE, and SQj and inafmuch as both 
 triangles have the fides S E, and S Q, equal to each other, it follows that the 
 anole Q S E will be greater than the angle B S A, and confequently the l ne 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 tlie fame 
 way of reafoning it will follow, that the angle D S C will be lefs than the angle 
 B S A, confequently che 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 demonftrated : And the fame confequences will follow if we 
 fuppofe the point S placed below the given plane of parallels 
 • Let us now imagine a plane, asEMNQ^to pafs through the parallels E M, 
 and Q N, it is manifeft that to the eye placed in the plane itfelf, or above or 
 belowit, as in Figure the 4 th, the two extremities M and N, which are fartheft 
 from the eye, wiU appear the neareft to each other, and the farther they are pro- 
 duced the nearer they will approach, till at laft being indeamtely produced, they 
 will feem to meet in a point, and the diftance will vaniih. 
 
 And the fame confequence will follow in whatfoever fituation the plane is placed,, 
 whether it be perpendicular to the horizon, or parallel to it, or inclined to it at 
 
 ^Hfn^wefeewhy rows of trees, of columns, of pilafters, why walls and the 
 fides of buildings contract themfelves and feem to grow narrower and narrower 
 the farther they are extended from the eye. ^ . 
 
 Hence we fee the reafon why floors and pavements of buildings leem to rile 
 upwards towards the eye of the fpeftator, as is very vifible in long rooms op 
 galleries, and why the cielings feem to fink gradually downwards towards the eye, 
 whilft the fides of the fame building feem to come clofer and clofer that the right 
 Side feems to approach towards the left, and at the fame time the left Side feems 
 to approach towards the right Side, each dimenfion growing letter and leffcr, 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 pointy 
 
 Hence we fee the reafon why the horizon appears higher than really it is, and 
 that the convex furface of the fea to an eye placed upon it appears curved and P rc- 
 tuberanr, and different from what it really is itfelf. And, . 
 
 Hence we fee alfo the reafon why ftatues and pictures placed at a confiderable 
 heiaht above the eye, alfo why ornaments placed upon the tops of churches 
 or other public buildings appear fo much (mailer than really they are, as%eH in 
 breadth as in height, and hence are drawn rules for giving them their due pro- 
 portion of magnitude according to the feveral ftations ailoted them, alfo for por- 
 traits drawn upon cielings or fet up at any confiderable height, and tor a great 
 variety of appearances too many here to enumerate. 
 
 Now inafmuch as the vifible magnitude of the lines A O, L r, M V, lee ti- 
 vure the 3 d, or their doubles, namely the lines A B, CD MN, are as the 
 tangents of the optic angles,. A S O, CSP, MSV> to the feveral radii S O, 
 
vi 
 
 The THEORY 
 
 S P, S V, or to their federal 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 10 is feveral diftances from it: 
 And hence, 
 
 The vifible magnitude of any body being given, and its diftance from the 
 fpectator, 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 tangent 
 of the fame angle of elevation increafed by the optic angle of the figure when 
 viewed upon the horizontal furface, and confequently the higher any object is 
 placed above the eye, the greater will be the difference between the tangents of the 
 feveral angles of elevation, and the tangents of the fame angles of elevation in- 
 creafed by the horizontal optic angle of the figure, and confequently the greater 
 muft the real magnitude of the object be made Ito appear of the fame bignels as 
 if it was placed upon the fame horizontal plane with the eye. 
 
 THEOREM II. " 
 
 If any line in the ohjett he parallel to the ground Line, its perfpective in the piclure 
 will be parallel to the ground Line alfo. 
 
 Let MNOP, fee Figure the 5th, be the picture or perfpective table, S the 
 place of the eye, ami 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, SB 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 perfpeftive of the line A B, the given objed, 
 will be parallel to the ground Line O P. 
 
 Imagine a plane as K A B L, to pais through the line A B, and to ftand at right 
 angles to the plane CD R Q, now becaufe the lines a b, and A B, are the common 
 inter feet ions of the parallel planes MNOP, 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 hypothefis, therefore its perfpective a bin 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 C D QJ*, 
 *he line A B is feated, provided it be parallel to the ground Line A B, or 
 a c whatfoever diftance from the eye the plane C D R QJs fixed, it follows 
 %at all lines that are parallel to the ground Line of any picture will, when drawn 
 
 in 
 
of PERSPECTIVE. 
 
 VH 
 
 in perfpedive, be parallel to each other and to the ground Line alfo. Again, becaufe 
 the triangles S a b and SAB are fimiiar, SX, will be toS x, as AB to ab, butSX, 
 is to S x, as S Z to S E therefore, by a fimilitude of ratios, a b will # be to AB as 
 S E is to S Z, that is, the length of the perfpedive line in any pidure is to the 
 IcncTth of its original line, as the diftance of the eye from the picture or per- 
 fpedive table to the diftance of the eye from the plane of the original object 
 
 'THEOREM III. 
 
 The wfpef- h* of any line, that is perpendicular to the ground Line in the ori- 
 ginal plane, will, when drawn on the p.rfpettive table, run up into the point of 
 
 /tg Lct Ss fee Figure the 6th, be the place of the eye, M N O P the perfpedive 
 table 1V1 N the horizontal line, E the vifual point, O P the ground Line, and 
 P R 'the eiven 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 pifture, the perfpedive of every point R in the 
 given line P R will be found fomewhere in the line E P, in the pidure. 
 Produce the lines S E and R P to G and Q, and draw the line S Qi 
 Becaufe S G and OR are parallel, and the line E P inters them both in the 
 points E and P, they will all be in the fame plane S Q^R G by the 4 th axiom;, 
 and becaufe the point of fight S, and the point R will be always found in this 
 plane, the perfpedive of the point R will always be found in the common inter- 
 fedion of this plane S QR G, and the plane of the perfpedive table M N O 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 mtei feds the ine E P 
 drawn from the point of fight 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 perfpedive at 
 the point R, and the farther the point R is removed from the point P, the higher 
 will its perfpedive r be in the table, and the nearer will it approach to the vilual 
 point E till at laft, being removed at an indefinite diftance from the point of In- 
 cidence P, it will be projeded in the vifual point E, and confequently the line 
 E P in the pidure will be the perfpedive of the right line P R, drawn perpendi- 
 cular 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 me, as O D, 
 indefinitely produced, that cuts the ground Line at right angles, will be represent- 
 ed in the perfpedive table by the line E O, drawn fom the point of fight E in 
 the table to O, the point of incidence or point where the line O D cuts the 
 
 gr °Wn d en^e n i e t follows, that all ft raight lines in the original plane, that cut the 
 ground Line at right angles, will, when drawn upon the peripedive table, meet 
 ex interfed each other in the point of fight. 
 
 THEOREM 
 
viii 
 
 The THEORY 
 
 THEOREM IV. 
 
 The perfpeclhe 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 
 pov.t 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 original line P R till 
 it iyiterfstl 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 interfefts them 
 in tne points A and P, they will all be found in the lame plane S A P R by the Ath 
 axiom, and confequently the perfpective of the point R will be found in the tab'e 
 in the point r, where the ray S R mall interfedt the line A P, the common in- 
 terferon of the plane S A P R, and the perfpeftive table MNOP, 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 diltancefrom the point P, its perfpeftive will 
 be in the point of the table at A, that is, the line A P will be the perfpe&ive ao 
 pearance upon the table of the line P R produced indefinitely, 
 i /\f ter the fame manner it may be proved, that any other ftraight line, as O D 
 indefinitely produced will be projected o,n the perfpedtive table into the ri^ht 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 thev 
 be parallel amongft themfeives, they will all unite or interfedl each other in fome 
 point in the horizontal line, and that point is called the accidental point • and 
 to find it, r ■ 
 
 From the eye point S, draw a line parallel to the original line upon the hori- 
 zontal table, and where this line cuts the horizontal line it will give the accidental 
 point. ° 
 
 Hence it follows, that if the eye be placed any where in the line A S, produced 
 rrom A towards S as far as you pleafe, the fame converging lines on the table 
 will be the peripeclives of the fame parallels in the ground Plane, and hence 
 innumerable points of fight may be afiigned for viewing the fame picture, and 
 hence we have a folution of that perfpc&ive paradox, That the fame reprefenta- 
 t.on of any original object will be proj-dted on the table in the fame lines; though 
 tne-eye mould change its place and diflance. 
 
 This propofition is of very great ufe, and therefore ought to be thoroughly un- 
 derstood, it being the main and principal foundation of all the practice in per- 
 fpechve and indeed the preceding or third therm is nothing but a particular 
 cafe or this general propofition. Though 1 have given it a place by itfelf for 
 order s fake, fin.e 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 drawino- 
 a line from the eye perpendicular to the piclure, and this will neceffarily give th? 
 point of fight to which all the lines, that fall perpendicularly upon the ground Line 
 theorem p!anC mUit neceffaril y tend i as has been proved in the third 
 
 And 
 
*/ PERSPECTIVE, ix 
 
 And inafmuch as the line drawn from the eye to the point of diftance upon 
 the perfpeclive table muft neceflarily form an angle of 45 degrees, with the prin- 
 cipal ray or the horizontal line, the containing fides of the right angle being equal, 
 it follows that the diagonals of all fquares, one of whofe fides 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 i and 
 where, if produced upon the table, they will all center. 
 
 THEOREMV. 
 
 The projection or perfpeclive of any line, that is perpendicular to the horizontal 
 or ground Plane, will on the piclure or perfpeclive table be perpendicular to the ground 
 Line. 
 
 Let N M O P, in Tig. 8. reprefent the perfpeclive table, C D K Qjhe 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 RTZXto pafs through the line A B, and 
 to be parallel to the picture MNOP-, now becaufe S B A is another plane inter- 
 fering the two former planes, their common fections, or the lines AB, a b, will 
 be parallel to each other by the 5th axiom, but A B is perpendicular to the hori- 
 zontal lineXZ, 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 in the horizontal table, it follows that the perfpeclive reprefentation 
 of all lines, that on the ground Plane are erected perpendicularly, will when pro- 
 jected on the perfpeclive table be perpendicular to the ground Line and parallel to 
 each other. And inafmuch 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 perfpeclive of A B, is to its ori- 
 ginal A B, as S E, the diftance of the eye from the perfpeftive 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 perfpeclive of the point A in 
 the ground Plane, draw xz 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 perfpeftive of the 
 line X Z on the ground Plane, and becaufe, by the fimilitude of the triangles 
 s a x and S A X, it will be as AX is to a x, fo is S A to s a, and fo is S E to SL, 
 and fo is a E, to a S, and fo is a b to A B ; whence it follows that x a is to X A, as 
 a b is to A B, that is, any perpendicular on the ground Plane is to its perfpeclive 
 in the pidure, as any parallel on the ground Plane is to its perfpeclive in the fame 
 picture, fuppofmg the Perpendicular anei Parallel at the fame diftance from 
 the picture* whence it fo'lows, that if the Perpendicular and the Parallel are both of 
 the fame length, their perfpectives in the picture will be of the famelength alfo. 
 And this is a property of no fmall life in the practice of perfpeclive ; for the 
 
 D length 
 
X 
 
 The THEORY 
 
 length of any original parallel or perpendicular being known, it will be eafy by 
 the help of a fector to give any part of a fcenographic projection its due dimen- 
 fions in any fituation upon the table. 
 
 Again, if from any point S, in the line SF, confidered as the place of the eye, 
 rays, as S p B, S q A be drawn to the extremities of the perpendicular 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 
 fame perpendiculars, are equal to each other,' whether the eye be placed at a 
 greater or lefs height above the horizon. 
 
 PROBLEM I. 
 
 To find the feat 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 ori- 
 ginal point from the table, being given. 
 
 Let NMOP, See" Fig. 9. reprefent the table, S, the place of the eye, S F 
 its height above the ground Plane C D K R, S E its diftance from the picture, 
 Q^the original point in the horizontal plane CDKR, and A Qjts diftance 
 from the perfpective table. 
 
 From S, draw the line SE, parallel to the horizon or perpendicular to the table, 
 to cut the tablein the point E, the vifual point in the table, and from Q, draw 
 the line Q^A perpendicular to the picture MNOP, to cut the ground Line in 
 the point A, the point of incidence. Now if a plane as T S F be imagined 
 to pafs through the lines, ST, F it will cut the perfpective table in the line 
 E A, their common interferon j and in this line of the table will the perfpective 
 of the point QJ)e found, and confequently in the point q, the interferon of the 
 diagonal S Qjdrawn from S, the point of fight, to 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 T QJF, as in Fig. 10. then will the point Q^in the horizontal 
 table coincide with the point Q^in the" ground Line, the point S or feat 
 of the eye, in the plane S F QT, will coincide with the point S in the horizontal 
 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 in the ground Line O P, will be as far diftant from its point: of 
 incidence A, as ir 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 Qjevolve about 
 the centers E and A, aid confequently always keep the fame diftance from 
 them, but the line E A, the common interferon of the two planes MNOP, 
 aid S T QJF becoming now the axis about which the plane of the table revolves, 
 remains the fame immoveable, and confequently the feat of the point QJn the 
 perfpectiv- table, remains in the fame place as at firft before the plane was fup- 
 pofed to revolve, and is therefore the true perfpeflive place upon the table 
 which being allowed, we mull have this general rule 
 
^/PERSPECTIVE, 
 
 For finding the feat in the perfpective table of any point in the horizontal table ; 
 
 (See Fig. 10.) Namely, 
 
 i . From the given point in the horizontal table, draw the line QA perpen- 
 dicular to the ground Line, to cut in the point of incidence A. 
 
 2. Set off the diftance A Q^of the point Q, in the horizontal Plane, from the 
 o-round Line O P, from its point of incidence A in the fame ground Line, to Q. 
 ° 3. From E, the point of fight, 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 lad 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 in the 
 ground Plane. 
 
 Now as every line is bounded by points, and every furface by lines, and every 
 folid by furfaces ; 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 de- 
 monftrated are fo general, that whofoever understands them readily will fee the 
 reafon of every ftep taken in drawing the fcenographic reprefentation of any ori- 
 ginal object upon any vertical perfpe&ive table. 
 
 THEOREM VI. 
 
 If the perfpe&ive table be inclined to the plane of the horizon at any given angle, 
 the perf/eftive of any original line, that is parallel to the ground Line, will in the 
 perfpective table be parallel to the ground Line alfo. 
 
 Let MNOP, in Fig. 11. reprefent the perfpective table, inclined to the hori- 
 zontal plane C A B at an angle equal toMOA; let S, be the place of the eye, 
 and AB a line parallel to the ground Line P O, whofe perfpedive is to be drawn ; 
 from S, the eye, let the vifual rays S A, S B, be drawn to the extremities A andB 
 of the given line A B, to cut the perfpective table in the points a and b ; now if 
 thefe points a and b are conne&ed together by a right line a b, I fay, this right 
 line a b, which is the perfpedive of the original line A B, will be parallel to the 
 ground Line OP. 
 
 Imagine a plane as R A B T to pafs through the given line A B, and to be pa- 
 rallel to the plane of the table MNOP. 
 
 Now becaufe the lines a b, and A B, are the common interferons of the 
 parallel planes M N O P, and R A B T, by the vifual plane SAB, they will be 
 parallel to each other by the 5th axiom ; but the original line A B is parallel to 
 the ground Line O P, by hypothefis, 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 pa- 
 rallel to the ground Line, their perfpectives upon the picture will be parallel to 
 the ground Line and to each other alfo. 
 
 THE- 
 
The T H E O R Y 
 
 THEOREM VII. 
 
 In any inclined plane, the perfpeelive of any line in the original pfane, that, beinr 
 produced, will cut the ground Line at oblique angles, will be found in the right line 
 that is drawn from the point of incidence P, See Fig. 12. to the point A, in the ho- 
 rizontal line of the table, which is found by drawing a line as S A, from the feat of 
 the eye at S, parallel to the original line P R, till it interfeSi the horizontal line of the 
 table M N. J 
 
 Becaufe the lines S A, and P R, are parallel bjr hypothefis, and A P a rio-ht 
 line intending them both, therefore a plane as S P R A will pafs through 
 them all, and therefore the perfpeftive of the point R, will be found in the 
 table in the point r, the interferon 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 P R, its perfpective will be found fomewhere in the line A P, and 
 confequently the line A P, in the table, will be the perfpedive 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 perfpedive upon the table will be always found in that right line which con- 
 neds 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- 
 terfed the table in the point of fight 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 perfpedive table, do run up and 
 unite in the point of fight, fo all other lines in the ground Plane that cut the 
 ground Line when produced at unequal angle?, will if they are parallel to each 
 other, when projected on the perfpedive table run up and unite in one common 
 point ; whence it follows, that the height of the eye and its diftance from the 
 inclined plane being known or given, the perfpedive representation of any origi- 
 nal 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. 
 
 ?o find the length of the principal ray intercepted between the point offaht, and the 
 ground Line; or which is the fame thing, the height of the eye in the inclined table, and 
 tts dijance from the table the perpendicular height of the eye above the horizon, and 
 the inclination of the perfpeElive table, being given. 
 
 Let O P, fee Fig 13 reprefenc the ground Line, F QC a line drawn at right 
 angles to it, S the feat of the eye, S F its perpendicular height above the ground 
 
 SSf ttdiSffe E C qS f ° rming 3n ^ Wkh the h0Hz0n£a " P lane 
 
 From 
 
of PERSPECTIVE. xiii 
 
 From Q, the point of incidence of the line E Qt in the ground Line draw AQ_ 
 perpendicular to the ground Line, and through S, the feat of the eye, draw S AE, 
 parallel to the line F C, to interfcft the line QE in E ; then .will E be the point 
 of fieht in the inclined plane, QJE the height of the eye, and S E the fpace be- 
 tween the vifual point E and the point of diftance S, whence the perfpedive of 
 any ground plot may be drawn on that plane. 
 
 THEOREM VIII. 
 
 In any inclined plane, «MNOP, fee Fig. if from E, the point of Jight, 
 through the point b, where the bafe F B, of the eye's perpendicular height S b cuts 
 the ground Line of the table, a line as E b be drawn and produced till it cut S F, 
 the line drawn from the eye at S, perpendicular to the horizontal plane C Op P 
 produced downwards in the point D, I fay, the perfpetlive of every line perpendicular 
 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 hoe 
 
 ^LefMNO P be the inclined perfpective table, OP its ground Line where 
 it interfeds the ground Plane C R T Q, S the feat of the eye, S F its perpen- 
 dicular height, E the point of fight 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 Eb drawn on the table j now if the lines S F and E b 
 are produced till they interfca each other in 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 2 be drawn, the perfpecYive of the line Z X ere&cd perpendicularly 
 over the horizontal plane, whofe point of incidence in the ground Line is x, 
 mall be found in this line z x in the table. . . 
 
 Becaufe the lines S F D and ABW are parallel by hypothecs, a plane as 
 S A B W D F will pafs through them, and becaufe the eye is feated in this plane 
 in the point S, the pcrfpeftivc of the line A B will be found upon the table in 
 the line ED, the common interaction of the two planes, which line produced 
 muft neceflarily cut the perpendicular S F, produced downwards in the point D 
 fince they all lie in the fame plane S Y W D. 
 
 Now if from this point D, a line as D x be drawn through x the point of ^inci- 
 dence of the line Z X, ereded perpendicular over the horizontal plane UI^, 
 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 hypothecs, a plane as SZXD 
 will pafs through them both \ and becaufe the eye is feated in this plane at S, the 
 perfpedive of The line Z X will be found on the table in the lme x z, the : com- 
 mon i interfeftion of the two planes, which being produced muft neceflarily cut 
 Se line S D in the point D, the interferon of the lame line SD with the plane 
 of the inclined table produced, whence the perfpeftiyes of the lines A B and Z X 
 on the table, will be the lines a w, and z q, intercepted between the rays S A, o B, 
 S X, and S Z flowing from the eye to the top and bottom of the given perpen- 
 diculars A B, and Z X. ^ nc j 
 9 
 
xiv 
 
 The THEORY 
 
 And af.erthe fame manner may the perfpedive of any other line elevated per- 
 pendicularly over the horizontal plane be drawn on the table. 
 ; For if we 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 revolution 
 pafs through every line that ftands perpendicular to the horizontal plane, and the 
 fucceflive interfedions of this plane with the plane of the table will be the fuccef- 
 five perfpedives of the feveral perpendiculars it (hall happen to pafs through ; 
 and as all thefe lines muft neceffarily center in the immoveable point D, as being 
 common to every fituation of the revolving plane, it muft neceffarily follow, the 
 eye remaining alio immoveable, that the perfpedive of every line that is perpen- 
 dicular to the ground Plane, will be found in that line in the table which is pro- 
 duced 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 perfpedive of objeds 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 letter will be the angle S D E, and the farther will the point D be removed 
 from the horizontal plane C R T Q, till at laft when the plane becomes vertical 
 the point of interfedion D vanifties, and the lines E b D and S F D 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 projeded on the table, be per- 
 pendicular to the ground Line alfo. 
 
 Again, the farther the point of fight S, is removed from the table, the greater 
 will be the diftance of the point of interfedion D from the horizontal plane 
 C R T till at laft the eye being fuppofed at an infinite diftance, the line S F D 
 will be removed at an infinite diftance from the pidure, alfo the point of inter- 
 fedion D will vanifh, and the elevation of all lines perpendicular to the horizontal 
 plane will become perpendiculars to the horizontal plane of the table, which is 
 the foundation upon which the Military or Bird's perfpedive is founded. 
 
 Again, the lefler the inclination of the table M N O P, the nearer does the 
 point of interfedion D approach to the point F in the horizontal table, the foot 
 of the eye's perpendicular, till at laft when the inclined plane MN OP, coincides 
 with the horizontal table CRTQ, the angle of incidence vanifties, and the 
 point of concourfe D coincides with the point F ; whence it follows, 
 
 That in all horizontal or optical projedions, the perfpedive of every line that 
 is ereded 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 perpendi- 
 cular through the bafe of the elevated line ; whence it follows, that the perfpec- 
 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 lhall interfed the horizontal table. 
 
 7 THEOREM 
 
of PERSPECTIVE. 
 
 xv 
 
 THEOREM IX. 
 
 If .the plane of any original figure be parallel to the table, its perfpedive will be 
 fimilar to its original, alike, aud alike fituated. UTVT . 
 
 Let S, fee Fig. 1 5. be the feat 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 perfpedive ap- 
 pearance abed upon the table (hall be fimilar to its original A BCD 
 
 For from S, the point of fight, draw the rays S a A, S b B S c C, and S d D. 
 
 Becaufethe planes MNOP, and HIKL, are parallel, S A B is a vifual plane 
 interfeding them, therefore the common interferons a b, and AB will be parallel, 
 therefore A B will be to a b as SB is to S b : And again, becaufe S B C is a vifual 
 plane interfering the fame parallel planes, therefore their commor 1 interferons, 
 namely the lines B C and be will be parallel, therefore BC will be to b e as the fame 
 ray 3 B is to the ray S b, wherefore by equality of ratios a b will be to be as 
 A B is to B C i after the fame manner it may be proved that be is to c d, as BC is 
 to C D, and c d is to d a, as C D is to D A, whence the perfpedive figure abed 
 is fimilar to its original A BCD; which was to be proved : Whenceitfollows that 
 the optical or horizontal perfpedive of all plane figures that are parallel to the 
 table, will be fimilar to their originals ; that is, that the perfpedive of fquare 
 fibres parallel to the horizontal or perfpedive table, w 1 on the table be fquare, 
 alio the perfpedives of circles will be circles, of hexagons will be hexagons, 
 
 Whence and from the laft corollary of the preceding theorem, the : reafons of 
 all the appearances in horizontal perfpedive are manifeft, and as all feadows are 
 nothing elfe but horizontal projedions of the feveral objeds, the candle or lumi- 
 nous body fupplying the place of the eye , hence it follows that every horizontal 
 projedion of any objed elevated above the plane, is the projedion of the lhadow 
 of the fame objed, and confequently the rules g,ven for forming of one will 
 ferve for forming the other. And inafmuch as the immenfe diftance of the fun 
 is infinite with regard to any terreftrial objed, hence it is that the rays that flow 
 from the fun to form the folar (hadow are fuppofed to be parallel > and hence it 
 is that every orthographic perfpedive of any objed elevated above the plane of 
 the horizon is the projeaion of the fhadow of theTame body, and confequently 
 in drawing of one, you draw the other alfo ; and the e feveral fhadows when 
 drawn upon the fcenographic table according to the rules of fcenographic pro- 
 jedion, will exhibit upon the fame table the madows of all objeds drawn upon 
 
 th A P ^Mnafmuch as the pradice of horizontal perfpedive proceeds after the fame 
 manner as does the pradice of fcenographic projedions, fo in problem the firlt, 
 
 P If -we^uppofe the eye in figure 10th in S, the point of diftance in that cafe, and 
 FQ to be the diftance of the eye from the given objed, the demonftrat.on for 
 onewillhold good for the other, and confequently, in proving the operation in 
 one, you prove the operation in the other alfo. Though. 
 
xvi The THEORY, 
 
 Though my principal view in this trad has been to render the demonftrations 
 plain and concife, and the number of "Theorems as few as poffible, 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 pradice of the feveral kinds ofPerfpemve 
 but what may be accounted for by fome one or other of the preceding laws • This* 
 together with thefollowing treatife, which I look upon as one of the beft practical 
 books of its fize that has appeared in the Englijh language, will, I hope, make the 
 whole as compleat and ufeful a piece as can be comprifed in fuch a volume as 
 this is. 
 
PRACTICAL PERSPECTIVE. 
 
 PART I. 
 
 SHEWING THE 
 
 DEFINITIONS 
 
 AND 
 
 PRINCIPLES. 
 
 O F 
 
 PERSPECTIVE. 
 
 E 
 
i PRACTICAL Part I. 
 
 Definitions, Names, and Terms of the Points, Lines and Figures ufed in the 
 
 following Work, 
 
 A Vol NT is that which is conceived to have no parts ; fuch as A, Fig, r. There are 
 three kinds of points ufed in perfpe&ive, called points of fight ox view, points of dijlance, 
 and contingent or accidental points, 
 
 A Lin e is a length without breadth ; fuch is A B, Fig. 2. There are five principal lines 
 ufed in perfpective, namely, 1. The line of jke bafe, called alfo the line of /be plane, or the 
 terrejlrial line, as C D, Fig, 3. 2d. The perpendicular or plumb line, which, falling on another, 
 makes the angles * on either fide equal : fuch angles are faid to be right ones, and the line 
 fo falling on the other called a perpendicular thereto. Thus, in Fig, 3. A B and E F, falling 
 on C D, and making right angles in B and G, is a perpendicular thereto. 3. The parallel 
 lines, which, being continued on the fame plane to infinity, never meet j as the lines N and O, 
 Fig. 6. The horizontal line is no more than a line dcawn parallel to the terrejlrial lines ; as 
 'fhall be down in its place. 4. The diagonal line, which ts 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 is fuppofed not to appear when the work is finiflied ; fuch is O N, Fig. 2. 
 
 A right Angle we have already faid to be that formed by a perpendicular. It is 
 here reprefented apart, by E F G, Fig. 4. to (hew what it is the more diftinftly* There 
 are two other kinds of angles, which comprife all thofe that are not right ones : the firft, 
 called obtufe, are fuch as are greater than a right angle : as H L 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 extremity or bounds of any thing : thus the points A and B, Fig. 2. arc 
 the terms of the line A B. 
 
 AFiGURgis comprehended under one or more terms; thus 7,8, 9, 13, &c. are figures* 
 A S qjj are has its four fides equal, and its four angles right ; fuch is A B C D Fig, 7. 
 A Parallelogram, or long fquare, has its four angles right, but not its fides equal 5 
 fuchisCDEF, Fig. 8. 
 An E ilateral Triangle confifts of three equal fides ; as G H I, Fig, 9. 
 The Section or Intersection of two lines is when they run acrofs, or cut each 
 other in a point, as in Fig, 1 1. where A B and C D cut or interfecl in E. 
 
 A Curve Line is that which goes indirectly, or about, from one point to another; 
 fuch is LM, Fig. 12. 
 
 A Circle isa plain figure, comprehended under one fingle line, called the circum- 
 ference, to which all lines drawn from the center are equal ; fuch is B C D, in Fig. 13. And 
 the point A in the middle thereof is called the center. 
 
 The Diameter of a circle is a right line B C, pafling through the center A, and 
 dividing the circle into two equal parts. 
 
 A Radius is any right line drawn from the center, of a circle to its circumference, as 
 the line A D. 
 
 An A r c h is any part of the circumference, as B D C. 
 
 The Chord of an arch is a right line drawn from one end of an arch to the other; as 
 B C is the chord of the arch B D C, and B D is the chord of the arch B D. 
 
 Every A r c h of a circle is meafured by its chord ; thus B D is the meafure of the arch 
 BD, and B C, the greateft of all chords, meafures the arch B D C. 
 
 AnOvAL, or Ellipsis, is an oblong figure, comprehended under one crooked, regular, 
 but not circular, line ; fuch is E, Fig, 14. 
 
 A spiral, or Volute, is a line found by a revolution about one or two centers $ 
 fuch is F, Fig, 15. ; 
 
 * An angle, the aperture or inclination of two right lines meeting in the fame plane, is u r ually ex- 
 prefled by three letters; the middle letter mews the angle, and the other two the lines that make the 
 angle; as in Fig, 5. H L M is the obtufe angle L, and H L K, is the acute angle L. 
 
2 
 
 PRACTICAL 
 
 Part I. 
 
 S e qju e l of the Definitions, Names, and Terms* 
 
 ATangent is a line, which being produced only touches or razes an 
 object, figure, or line, without cutting it: thus the lines A B are tan- 
 gents to the circle C, in the points D D. I 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 efteemed a right 
 angle, and all the lines CCC, &c. to be efteemed as perpendiculars to the 
 plane, as D F is ; and the lines A B, G I, and H K, as perpendiculars to 
 the the terreftrial line. All the lines drawn to the point of fight, whether from 
 above or below, or from either fide, are called Rays, or Visual Rays. 
 
 APlan, Ichnography, or Groun d-P l a t, is a firft draught or defign 
 of a work, reprelenting the traces or paths of its foundation on the ground, fo 
 as to exhibit the extent, divifion, and diftribution of its various parts, in their 
 feveral magnitudes and proportions, refpectively, at one view. This is what I 
 have reprefented in L and M. 
 
 A Poly g on is a figure containing feveral angles j as L. 
 
 A Degree is a fmall arch or portion of a circle. Every circle is fuppofed 
 to contain 360 degrees, and an arch is eftimated by the number of thofe degrees 
 it takes up. Thus N O is an arch-of 30 degrees. Aftronomers fubdivide each de- 
 gree into 60 minutes, and each minute into 60 feconds, &V. But fuch fubdivi- 
 fion has no place here. It is enough we know that degrees are thofe little divi- 
 fions in the circle NO PQ^ whereby all angles are meafured. To know their 
 quantity, an arch is defcribed, having its center in the point of the angle. From 
 them we derive an eafy method of making all forts of polygons, namely, by 
 dividing 360 by the number of angles the figures are to confift of. Thus,' for 
 inftance, if I would make a fquare, divide 360 by 4, the quotient, is 90, which 
 giyes the right angle N M O : and fo for the reft. Such as are unacquainted 
 -with arithmetic, wtfl find geometrical methods of doing the fame in plate IV. 
 
3 P R A C T I CAE Part h 
 
 Methods of defcribing the Lines and Figures, 
 
 i.Hp^O raife perpendiculars : If it be in the middle of a line that a perpen- 
 dicular is required, open the compaffes 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 : Do the like at the point E, and the 
 two interfe&ions 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 interfering 
 each other in H ; then draw a line from H to G. 
 
 3. ¥0 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 compaffes 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 compaffes, 
 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 MN 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 P S, as the point Q, and from this point de- 
 scribe a circle paffing through the point P, and cutting the line P S in fome 
 place, as S ; then from S draw a line through Q^to the circumference of the circle 
 T, and the point T gives the extreme of the perpendicular T P. A juft fquare 
 fhortens all thefe operations. 
 
 5. ¥0 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 through 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 aline, to let fall a perpendicular 1 Suppofethe 
 ; 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 K N into two equal 
 parts, and from the middle point O, draw an arch through K ; and from the 
 point P, where the arch interfects the line LM, draw the perpendicular K P. 
 
 7. A parallel line, if truly drawn, will be a tangent to femi-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 femi-circles L and X. 
 
 8. ¥0 divide a line into equal parts: Suppole the line be A B, draw another pa- 
 rallel thereto, either above or below it, as C D ; and on this laft, which is either 
 to be greater or lefs than that to be divided, fet off as many parts as A B is to be 
 divided into, for example, into feven ; from the firft and laft of thefe divifions 
 draw lines through the extremes of A B, interfering each other in fome point, as E ; 
 from which point drawing lines to ail the divifions of the line C P, the line A B 
 will be divided into feven equal parts. 4 
 
4" PR APICAL Part U 
 
 ME THO DS of Defcribing the Figures. 
 
 1. \ Line as A B, Fig. I. being g'ven to form a fquare on, fet one foot of the compafies in the point 
 l \ A, and extending the other the length A B, defcribe the arch B C ; then from the point B 
 defcribe another arch A D, interfering 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, isc. the fquare is formed. 
 
 Or thus : upon the given line A B eredt a perpendicular AC equal to A B; then, taking the length 
 AB in your compafles, 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 fquare ABCD, 
 
 2. 1o defcribe a parallelogram , or long fquare, on the term E, of the given line E F. Ereft a perpen- 
 dicular either greater or lefs than the lame, as E G ; then taking E G in your compafles, fet one foot 
 in F, and with the other defcribe an arch ; takealfoEF in your compafle*, and fettingone foot in G, 
 defcribe a fecond arch, cutting the former in H : this will give you the parallelogram required. 
 
 Of Circular Polygons, which are Figures of feveral angles infcribei in circles. 
 
 3. To\defcrile an equilateral triangle : The compafles being open to the radius of the citcle, fet one 
 foot in the point A, defcribe the arch D E, and draw a right line D E, which will be the fide of 
 the triangle DEF. 
 
 4. For a fquare, draw two diameters at right angles, and join their extremes ; thus you will have 
 the fquare ABCD. 
 
 5. For a pentagon, or five-angle, draw two diameters, and take D G, half the femi-diameter DI, 
 and from the point G, with the interval G A, defcribe the arch AH; the chord of which is the 
 ;iide of the pentagon. 
 
 6. For the Hexagon, or Six-Angle, the femi-diameter is the fide of the hexagon. 
 
 7. For the Heptagon, or Sept- Angle, take half a fide of the equilateral triangle. 
 
 8. For theOtlogon, or Eight- Angle, take half a quadrant of the circle. 
 
 9. For the Enneagon, or Nine-Angle, take two thirds of the femi-diameter for the fide; as E B. 1 
 
 10. For the Decagon, or Ten- Angle, divide the femidiameter 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 fide of the 
 
 •decagon. 
 
 11. For the Undtcagon, or Eleven-Angle, draw two diameters at right angles, and from the point A, 
 with the interval of a femi-diameter, defcribe an arch B C ; then from the point of interfedion C, 
 draw a line to E ; the portion C D will be the fide of the undecagon. 
 
 1 2 . Dodecagon, or Twelve-Angle, divide the arch of a hexagon, A B, into two equal parts ; the 
 chord of the moiety will be the fide. 
 
 1 %. An Oval is formed divers ways ; in all which the figure is either a compound of feveral por- 
 tions of circles, or ic is one line drawn from two centers. The moft ufual methods are thefe : having 
 defcribed 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 compafles in D, and with the 
 
 - other taking the interval E, we defcribe an arch E F. The like being done on the other fide, the 
 
 • oval is formed. 
 
 14. For a rounder Oval, draw a fingle line, and from A, as a center, defcribe a circle, the inter* 
 feftion whereof with the right line in the point B, will be the center of another circle. Now, to 
 form the oval, take in your compafles the whole diameter of one of the circles, as from A to F, and 
 in one of the interferons of the circles, as D, fetting one foot of the compafles, with the other draw 
 the arch G H : the like do from the point E. 
 
 15. Othervjife we have an eafier and a more ufeful manner of defcribing ovals than any of the pre- 
 vcedingones ; the fame rule ferving for all forms, long, narrow, broad, lhort, c3V. thus : fet two nails 
 or pins in a right line A B, 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 obferve 
 the contrary for a fhortone ; for if the nails Hand clofe together, the figure will be a circle. 
 
 1 6. For a Spiral, or V olute, take two points in a line A B ; the points to ferve, one after another, 
 as centers, For inftance, having drawn the femi-circle A B, fet one foot of the compafles in B, and 
 open the other to the length B A, and defcribe a femi-circle A C ; then fetting one foot in A, take the 
 interval A C, and draw the femi-circle CD ; and this continuing as long as yoaipleafe, ftill fluffing 
 centers. Vignola gives us another method. 
 
5 PRACTICAL Part f. 
 
 Of the Visual RAYS. 
 
 TJ 7 an object be a Jingle point, it fends only one vifual ray to the center 
 JL of the eye; and that ray is called the axis, or central ray, as being 
 the moft vivid of all rays : fuch is A B. 
 
 If the object be a right line, the vifual rays form a triangle, as CAD, 
 whofe bafe is the line CD, and fides the two extreme rays A D and AC; 
 AB is the central ray. If the line was feen end-wife, it would appear as 
 a point. 
 
 If the object be a furface, 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; of which the 
 central A B is the ftrongeft, the others growing weaker, as they are re- 
 moved farther therefrom, though they ftill retain a competent ftrength* 
 till they make a right angled triangle. Such as go beyond this, become 
 fo feeble, that they appear very confufedly, fo that to have diftinct vifion, 
 the extreme under which an object is comprehended, muft, at moft, 
 fubtend a right angle in the eye. If the furface was viewed edge-wife, k 
 would appear no more than a line. ' 
 
 Why a Piece ^Perfpective is feen better with one Eye than with tw&. 
 
 Some hold that all objects appear better with one than both eyes ; al- 
 ledging, that the fight is rendered more penetrating by the vifual rays o^ 
 the fhut 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 diffufed 
 through both, is now fuppofed to be colleded into one ; and this reinforce- 
 ment muft neceffarily render it ftronger, more piercing, &c. than both. 
 
 Be this as it will, it is certain, we fee a piece of perfpective with one 
 eye better than with both. The reafon is, that the central ray, in this 
 cafe, is directed to the point of fight where all the radials of the piece unite 
 and center, which is what mews a picture in its higheft perfection. It 
 is for this reafon that we do not fay, the points of the eyes, but, the point of 
 the eye, as infinuating, that perfpective is moft pleating when viewed by a 
 fmgle eye, 4 
 
6 
 
 PRACriC AL 
 
 Part I. 
 
 Firfl Definition. 
 
 "PERSPECTIVE . g ^ e ^ ^ reprefenting objects feen through Tome 
 Jt tranfparent medium, which the vifual rays penetrate in paffing 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 Perfpefiive. And fince we fee nothing but 
 through thofe mediums, it is certain all we fee is in perfpective. 
 
 The end of perfpe&ive is to exhibit objects upon a plane, fituate be- 
 tween the eye and them, for example, on the plane E F G H, to reprefent 
 the objects ABCD, in the points I K L M. 
 
 The better to conceive this, fuppofe an object ABCD on the ground, 
 and a fpectator's eye in O, if a tranfparent body E F G H be placed be- 
 tween the two, the interferons of the vifual rays with the perpendiculars 
 Qjl S T, will give the figure I K L M, fuch as the object appears on that 
 plane. Perfpective, therefore, confifts altogether in the interferons of 
 lines: whence it is, that Marolois always calls any thing put in perfpective, 
 the appearance of the feflion j fmce the plane EFGH cuts the vifual py- 
 ramid ACBD and O, and gives I K L M for its fection. 
 
 The reafon of thefe fections is, that onefingle line determines nothings 
 but there are two required to cut one another, to give a point. Now, as 
 it is evident, that between our eye and an object there is always a right 
 line, or ray, that can never be wanting : but to get the other, which is 
 to cut it, it is necelfary we conceive, that from our foot as a center, there 
 are a number of lines, or rays, continually flowing to the angles of the 
 objects we fee ; as from P to the angles ABCD: all which rays being 
 cut by fome tranfparent plane, as EFGH, the rays PB, PA, PC, PD, 
 which before were horizontal, are now erected and become perpendicular : 
 P B, for inflance, becoming QJV1, P D becoming R L, &c. For if they 
 continued horizontal, the vifual rays would never interfect them, till they 
 both met in the object itfelf. It is for this reafon we always fuppofe a 
 plane, which, reflecting the rays, gives them an occafion of interfering, 
 and fo of finding the points to form the appearances of objects. 
 
Part T. PERSPECTIVE. 
 
7 
 
 PRACTICAL 
 
 Part I. 
 
 Second Definition. 
 
 TPC hnograph'y'is the plan of any work, on the view of it, cut off by 
 J[ a plane parallel to the horizon, juft at the bafe or bottom of it. A 
 geometrical plan, as that in page 2, exhibits the various parts in their juft 
 proportions, and their different magnitudes may be afcertained by the ufe 
 of a fcale. A perfpective plan, is one conducted and exhibited by degra- 
 dations and diminutions according to the rules of perfpective; thus ABC D 
 is the Ichnography, or perfpective plan, of a fquare body. 
 
 'Third Definition. 
 
 Orthography is the delineation of the front or fore-fide of an ob- 
 ject, as an houfe or a cube, &c. Or the elevation of any object, as a houfe 
 or a cube, &c. directly oppofite to the eye. Thus EFG H is the ortho- 
 graphy, or fore-part, of a cube. As the ichnograpby reprefents the plan, 
 the orthography reprefents the fide oppofite to the eye. 
 
 Fourth Definition. 
 
 Sce nogr A phy exhibits the object quite raifed, and perfect, in the 
 front, top, and that fide which is vifible from the fituation of the fpectator's 
 eye. Thus IKLMNOPisa Renography , or perfect cube. This is the 
 whole object compleat^ and comprehends the plan and front as parts 
 
 The fum of what has been defined is, the Ichnography of a building, &c, 
 reprefents the plan or ground work of the building. The Orthography, the 
 front or fore-right plane. And the Scenography, the whole building, front, 
 fides, height and all. Preferring the more familiar terms, for the future' 
 I mall call the Ichnography Plan, the Orthography Front, and the 
 Sccftograpby Elevation. 
 
8 
 
 PRACTICAL 
 
 Part I. 
 
 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. Suppofe 
 a fpectator's eye in the middle of a line at -f, it is evident, that if 
 it would fee the two extremes thereof, A and B, it muft. take in a femi- 
 circle V X, whofe center is in the eye itfelf, and whofe central ray is the 
 line + T. By taking in this femi-circle, it will perceive the objects on 
 eithe r fide, and in fuch manner, as that thofe fartheft off from A will 
 appear to approach towards the center T, and thofe on the fide B feem 
 to approach likewife. 
 
 Now it is afked, whence it is, that objects ranged on ftrait lines fo wide 
 afunder, fhould feem to approach and join each other, and that whether 
 the ranges are fituated fide-wife, or one over the other ? 
 
 The anfwer is in few words. All objects appear under the vifual angle 
 they fubtend at the eye. Now, be they columns, trees, animals, or any 
 other things placed on the fide A, K the remoter!: will feem to border on 
 the center T, by reafon they are feen under an angle, or ray, that is near 
 thereto. The ray -j. K, for inftance, being much nearer the central ray 
 T, than is the ray + C or + D, of confequence muft. appear nearer to it. 
 If the range of objects was prolonged, they would ftill approach nearer the 
 central ray T, till fuch time as they feemed contiguous, and only to form 
 one point therewith. 
 
 Now, in perfpective, the fides A K and B S do not continue parallel, 
 hut become vifual rays, which contract themfelves till they interfect each 
 other in the point of fight, and by that means give the diminutions of ob- 
 jects. Thus, for inftance, in the fecond figure, the eye being at adiftance 
 capable of feeing the line A B j from the two angles A, B, arife two rays, 
 which proceed to the point of fight T ; which rays AT and BT receive 
 the interferons the point of diflance makes with the objects, which all 
 the while contract themfelves proportionably ; as will be fhewn in the 
 defcription of diagonals and their fections. By fuch means the whole pa- 
 rallelograms A K B S, and all the objects on either fide become reduced 
 into the narrow compafs A V, BX: and if the eye were more remote, 
 that fpace would be ftill fmaller, fince the farther an object is off, the 
 fmaller it appears, as will be made appear in the following page. 
 
9 PRACTICAL Par* I. 
 
 Why Obje&s appear the /mailer as they are at the greater Dijlance. 
 
 I h 't e a ! rCa u y obfe 7 ed ' that ob i e ^ appear Urge or fmall according to the angle 
 * "her™ are ieen, and that this angle is taken at the eye, where two rays 
 drawn from the two extreme points of an objecT: meet. The eve A for inftance 
 jew™ ^EC, will draw the rays L B and A C, whS gi ^thS^ 
 
 under , i?£ ^ r ? CWcd ^ * greatcr * n % k a PP ea ™g large, and another 
 under a letter angle, little; and among equal object, thofe atThe freateft diftance 
 appearing under the imallcft angle, it confequently follows that in all perfpedives 
 the remoteft objeds muft be made the final left. Toilluftratethis by an example 
 if the eye be in A, the objetf B C, which is the neareft, will appear the biS 
 becaufe-feen under the greateft angle ; and the fecond, third, fourth and fifth obi 
 jects, though of equal magnitude, will all appear fmaller and fmaller, inafmuch as 
 the angles under which they are feen, diminifh in proportion as the objeas recede. 
 B the eye were removed into M. K L would appear the largeft ; and B C, in this 
 latter cafe, feem no bigger than N O. ' S 
 
 The fecond figure is a.fequel of what I have ad vanced. For, fuppofing the ap~ 
 parent magnitude of objed.s, to be fuch as is. the angle they are feen Snder, it 
 tol ows, hat if feveral lines be drawn between the fides of the fame triangle, then 
 w.II all of them appear equal Thus, all the lines comprifed between, die fides 
 ON, O F, of the triangle NOP, will appear equal to each other , and as ob- 
 
 1 a ZZ m?rG i 6 r Under the fame an S le feem all comprehended under, 
 
 agieater angle, feem greater, andallunder a. fmaller, fmaller. 
 
 Thus much premifed : if there be a number of columns, or pilafters, to be 
 unged in-perfped.ve on each fide of a hall or church, they muft of neceffiry be 
 
 h riTnn 0 Un i er f v™- ^ ^ *" t0WardS ° ne COmm0 " P°™ ^ the 
 
 i^'nr '# 3d. For inftance, the eye being placed in A, viewing the firft ob- 
 ject U h ; if; from the points D, E$. you draw the vifual rays D O, E O, they will 
 make the mangle DO |, which will include, the columns D£, FG, HI KL 
 M;N, fo as they. will, all appear equal in magnitude. 
 
 What has been foidof the fides, is likewife to be underfiood, of the cieHng* 
 
 Thn J o V Tf nCS \ dim,nuti0 J ns of the angles, of remote objeds, placed eith?r 
 above or below b e ,rg,governed by the fame rule as thofe placed laterally. I need, 
 no therefore add any thing farther; unlefs, that care be taken there be as many 
 
 ST SS 15 TT ? C r , e r teft ° b j ed:s «^ween the neareft : for in tbu 
 cale though d,ftant objects be clofer as.they are farther from us, they w.ll appear 
 
 tilfZZ % t0 . PrCfCrVe ^ heif dm r CC} thuS ' in BC ' D E > the interval between, 
 
 we Z fn C °'TnS fixiecn fqUareS5 and nafsw£r than teeerLb^ 
 *w«en the Tout remote!* KL, M.N..j%. 4, 
 
JO 
 
 PRACTICAL 
 
 Part I. 
 
 The Obfervatio7i$ of the former page, applied to praEtice. 
 
 T T follows from what was faid in the foregoing page, that if you join 
 J_ two triangles, as in the laft figure but one, for the fides, and two 
 others, of the laft, for the top and bottom of an object, all four will 
 terminate in one fingle point A, which is the point of fight, wherein all 
 the vifual rays meet. And this will give a proof of what I advanced, 
 namely, that objects diminifh as they remove j the lower objects rifing, 
 the upper falling, and the lateral clofing or approaching nearer to each 
 other. An example of all which you have in Fig. I. which exhibits, as 
 it were, depths and diftances falling back, and receding from us, though 
 all the parts of the defigjn are in fact equally near the eye, being all of them 
 drawn on the fame plain furface ; but this ingenious effect is produced, 
 and the appearance of a diftant view procured, by comprehending and 
 diminishing the obje&s within the triangles. 
 
 The trees in the lower figure being ranged by this rule, have the fame 
 effect as the columns, &c. The two rows are each of them compre- 
 hended within the fide-triangle, and diminifh as they approach the point 
 of fight A. The third or bottom triangle, is the earth between the trees, 
 and the fourth or upper one, is the air ; and thus an elegant defign, highly 
 entertaining the eye, is eafily constructed. 
 
 I fhall next (hew, how you are to proceed in putting any plane body* 
 or other figure, 'in perfpective. 
 
11 PRACTICAL Parti. 
 
 Of the Hori zon. 
 
 WHAT we call the Horizon, in perfpeclive, is only a line given us by 
 the height of our eye. Thus, if we be rai fed on an eminenct, as is the 
 man in the firft figure, our horizon will be high. If we (land only on the plane 
 as represented in the fecond figure, the horizon will be our own pitch. And if we 
 be feated as is the third, the horizon will be low. So that it is the horizon (hews 
 how high the eye is above the ground. 
 
 m This, in effect, is the principal article in a picture, and that which dire&s and 
 gives law to all the reft y both as to the Hope and inclination of buildings and 
 to tne meafures and heights of the figures. This has occafioned a little difpute 
 among our beft painter* ; fome of them affert, that all paintings mould have their 
 horizon in the work itfelf, and that perfpedive allows, whare the painting 
 ra.fed very high above the eye, that it have its particular horizon. Others do 
 not allow of a fecond hor.zon, but always ufe the natural one, where-ever the 
 painting be placed ; as imagining that the whole height and breadth before them 
 is, as it were, one large painting, from which that which is raifed above oueht 
 to take its meafures. The refped I bear to the patrons of each opinion will not 
 al ow me to determine between them; efpecially, as feveral good authors have 
 tolerated both. But if my own fentiments were afked, I mould make no fcruple 
 to profefs myfelf of the opinion of thefe latter, becaufe every thing in the painting 
 will thereby appear the more natural. truing 
 
 In this horizontal line are always found the points of fight and diftance and 
 fomet.mes the contingent or accidental point. It is this line that terminates the 
 view, and which to our apprehenfion when at fea, or on a large plain, feparates 
 heaven from earth : it is always parallel to the bottom of the piece, or the plan the 
 objedfc is placed upon. Hence it appears, that nothing ought to be placed aoove 
 the horizon, but what furpaffes the height of the. eye'; and if an objedt be fo high 
 as that it furp iflesthis horizon, the plan of the fame objed mufl: be placed below 
 it. Thus, a tree or mountain may have its top above the horizon, but its bottom 
 mult be a good deal below it. 
 
 Whatever is below the horizon mews its top ; but in objecls ever fo little above 
 it, the top is invifible. Thus the two blocks A, B, placed on the ground of the 
 
 fh f SU ^ by reaf ° n the horizon is over them 5 but in thofe of 
 
 the iecond figure C, D 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 it is the hori- 
 zon makes all the difference. l 
 
12 
 
 PRACTICAL 
 
 Part L 
 
 Of the Terreftrial Line. 
 
 THE Terrestrial Line, B a s e L i n e, or Line of the Plan, is 
 the bottom line of the drawing or plan. This is always parallel to the hori- 
 zon, as is feen in A B of the firft Figure, F G of the fecond, and N O of the third. 
 It is the firft line drawn for the plan of a place ; and whereon all the meafures are 
 to be fet, as will hereafter be fhewn. 
 
 Of the Point of Sight. 
 
 t~tr\ H E Point of S ig ht is a point in the axis of the eye, or in the central 
 < 1 ray, where the fame is interfered by the horizon ; or in other words, a point 
 in the horizontal line where all the vifual rays terminate. Thus the point E in 
 the firft figure is the point of fight 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. It is alfo called the principal 
 point, or point of perfpective. 
 
 Of the Points of Diftance. 
 
 TTJoint of Distance, or Points of Distance, is a point, or points 
 JL (for there are fometimes two of them) placed on the horizontal line at equal 
 diftances on each fide from the point of fight. They are thus denominated, by 
 reafon the fpectator ought to be fo far removed from the figure, or painting, and 
 the terreftrial line, as thefe points are from the point of fight. Thus H I being 
 the horizon, and K the point of fight, L and M are points of diftance, ferving to 
 give all the fhortnings. Thus, for example, if from the extremes of FG, Fig. 2d. 
 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 F M cut the lines 
 F K and G K, in the points X and Y, will be the line of depth, and the fhortning 
 of the fquare, whereof F G is the fide and bafe. The lines drawn to the point 
 of fight are all vifual rays, and thofe to the points of diftance, all diagonals. 
 
 Of the Accidental Points. 
 
 Contingent, or Accidental Points, are certain points, wherein 
 fuch objects as may be thrown negligently and without order, tend to termi- 
 nate in the horizon. They are cal'ed accidental, becaufe they are not drawn to the 
 point of fight, nor the points of diftance, but meet accidentally in the horizon as 
 the fituation of the objects happen. Thus, for inftance, the two pieces of wood 
 X and Y terminate in the points V, V, V, V, in the horizon P Q, not in the 
 point of fight which is R, nor in the points of diftance S and T. Indeed fome- 
 times the objects are fo ill difpofed, that thefe points muft be made out of the 
 horizon, as I (hall have occafion to (hew hereafter. They ferve particularly in 
 the apertures of doors, windows, ftair-cafes, and the like. 4 
 
Part I, 
 
 PER8PEC T I V E 
 
 tz 
 
 M TBnvt of Th/tance K. ef Suftt f*mk of Htjlance I, 
 
 Q, T Total accijgntatl Tom^t ty^. 
 
IS 
 
 PRACTICAL 
 
 Part I. 
 
 Of the Point of the FRONT. 
 
 F t i H E point of Direct View, or of the Front, 
 J[ is when we have the object directly before us, and not 
 more on one fide 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 fides, unlefs the object be poly- 
 gonous. Thus the plan A B C D is all in front, and, if it 
 were raifed, we fhould not fee any thing of the fides A B, 
 or C D, but only the front A D. The reafon is, that the 
 point of fight E, being directly oppofite thereto, caufes a 
 diminution on each fide ; however it is only to be under- 
 ftood where an elevation is the object, that the front or fore- 
 part can only be feen, for, if it be a plan, it fhews the whole, 
 as ABCD. 
 
 Of the SIDE POINT. 
 
 THE point of Oblique View, or of the Side, is 
 when we fee the object fideways, or aflant. In view- 
 ing the object obliquely, it prefents us two faces, or fides ; 
 and the point of fight, inftead of being in the middle of the 
 horizon, as in the former inftance of the point of direct view, 
 is now placed in the fide of the horizontal line. For ex- 
 ample, if the point of fight be in F, the object G H I K will 
 appear athwart, andfhewtwo faces, GKandGH; in which 
 cafe it will be a fide point. The practice is the fame in the 
 fide points as in the front points ; a point of fight, points of 
 diftance, & c. being laid down in the one as well as the other, 
 
 4 
 
 i 
 
*4 
 
 PRACTICAL 
 
 Part I 
 
 Of the Visual Ravs. 
 
 IT is an univeYfal rule, that all the lines, which in a geometrical plan, are perpendicu- 
 lar to the terreftrial line, be always drawn to the point of fight, when the fame plan is 
 to be put in perfpective. Thus, in the little plan AO, OB, Fig. i. A B is the terref- 
 trial line, to which aft the lines Z, Z, CSV. are perpendicular. But if the plan be to be 
 thrown into perfpedYive, and either a greater or a lefs line than that of the plan be pitch- 
 ed on, for example, the line A B, Fig. ?. which has the fame number of divifions as the fmall 
 one ; from the feveral divifions Z, the lines are to be drawn directly to the point of fight Bf 
 Such lines are properly denominated radials or vifual rays; and the laft of them, the e?jr 
 tremes, as being drawn from the extremities of the terreftrial line A B. 
 
 i ■ 
 
 Of the Diagonals, or Diametrals, and their Sections. 
 
 It is lilcewife a rule, that all the diagonals of the fquares in a geometrical plan, be drawn 
 to the point of diftance when the plan is put into perfpective. Thus, in the little plan Fig. 3. 
 the diagonals, G O and F O, are drawn to the points of diftance, when the fame plan is- 
 exhibited in perfpective, and thereby the fhortnings or diminutions of tfre objects are procur- 
 ed. For example, if from the extremes of the bafe line F G, Fig. 4. lines be drawn to the 
 points of diftance L M, they will be diagonals ; and where thofe lines interfect the extreme 
 rays F K and G K in the points O, O, will -be marked out the diminution of the fquare, 
 whereof F G is the fide. And where thefe diagonals cut the lines Z, Z, &c. in the points 
 Qs &c. parallels to the bafe line are to be drawn, which will give the diminution of 
 all the fquares, and the fame number of fides as in the little plan. The more remote the 
 points of diftance are from the point of fight, the more the objects are dimintfhed ; hence 
 the beauty of a perfpective depends on fixing the points of diftance, at a proper diftance 
 from the point of fight. On this account* 1 have added Fig. 5. with a diverfity of in- 
 tervals between the point of fight, and points of diftance, to evince the truth of what h 
 juft now obferved. Suppofe then R to be the point of fight,, and R S, R S, the extreme 
 rays ; if the point of diftance be at T, it will cut the ray SR in the point V, which will 
 give the diminution of the fquare, whereof S S, is a fide. But it would be ridiculous to 
 fee a fquare fo extravagantly deep, occafioned from the point of diftance T being fo much 
 too near the point of fight R. The. leaft fpace in any-wtfe allowable, is for the point of 
 diftance to be removed from the point of fight, half the breadth, of the whole draught or 
 perfpecYive; (fuch as is the diftance of X from R, viz. equal to that from the central 
 ray C, toS;) by reafon fuch a diftance makes a right angle at the fpectator's eye. 1$ 
 would, however, be ftill more agreeable at 1, the line in that cafe cutting the fquare 
 at 2 ; and it would be better yet at 3, cutting the extreme ray at 4 ; and beft of all at 5 ; 
 being then remote enough, and making the fquare (horter at 6 : the reafon thereof will be 
 affigned in the next page. 
 
 It may be demanded, why, throughout the courfe of this work, I have put the points of 
 diftance fo near the point of fight, when they have fo much better effect at a greater dif- 
 tance ? The anfwer is, that the book not being intended to be viewed merely, out ofcuri- 
 ofity, but to inftruct, it was neceifary every circumftance (hould be feen, that the various 
 methods of practice might be the better conceived. For this reafon I have included as 
 much of the feveral operations as poifibly I might. 
 6 
 
15 PRACTICAL Part I. 
 
 Distance, ^Removal, 
 
 T Have already obferved, in fpeaking of the vifual rays, page 5, that the eye 
 cannot commodioufly take in more of them, than are included in a right angler 
 that is, that the fight does not receive the forms of objects fully and diftinctly," 
 when the rays tranfmitted from.their extreme points, extend beyond aright an°Ie' 
 The reafon is, the pupil being nearly in the center of the eye, does not well admit 
 more than a quadrant of a circle, fo that whatever rays exceed that portion, are 
 either not feen, or produce only a dim confufed effect. On this account, objects are 
 feen to greater advantage under an angle lefs than a right angle rather than greater; 
 for inftance, two thirds of a right angle, orfixty degrees, but not lefs, becaufethe 
 rays, in fuch cafe, being fo ftraitened become indiftinct, the angle being little more 
 than a point in the pupil. To (hew this difference in figures. Suppofe the plans and 
 fquares the fame as in the lad figure, and the fpedator's eye at the diftance of T 
 from the terreftrial line"; the oppofite figure demonftrates it would be necefTary 
 the angle mould open much farther, to fee the extremes Y, Y. If it only opened 
 to a right angle, the eye could not fee all the figure, as T for inftance could not 
 fee beyond the points V, V. Whence would arife a very faulty perfpe&ive, in- 
 afmuch as what would exhibit a fquare, will now only form a parallelogram. 'The 
 neareft diftance for the eye is in the point X, which is the juft meafure of a right 
 angle comprehending the whole piece Y Y . If the diftance be carried ftill farther 
 back from the point of fight, it will be ftill more agreeable, as in I, where the 
 angle will be only 72 degrees. If it be brought back as far as Z, it will be in 
 perfection, inafmuch as the rays being now 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 cannot be taken in the difpofal of point's of fo much im- 
 portance i with regard to which it muft be efteemed a certain rule, that the di- 
 ftance be at leaft equal to the fpace between the direct ray and the corner of the 
 perspective. + R, for inftance, is the direct ray and X + the leaft diftance, 
 which is equal to + Y. This meafure being taken, muft be fee off each way from 
 the point of fight to fix the points of diftance, as here from R, to S, S ; or only 
 one way, as in the following page, for a fide point. 
 
 Thus much we learn from reafons that regard the eye ; but experience furnifhes 
 another noble rule, which may be general too, provided it be ufed with judgment, 
 namely, that having chofe the place where the perfpeitive is to be made, you are 
 to determine from what quarter it is to be feen to the beft advantage ; then taking 
 the diftance from this place to the terreftrial line, fet off this interval, by a little 
 fcale, from the point of fight to the point of diftance, provided it be not too re- 
 mote. Which is a circumftance that wiH require fome difcretion, to avoid the 
 inconvenience either of placing it too near, or too far ofn 
 
i6 
 
 PRACTICAL 
 
 Part I. 
 
 Observation I. Relating to the Side-point 
 
 THE rales for the front point, are not varied in drawing the points of the 
 fides, they are both founded on the fame caufe, which always produces the 
 like-effects. Fig. i. will -fufficiently fhew, that the method of practice for the fide 
 point, is the fame as for that in front. Set off the divifion on the terreftrial line 
 A B, and if the point of fight be fuppofed in C, and the point'of diftance in D, 
 from the feveral points of divifion draw the rays to C, then draw the diagonal 
 line A D, and you will have the interferons Q, Q, &ff. which give the diminu- 
 tions of the fquares in the fame manner as thofe in the preceding plates. The reft 
 will be learnt from the following rules. 
 
 Observation II. Of the Depths or Hollo wings. 
 
 A perfpective may be funk to any depth, by making new terreftrial lines and 
 diagonals in the following method. Forexample, Fig. 2. from the terreftrial line 
 E F, draw to the point of diftance H I, the diagonals EI, F H, and where they 
 interfect the vifual rays EG and F G, in the points K, K, the diminution of the 
 iirft fquare will be. Now, if we take this line K K for a new terreftrial line, 
 and from its extremes K, K, draw diagonals to the points of diftance where thefe 
 cut the fame lines EG and FG, namely in the points L, L, will be the diminu- 
 tion of the fecond fquare, which will have as many divifions and fquares as the 
 firft. Again, if we take this line L L, and repeat the fame operation, we (hall 
 have the diminution of the third fquare in the point M. And if we begin again 
 with this, we fliall have a fourth; and fo on, till we arrive at a point, which 
 will be a length that will appear prodigious. By fuch means, it is eafy either to 
 fink the perfpective plan deeper, or to fhorten it. Thus, if you would have the 
 depth, twice its width, proceed as already directed, by drawing new diagonals 
 at K, K : and if you would have the depth but half the width, a line drawn at N, 
 at the interfe&ion of the diagonals, will give your requeft. 
 
 Since it is infallibly certain that as many vifual rays as cut the diagonal line, 
 fo many fquares of depths you have ; it follows, as has been already hinted, that 
 you may give the perfpective 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 
 you will want two fquares of the other diminiftied fquare R ; and if you would 
 have two fquares more than the fquare R, draw a line from the fame point O, 
 cutting two rays, to V : if you defire four, take X ; if fix, % ; and if the intire 
 fquare, Z : which is very eafy, when well underftood. 
 
PRACTICAL 
 
 Part I. 
 
 Observation III. Of the Meafures upon the Dafe. 
 
 BY the bafe line alone, one may give any depth, and in any part of the perfpective at 
 pleafure, without the ufe of fquares ; which is a very expeditious way, though fome- 
 what difficult to le.arn. I (hall, however, endeavour to make it understood, becaufe I (hall 
 make frequent ufe thereof. For an example, Fig. t. Supp fe BS the bafe line ; the point 
 of view A ; and the points of diflance D, E; if now you would make a plan of a cube, of 
 which B C is the fide, draw two occult, or dotted lines, from the extremes B C, to the 
 points I fight. -Then, to give the breadth, take the fame meafure B C, md fet it off on 
 the terreffrial line C F ; and from F draw a line to the point of diftance D j and where this 
 line imerfects the firfl: ray C, in the point G, will be the diminution of the plan of the 
 cube BHGC. 
 
 If you would place the cube farther towards the middle, take the meafure B C, and trans- 
 fer it on the bafe line to the diftance required, as I K ; and to attain the depth, fet the 
 fame as you would have it on the bafe line, as L from L meafure the width, asLM; then 
 from L and M draw occult lines to the point of diftance D, and from the points N O, 
 where thofe lines interfect the ray K, draw parallels to the terreftriai line, and you will have 
 the fquare Q^P O N in the fituation you wanted,. 
 
 You may fet the cube on the other fide of the fquare, by transferring the meafure of 
 the fide to W S on the bafe line, from whence draw the rays S A, W A, and perform the 
 operation as already directed. The cube B HG C is here transferred to V, by lines drawn 
 from the points C, D, to the point of diftance E. The interval M T, intended for a 
 border, is (hewn in the narrow figure X, as being very near. 
 
 Observation IV. Of the Bafe Line, and a fingle Point of Diftance. 
 
 Since the depths and widths may be procured by means of this bafe line, we need not 
 give ourfelves any farther trouble in the making of fquares j as (hall be fhewn in this ex- 
 ample. Suppofe a row of trees, or columns, is to be projected on each fide j on the bafe 
 line lay down the place, and the diftance between them, with their breadth or diameters, 
 as A B C D E F G, then laying a ruler from the point of diftance O., to each of the points 
 ABCDEFG, the interferons it makes on the extreme vifual ray AH, will be the 
 bounds of the objects defired. To fet them off on the other fide, upon the ray GH; 
 fet one foot of your compafles on the point of fight H, and with the diftance H G, ftrike 
 an arch-: The point wherein this cuts the ray G H, as in N, will be the correfponding 
 bound. Thus N will be the fame with M, and fo of the reft ; through which drawing 
 parallels, 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 H ; and where this 
 cuts the other parallels, will be formed the plan required : which you may make either round 
 ©r fquare. 
 
 Observation V. Not to deceive one's felf in the Meafures. 
 
 Never put any objects that are intended to be within the plan, on the fide of the point 
 of diftance, where you are to draw lines for managing the depth. Thus, fuppofe A S the 
 vifual ray whereon the meafures are to be marked j if you would produce the points C and 
 D through the fame, do not draw the lines from the point of diftance E, but from that 
 oppofite thereto, F. Or if C and D were on the infide, as G and H are, you fhould not 
 draw from the point F, buc from E i by reafon the line of interferon is found between the 
 two. Confequently, the two will cut each other in the fame points I, K. 
 
Part I. PERSPECTIVE. 
 
 D 
 
 >.... £ y< 
 
 A. • P 
 
 1 B 
 
 — 
 
 D 
 
 B. 
 
 E 
 
 G 
 
 E 
 
 
 
 
 
 
 Fl 
 
 1 2 
 
>$ r RAC'TiCAL Part J, 
 
 Observation VI. Of a fingle Point of Dijlance. 
 
 TH E artift is fametimes fo ftraitned for want of room on the place on 
 which he exhibits his draught, that ip is impoffible to make above one 
 point of diftance. On which occafion, fuch as have been always accuftomed to 
 two, find thernfelves at a lofs. This I am now to recover him from, and to 
 give him to underftand how a fingle point fufRces for the operation, Suppofe, 
 then, we have a pavement to make of fquare (tones, and that we have already 
 drawn all the vifual rays to the point A; to get the diminutions of them, draw 
 lines to the points of diftance, the interfedions whereof will give us points for 
 parallels to be drawn through. But here being only one point of diftance, name- 
 ly B, draw the fingle diagonal ftroke C B, to cut all the vifual rays. Then mark 
 the fame interfedions on the oppofite rays, for the drawing of parallels. Set, as 
 already direded, one foot of your compafies in the point A, and fweep the other 
 through all the interfedions, as I P. This however is only advifeable for what 
 is to be viewed in front; another method is to be given for plans to befeen 
 fidewife, viz. fet 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 per- 
 pendicular 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 ot all the other interfedions. 
 
 Observation VII. How to perform without making Vfe of 
 
 the Diagonal. 
 
 I f one would ufe the extreme ray G H for the line of interferon, the objects 
 KLMNO 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 poffible that the 
 diminution of the perfpedive may have the better efFed. For if that point 
 were too near the point of light G, the objeds would be too flat; I mean, for 
 example, that a fquare would appear a parallelogram. Then from the point I 
 draw lines to the feveral objeds KLMNO, and mark the interfedions thereof 
 •on the ray G H, and through thefe interfedions draw parallels to the terreftria! 
 line, as here P &c. This method is not much in ufe, though fome fet a 
 value on it. 
 
 Observation VIII. Other methods of Shortning or Diminifliing. 
 
 I f you chance to be ftraitned for fpace on the plane you draw upon, and can- 
 not remove the point of diftance far enough ; from the foot of the ray R S 
 ered a perpendicular T S, which will receive the interfedions, and give a greater 
 diminution. And if you would have the diminutions ftill more, draw a fiope 
 line, as X, which by means of its inclination, will give the interfedions 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. 
 
PRACTICAL PERSPECTIVE. 
 PART II. 
 
 ♦ 
 
 SHEWING THE 
 
 METHODS 
 
 OF PUTTING 
 
 PLANES 
 
 I N 
 
 PERSPECTIVE. 
 
19 
 
 PRACTICAL 
 
 Part II. 
 
 Of Planes viewed direftly, or in Front, 
 
 FROM Obfervation III. and IV. page 17, as well as from the elevations that fol- 
 low ; it will appear that my intention is not to ufe geometrical plans, in order to the 
 drawing of perfpeftives. That being a double labour ; and there being fcarce any Painter 
 would give himfelf the trouble, feeing I teach him to do the fame thing, by the ufe of the 
 terreftnal line; But as there is no rule fo general, but has its exception j fo there are cer- 
 tain figures which cannot be put in perfpeclive without the ufe of fuch plans Befide 
 the confufion a man would be under, mould a plane be given him to be exhibited in perl 
 Ipeclive if he had not been inftruded how to proceed. Therefore I am induced to give 
 the following rules; which may fuffice to fhew how any plane that can be required or 
 even imagined, may be put in perfpeclive. 
 
 I Tojhorten, or diminijh afquare ; as A B C D. From A and B, to the point of fight E 
 draw the lines A E, BE: and from the feme angles A and B draw two diagonals F B* 
 AG; and the points H and I, where they interfedl the rays A E and B E, will give the 
 fquare A BCD, diminiftied in AH IB. To do it without the geometrical plan: draw a 
 line from B to F, or from A to G ; or fet off the line A B on the terreftrial line : as in 
 
 H £ fron * K draw another ,ine ^ F : which will give the fame interfeclion I, on the 
 ray B E. 
 
 2. To diminijh afquare viewed by the angle D. Having defcribed the plan ABCD con- 
 tinue the fides DA, and D C, to cut the bafe line in H, and I : from the points H and 
 I, draw lines to the points of diftance G, and P j and from the angle B, of the fquare 
 which touches the bafe line, draw to the fame points two others B G, and B P- their in- 
 terferons being joined will give you the fquare KLMB. To do without the plan ■ fet 
 of the diagonal D each way from the middle point B; as to.H and I, and draw the 
 diagonals as before. But in either cafe no line is to be drawn from the point of fight, O. 
 
 3. To diminijh a Circle. Draw a diameter S T, perpendicular to the ground-Line and. 
 another RQ_at right angles, which will divide the circle in four equal parts : afquare 
 A B CD defcribed about the faid circle, and drawing the diagonals AD, B C, will divide it 
 into tight parts : from each of thefe points O, O, &c. draw perpendiculars to the ground- 
 Line, and from each of their interfeaions with the faid ground-Line, draw lines to the 
 p^nt of fight H ; and where they are interfeaed by the diagonals A K, and B I, make 
 points ; the ipo laft of which, M N, give the fquare, which is to be divided iato four, l*y 
 diagonals, interfering each other in the point P. Laftiy, from the extremes of this crofs 
 draw curve lines through the faid points, which will give the form of the circle in perfpec* 
 t.ve This method may ferve for fmall circles; but for large ones we mall give another 
 method, more exaa. 
 
 4. This figure is a compound of the two firft; which is all we need:to fay about it; 
 
 5. Thus too depends on the two firft.; only here is a lift, or border, going round, which, 
 :he others, have not. To put the lift in perfpeaive: from the four rays A BCD draw 
 lines to the point of fight G; and where the inner rays B,C interfect the diagonals A F 
 and D E, draw parallels to the bafe-line ; and you will have your defire. 
 
 Tbefixth is the fame as the feqond ; except that it is furrounded with two borders. 
 
to 
 
 PRACTICAL 
 
 Part II. 
 
 The perfpe&ive appearance ^/PlANs viewed 
 obliquely y or fide-wife. 
 
 THESE plans, being much the fame with thofe al- 
 ready difpatcht, are to be managed after the fame 
 manner. It would be lofing time to repeat the method 
 of operation how they are to be diminiflied in perfpec- 
 tive ; a bare infpe&ion of the figures and lines fufficing 
 to ftiew, that all the difference between thefe and the for- 
 mer, confifts in the fltuation of the objects, which are here 
 fliewn laterally, and there in front. 
 
 All the AAA's are points of fight, and the BBB's points 
 of diftance. The fide-point has been defcribed, page 1 6th» 
 
21 
 
 PRACTICAL 
 
 Part II. 
 
 The Method to find the perfpe&ive Appearance of a 
 
 TRIANGLE. 
 
 TRIANGLES, according to the order of numbers, ought to pre- 
 cede fquares j but, according to reafon, they are to come after 
 them in this work, as being more difficult, to put in perfpective. Not 
 on account of the plan, which is eafy enough, as only confifting of 
 three lines joined together, but on account of the obliquity of its fides. 
 
 I come now to apply fome of the obfervations, page 17th, relating 
 to the meafures on the bafe line AB: for, to exhibit this triangle in 
 perfpective, whofe bale 1. 3. is parallel to the fundamental line A B, 
 from all the angles thereof, 1, 2, and 3, perpendiculars are to be drawn 
 to A B. Then fetting one foot of your compaffes in the interfections> 
 with the other fet off the diftances of the parts of the object from the 
 terreftrial line, along the fame line, by ftriking arches, as from 2 to z > 
 from 3 to 3, &c. This done, having drawn another bafe line in ano- 
 ther place, as here under E F, transfer the meafures from A B to E F, 
 and to the point of fight C draw lines from the points 1, 2, 3, 
 Laftly, having pitched one point of diftance D, draw lines thereto from 
 the other points of depth, 1, 2, 3, &c. And between the interferons 
 made by thefe with the vifual rays, lines, being drawn, will give the 
 triangle required. 
 
 If you would give it the lift or breadth, repeat the fame over again for 
 the feveral inner points thereof ; only ufing other figures to prevent 
 confufion j as, next to 1, 4; next 2, 5 ; 3, 6, &c. Then drawing 
 perpendiculars to the point C, and between the points where they inter- 
 feet the others, draw lines as you fee imthe fcheme.- 
 
 The equilateral triangle, fuch as that here defcribed, is infcribed in a 
 circle, that is a circle may be drawn about it, every fide fubtending 120 
 degrees. 
 
 Note. The fame operation will ferve for all forts of triangles. 
 
22 
 
 PRACTICAL 
 
 Part II. 
 
 To exhibit # PENTAGON, or figure of Five- Angles, 
 
 in perfpe&ive* 
 
 THE way to conftrucl: a pentagon is to defcribe a 
 circle, and divide it into five equal parts, of feventy- 
 two degrees each. Then, for putting it in perfpective, the 
 method is the fame as has been fhewn for the triangle, as 
 will appear in viewing the figures and the lines of ope- 
 ration. The lift or breadth is added, becaufe when I come 
 to treat of elevations, inftances will be given in objects that 
 have broad edges. The exterior pentagon muft be firft 
 compleated on the bafe line, and the inner one afterwards, 
 by the fame method of proceeding. The reader was in- 
 ftru&ed herein, in drawing the rim of the triangle in the 
 former page. The point of fight, both of the front and 
 fide, is A ; the point of diftance B ; the vifual rays, which 
 .are the perpendiculars drawn from the angles of the plan to 
 the bafe line, are drawn to the point of fight 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- 
 ed 2, which gives the angle 2, 4 gives the angle 4; and 
 fo of the others. All the reft is clear enough ; regard, how- 
 ever, is to be had to one thing, that all the angles tend to- 
 wards the center 6 : for this reafon the center is to be mark- 
 ed in the plans in perlpe&ive, as well as in the geometrical 
 plans. 
 
PRACTICAL 
 
 Part II, 
 
 To fijtd the ferJpeSlive Appearance of an HEXAGON, 
 or Figure of Six -Angles. 
 
 i | ^ H E Hexagon is a plane with fix angles, and as many fides. 
 
 If the fides be equal, it is a regular hexagon, and the eafieft 
 to defcribe of all the polygons, (figures of more than four fides and 
 angles) by reafon the fame aperture of the compafTes, which circum- 
 fcribes it within a circle, is the meafure of its fides, viz. 60 degrees 
 each. In other words, the fide of a hexagon is equal to the radius 
 of a circle circumfcribed about the fame. As to the putting it in per- 
 fpective, 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 fight, and B that of diftance. 
 
 Since I have a good deal of room in this page, I think it not amifs 
 to give a brief method of putting the lifts or thickneffes of all polygons, 
 regular or irregular, in perfpe&ive. And the prefent hexagon mail 
 ferve for an example of this propofition. Suppofe the exterior lines of 
 the plan of Fig, 3. to be only laid down, and it were required to give 
 it a lift or thicknefs within : to do this in perfpective, lay your ruler 
 along the fides, and make points in the horizon where it cuts the fame ; 
 thus laying it along the fide A B, it will cut the horizon in C ; then 
 laying it along BD, it will give the point E j and the like of the other 
 fides. Before you proceed any farther, draw occult lines from the fe- 
 veral angles through the center F, which lines are to receive the inter- 
 ferons 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 firffc 
 breadth to the point of diftance G, and where the line G H cuts I, will 
 be the bound of the thicknefs of the firffc fide, which is to determine 
 for all the reft. For from this point a line is to be drawn to the point 
 correfponding to this fide C, and the interferon of this line with K will 
 give the diminution ; from the point whereof drawing a line to the 
 point E, correfponding to the line B D, you will have the diminution 
 for the point L, which ferves for the laft fide L M. Then transferring 
 all the fame meafures to the other fide, you will have the figure com- 
 plete, by the formation of the inner hexagon. 
 
 Hereafter we mall have occafion to give another method. 
 
24 PRACTICAL Part IL 
 
 "To exhibit the perfpeBive appearance of AHeptagon, 
 or figure confijling of feven fides and feven angles. 
 
 t | ^ H E Heptagon is formed within a circle, as the other poly- 
 gons are ; in order to which the circle is divided into feven parts, 
 each fide fubtending 51 deg. 25 min. and fometimes more. The me- 
 thod of putting it in perfpedtive 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 diminution, 
 and the lines that give the points of the angles, it is different, and rather 
 according to the feventh Obfervation, page 185 though I do not abfolutely 
 approve that, as thinking the eighth Obfervation the better. Buttocondefcend 
 to fuch as do ufe it, and fhew them that it does not diminifh 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 fide, as A B, to receive the interfecYions of the parallels drawn through 
 all the angles. Thus, the firft angle being placed on the terreftrial line 
 of 2 and 7, I draw a parallel through both, cutting the perpendicular 
 in C. After the fame manner, the angles 3 and 6 give the interfeclion 
 D, and 4 and 5 the interfedion E. This line A B, thus divided, muft be fet 
 off the bafe line of the plan to be diminifhed, beginning to put the point 
 B in F, as in the figure. Then making the other divifions C D E, and 
 from thefe drawing lines to the point of diftance O, from the interfec- 
 tions of the extreme ray draw parallels to the terreftrial line, and where 
 thefe cut the rays that bear the numbers of the angles, points are to 
 be made, which, being joined by right lines, will give the figure defired. 
 .As to the thicknefs, or lift, it is to be made after one of the preceding 
 manners. 9 
 
PRACTICAL 
 
 Part II. 
 
 "To exhibit the perfpetlive Appearance of the Octagon, 
 or Figure of Eight Angles. 
 
 rpHE octagon is formed of a circle divided into eight 
 parts, of forty-five degrees each, from the divifions 
 whereof, lines being drawn, will form an octagon, that is, 
 a figure compofed of eight angles, and as many fides. The 
 rules already delivered, fhew abundantly how it is to be put 
 in perfpective, whether for a front or a fide view. I fhall 
 only obferve here, that the front plan is to be diminifhed 
 according to Obfervation VIII. page 18, and the fide 
 plan according to the VHth Obfervation in the fame 
 page. The point of view is A, and that of diftance B. 
 The reft is too obvious to need an explanation. 
 
26 
 
 PRACTICAL 
 
 Part II. 
 
 Another Method for exhibiting the OCTAGON//* 
 
 perfpe&ive. 
 
 r | 1 HI S method of conducing the Octagon was invented by 
 \ Serlio. The practice is thus : having found a fquare ABCD the 
 ordinary way, divide the bafe line C D into ten parts, and, leaving three 
 on each hand, from the third of either fide E and F, draw lines to the 
 points of fight, G, and through the interfe&ions of thofe lines with the 
 diagonals O, O, draw parallels to the terreftrial line, cutting the fides of 
 the fquare in the points H, I, K, L : then joining the points EH, IE, 
 FK, LF, by lines, yon will have an octagon, as in the preceding figure. 
 
 To find the perfpeEiive appearance of the HEX AGON, 
 or figure of Six Angles, by the above method. 
 
 f | V HE fame Serlio has contrived a likeVay of managing the Hex- 
 J[ agon. Suppofe, as above, a fquare ABCD, and the bafe 
 line A D divided into four parts, from one of which, on either fide E 
 and F, draw lines to the point of fight H ; then through the interferon 
 of the diagonals, which is the middle of the fquare G, draw a paral- 
 lel to the bafe line, cutting the fides of the fquare in I K 5 laftly, draw- 
 ing lines through thefe points E, I, E, and F, K, F, there will be found 
 a hexagon. 
 
 I mail fay nothing of the octagon, Fig. 3. viewed fidewife; fince, as 
 it has been fo often repeated, the method is the fame as for that viewed 
 in front, Fig. 1: the operation is plain and iimple, the lines drawn at 
 Fig. 3, (hew it at the firft infpeclion. 
 
27 
 
 PRACTICAL 
 
 Part II. 
 
 Of the Double Octagon, or the method of ad- 
 ding breadth or thicknefs to an oclagon y by the 
 operation of the circumfcribed fquare. 
 
 SUPPOSINGa fingle octagon already made, if it is required -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 fquare 
 which circumfcribes the octagon, as here at A B ; and from thefe 
 points draw lines to the point of fight C ; and where thefe lines cut 
 the diagonals, as in O, O, draw parallels D D, which will form a fort 
 of band within the fquare ; laftly, draw occult lines from angle to angle, 
 interfering each other in N ; and where they cut the lines of the inner 
 fquare, namely, in the points E, F, G, H, I, K, L, M, will be the 
 bounds of the inner octagon. 
 
 Of the Double Hexagon, 
 
 AN hexagon circumfcribed with a fquare, will receive a lift, 
 or inner hexagon, by the fame method of operation. It would 
 be needlefs to repeat particulars, fmce the figure will clear any doubts 
 that may arife. 
 
 The octagon viewed fidewife, is managed precifely as that viewed 
 in front ; the point of fight is A, and that of diftance B. 
 
M 
 
28 
 
 PRACTICAL 
 
 Part II. 
 
 To exhibit the perfpeEtive of a Circle. 
 
 IF the circle be fmall, you are directed, page 19, to an eafy method 
 of projecting it, by circumfcribing a fquare about it. If the circle be 
 large, take the following method, which Serlio has directed. Set one 
 foot of your companies in the middle of the fundamental line, with tho 
 other defcribe the femi-circle A Z B, divide it's periphery or circum- 
 ference into any number of equal parts at pleafure. You will fee in 
 the procefs, that the more of thefe divifions, the eafier it will be to 
 form the circular lines, from the junction of which the circle receives 
 it's ^ appearance. The femi-circle A Z B is here divided into eight parts, 
 which is the ufual practice. From the feveral divifions Z Z, &c. per- 
 pendiculars are raifed 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 removed beyond the compafs of the plate, but which are to be 
 fuppofed, as ufual, in the horizon. Thus you get a fquare A H I B ; 
 and this fquare thus formed, draw lines or rays from all the points E 
 towards the point of fight, as far as the line H I, and through the 
 interfections of thofe lines with the diagonals, draw parallels; then, 
 beginning in the middle of one of the fides of the fquare to make a 
 point, as a> connect it by a circular line with the oppofite angle b, and 
 proceeding thus with arches from angle to angle, according to the direc- 
 tion of diagonals through the points a b c d e f g b i k I m n 0 p q y 
 you will have your circle in perfpective. 
 
 By this method, it is apparent how any curvilinear figure may be pro- 
 jected on a plane, and therefore how necefTary it is, to have this rule 
 of the projection of the circle very familiar, becaufe of the frequent 
 ufe thereof in columns, vaults, arches, apertures of doors, windows, &c. 
 
 9 
 
29 
 
 PRACTICAL 
 
 Part II. 
 
 To exhibit the appearance of a Double Circle. 
 
 J~TT"^ H E outer circle is fuppofed the fame that I have juft now been 
 1 defcribing j and it is required to give it a thicknefs, or lift, by 
 making another within-fide thereof. Thus, give it any breadth at 
 pleafure, as, for example, A C : from G the center of the outer femi- 
 circle, defcribe the inner one C D, which you are farther to divide, 
 like the great one. Thefe divifions are eafily procured, by drawing 
 lines from the divifions of the great femi-circle to the center G ; the 
 interfecYions of thofe lines with the inner femi-circle at 1 1 1 I, &c. 
 are the points of it's divifions. From thefe points raife perpendiculars 
 to the bafe line AB, and,, to prevent confufion, let thefe laft lines be 
 dotted. This done, proceed by drawing lines from the new points 
 C I I I I D on the bafe line, towards the point of fight F, as far as the 
 line H K, and through their interfections with the diagonals draw 
 the two parallel dotted lines M N, which will give the breadth the 
 circle is to have at G and it's furtheft diminution. Laftly, draw 
 lines from all the angles on which the great circle is produced, towards 
 the center, and the points wherein they interfect the dotted lines 
 ab c d e fg hiklmnop q r . will be the points, which, connected with 
 curve lines, will form the inner circle's circumference. 
 
 A perfon who mould delire a plan of three, four, five, or fix circles 
 in perfpeclive, muft lay them all down in the geometrical plan after 
 the fame manner as the fecond femi-circle is done in this example^, 
 and then.obferve the fame method of procefs. 
 
 * 
 
I 
 
3° PRACTICAL Part II. 
 
 To exhibit the appearance of the Plan of a Square 
 
 viewed Angle-wife. 
 
 T F it be required to draw a fquare, viewed by an angle directly 
 A oppofite to the eye, there is nothing more requifite than to fet off 
 the diagonal of it upon the bafe line ; as here A C is equal to the dia- 
 gonal of the geometrical plan of the fquare to be projected. Then 
 from the points A and C to draw two lines to the point of diftance D, 
 then to fet off the meafure of the line A C on the bafe line towards 
 A E, and from E A to draw lines to the point of diftance F, and the 
 three interferons of the lines H I K will be the bounds of the fquare 
 defired, viz. 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 fquares 
 on each fide, and fixty-four in all. 
 
 If in the fame plan, thus viewed by the angle, inftead of the divi- 
 fions in the fiirft figure, it were required to have little plans in the four 
 corners, as four lodges, columns, trees, or other objects, fet the width 
 of each on the bafe line, as B D, E A, on the neareft fide, A F, G C, 
 on the other fide ; from which points drawing lines to the points of dif- 
 tance H I, their interferons will give the four plans KLMN required. 
 
Part II. PERSPECTIVE. 
 
 3° 
 
 3v 
 
 D 
 
 H 
 
 G Ct 
 
PRACTICAL 
 
 Part II, 
 
 To exhibit the perfpeSiive of a Pavement ^Square- 
 Stones, viewed by the Angles. 
 
 AT O W we are about places viewed angle- wife, it may not be amifs 
 to mew how the pavement of a hall, church, or other place, is 
 'to be conducted. Having drawn the horizon parallel to the terreftrial 
 line A B, the point of fight C, and the points of diftance D and E,. di- 
 vide the bafe into as many parts as you would have fquares j then draw 
 lines from the extremities thereof A and B, to the point of fight C, and 
 from the fame points A and B, draw two diagonals to the points of 
 .diftance D E, the points of interfection F G will give the fquare of the 
 hall, and through them the line of depth H I is to be dra wn. Then draw 
 lines from all the divifions of the bafe line A C and B C,. to the points 
 of diftance D and E, and between the rays A C and B C, you will have 
 your defire; as appears from the figure. But here arifes a difficulty, 
 namely, how to fill the vacant fpace B B and G I, A A and H F, with 
 the fame fquares j for it is fuppofed the bafe line cannot be prolonged any 
 farther. On fuch occafion, take the meafure of one of the fquares, as 
 G K, on the line F G, and fet it off on the fame line H I as often as it 
 will go, and you will have the points LMNOPQ^andR, through 
 which drawing lines to the point of diftance,- you will have the fame 
 fquares as before ; fuch are thofe here marked with dots*. The fame 
 method of fetting off the meafures on the line of depth, will be ex- 
 emplified in other pavements hereafter. 
 
 To exhibit the perfpeSiive of a Pavement of Squares 
 encompaffed with a Lift or Fillet. 
 
 T H E method of managing this fecond pavement with a band 
 around it, is the fame with that of fingie fquares viewed in front ; 
 I (hall therefore decline to wafte any time in teaching it, fince I have al- 
 ready given fo many figures thereof. It may be proper, however, to 
 ^dd, that the bafe line is to be divided into unequal parts, as A, B and 
 C, hecaufe of the fillets, and lines to be drawn from all thefe divifions 
 to the point of fight D, and through the points where thefe are inter- 
 fered by the diagonals A E, and G F, parallels to the bafe line are to 
 be drawn. By this very plain operation will be produced the appearance 
 <of the pavement fhewn in the oppofite figure. 4 
 
32 
 
 PRACTICAL 
 
 Part IL 
 
 To exhibit the perfpeSiive appearance of Pavements 
 viewed angle- wife y encompaffed with a band or fillet. 
 
 FOR fuch kind of Pavement, the bafe line A B is to be divided 
 into unequal parts, the largeft whereof are to be for the fquares, 
 and the fmaller for the band or fillet ; and from all thefe divifions, lines 
 » re to be drawn to the points of diftance E F, As has been already 
 directed in {ingle fquares.. 
 
 To exhibit the perfpeSiive appearance of Pavements of 
 Squares viewed in fronts encompaffed with bands, or 
 fillets, whofe fquares are divided by the angle. 
 
 FOR this fourth kind of pavement, the fame method is to be 
 taken as in the fecond, by fetting the meafures of the firft range 
 of fquares and fillets on the bafe line, and from thofe points to draw 
 the lines according to former directions. Then to make the inner 
 fquares which are feen angle-wife, nothing more is required than to 
 bifecT: the loweft fide of each fquare of the firft range, and from thofe 
 points, as A, B, C, D, E, F, G, draw lines to the two points of dis- 
 tance, and their interfe&ions with one another will produce the feverai 
 inner fquares or lozenges throughout the plan. 
 
33 PRACTICAL Part N, 
 
 To exhihit a pavement of Squares viewed angle-wife^ 
 with chains of Squaresy^ in front. 
 
 T Shall fuppofe the perfpe&ive, or diminution of the fquare, by draw- 
 X ing the line of depth, to be already done, that I may fave the trouble 
 of too frequent repetitions in the enfuing pavements. 
 
 To manage this fifth fort of pavement, divide the bafe line into 
 equal parts, to anfwer the number of fquares, and from the points of 
 the fquares to be divided in front, as A B C, draw lines direftly to the 
 point of fight, and from the points of thofe to be feen obliquely, draw 
 lines to the points of diftance, but without marking them through- 
 the chains. After all the fquares which are thus viewed by the angle 
 are drawn,, the fquares of the chains will be eafily formed by parallels 
 from the oppofite angles of the oblique fquares on either fide. As 
 for example, from the angle D and E draw the parallel line F, and fo for 
 all the reft, as is (hewn by the figure. Care is ftill to be taken, that 
 there be always the fame number of fquares between the chains • as 
 here we have three between A B. The meafures on the bafe fine 
 rightly laid down, will prevent any error of that kind. 
 
 ^^^^^^^^^^^^^^^^^^^^^^^^^ 
 
 To exhibit a pavement of Squares in fronts with chains 
 tf/^ Squares angle-wife, 
 
 f | s H I S fixth fort of pavement is performed much after the manner 
 J[ of the preceding, by dividing the bafe line into equal parts, 
 according to the number of fquares, and from the points of divifions 
 drawing lines to the point of fight, to form the bands or chains 
 G H I 5 yet [fomewhat more in it, care being taken to make the 
 crofs there is, of the fame breadth as the others that tend to the point 
 of fight O, and that there be the fame number of fquares between the 
 vacuities. The reft is obvious enough, 
 
PRACTICAL Part II. 
 
 To exhibit a pavement of O&agons intermixed with Squares. 
 
 TT ftiould never have done, was I to give all the varieties of pave- 
 ments : invention would find endlefs employment in their construc- 
 tion. This feventh inftance is obvious enough j all I add it for, is to 
 open the mind, and furniih occafion for the contriving of others. All 
 that is required to produce this kind of pavement, is to divide the fcafe 
 line into a number of parts equal to the number of fquares to be for- 
 med, as has been already directed. Of which fquares a certain num- 
 ber is to. be taken, as here nine, fi"e whereof are full, and the reft 
 only halves j the full ones give the infide of the figure 12345, and 
 the diagonals of the reft, 6789, give the fides : the reft is evident. 
 
 To exhibit a pavement of fingle Squares viewed in front, 
 
 HIS form I have put the laft, not as being the moft difficult, 
 j| 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 
 others being feldom added but by way of ornament, and this ferving 
 as the foundation whereon any folid is to be raifed, and the elevated 
 parts made appear. As will be ftsewn hereafter. 
 
PRACTICAL Part II 
 
 Plan of a Garden in perfpe&ive. 
 
 \"\ 7 ^ ^ ^ we ^ ave ^ een °bf ervm g> * s confirmed by this 
 YV pl an > which {hews with what facility the projec- 
 tion is made by the foregoing rules. For, drawing lines 
 from all the divifions on the bafe line to the point of 
 fight, the diagonals will give the depth of the whole 
 plan, and the diminution of all the little fquares. Laftly, 
 marking the walks, borders, and figures of the geometri- 
 cal plan in the correfponding fquare of the projected plane, 
 the whole parterre will be found in perfpective. 
 
 . Let the plan given you to put in perfpective, be of 
 what fort foever, the readieft way will be to draw a 
 fquare about it, and divide that into feveral lefler fquares. 
 For after the grand fquare, with all the leffer ones, are 
 projected by the ordinary rules, you have nothing farther to 
 do, but take care that every part is comprifed in the fame 
 number of little fquares in the diminished plan as in the 
 geometrical one, and the figure of the one will be exa&ly 
 found in the other. 
 
Part II. 
 
 PERSPECTIVE- 
 
 o 
 
3 6 
 
 PRACTICAL 
 
 Part IL 
 
 Plan of a Building m perfpe&ive. 
 
 SERLIO, in his treatife of Perspective, fets a 
 great value on this method of putting plans in perfpeo 
 tive, as a thing of lingular ufe in architecture, whereby a 
 perfon is enabled to fhew one part of a building raifed, and 
 the reft in platform. But this method for exhibiting the 
 projected plans of buildings, being the fame with that I 
 have already laid down for a garden, I need not fay any 
 thing farther thereof: the figure is fufficient for the reft. 
 And from this one figure meafures are ea*fily taken for any 
 other, either more eafy or difficult ones. 
 
Part II. 
 
 PERSPECTIVE. 
 
 O 2 
 
37 
 
 PRACTICAL 
 
 Part IF* 
 
 Plan <?/ ^ Church, in perfpe&ive. 
 
 rTPSHI S plan is conduced according to Obfervation VH. 
 
 page 18. That is, all the fides 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 fight ; and all the other fides parallel to the bafe line, as 
 are here the breadths, §f £. drawn to a line on one fide, O Y% 
 which thus (hews the points abcdefghikl. Thefe points, 
 transferred hence upon the bafe line as ab, 8cc. and lines 
 drawn from them to the points of diftance, their interfec- 
 tions with the extreme ray, give points for drawing parallels 
 through, exhibiting the diminution of every thing : as fhewn 
 by by c> &c. 
 
 This method of diminiming on the extreme ray is prac- 
 fifed by many ; and yet fuch as would take my advice, 
 fhould let it alone, and rather follow the method directed in 
 Obfervation VIII. where a perpendicular is raifed on the end 
 of the bafe to receive the interfe&ions, and to obviate the 
 defedfc of the prefent method, which does not diminish 
 enough, unlefs where the points of diftance are very remote: 
 for in that cafe, the effect is the fame as in the other methods. 
 
Part IT. 
 
 PERSPECTIVE 
 
 37 
 
 37 
 
 =T7 = 
 
38 
 
 PRACTICAL 
 
 Part II. 
 
 Plan of a Houfe with a Garden. 
 
 THE method of putting this plan in perfpe&ive, is 
 the fame with that of the garden alone; fo that 
 what is there faid may fuffice for both. My defign in 
 putting it here, is to fhew, that one may diminifh all forts 
 of plans, whether confifting of equal or unequal parts. 
 
39 
 
 PRACTICAL 
 
 Part II. 
 
 Plan oj cl Fortification in perfpe&ive* 
 
 f"*^p^O put a Fortification, or other plans of the like 
 j[ kind in perfpe&ive, the Vllth and vlllth Obferva- 
 tionS) page J 8, are to be ufed. The fame in effecl: is the me- 
 thod already laid down for the Church and House, pages 
 37, 38, namely, by raifing perpendiculars from all the angles 
 to the bafe line, and producing rays from their interferons 
 with the bafe line, to the point of fight ; and from the fame 
 angles drawing the parallels to the terreftrial line, and mark- 
 ing the divifions on a fide line, A.B. Thefe divifions being 
 transferred thence to the bafe line, and lines drawn from 
 them to the point of diftance, we (hall have the line of in- 
 terferons C D. But, becaufe there is not room on the plate 
 to put it on the bafe line, I have added it underneath the 
 figure, as in A B. Laftly, having fixed the point of diftance 
 in E ; draw lines thence to all the divifions of A B, cutting 
 the line of interferon C D in fo many parts ; which line, 
 C D, with its divifions, is to be transferred to the bottom 
 of the extreme ray, in the perfpe&ive plan, or rather fet on 
 each fide, as DD; and from all the points of the lines D C, 
 D C, 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. 
 
Part II. 
 
 PERSPECTIVE. 
 
 39 
 
 Horizon 
 
 57 
 
40 
 
 PR ACTIG AL 
 
 Part II. 
 
 An irregular Plan and Figure in Peripective. 
 
 WHOEVER can perform what is directed under 
 the laft article, will find no difficulty in project- 
 ing any other figure, that being the moft intricate of all 
 kinds of plans in perfpective. It was judged, however 
 proper to add fome irregular form, which might appear 
 at firft fight to be difficult, in order to fhew that thefe rules 
 are adapted to all the variety of poffible figures, and that 
 every form and fhape, in whatever view or afpecl: it is to be 
 feen, may eafily be projected in perfpe&ive. 
 
 The lines in this plate are marked as in the former : to 
 repeat the operation is needlefs* 
 
4* 
 
 PRACTICAL 
 
 Part II. 
 
 Another plan c/^Church, in PerfpeElive. 
 
 manner of projecting the perfpective of this plan, (hould feem 
 A very different from what I have hitherto delivered, by rcafon of 
 its different difpofition j but that I own is a thing done defignedly, to 
 fhew that though there be diverle ways and manners of operation, they 
 are all reducible to one. For this projection, in effect, is the fame with 
 what I have already prefcribed for fortifications, irregular figures, and 
 other plans, with only this difference, that the parallels to the bafe 
 line are there marked on a fide line, and here, on a line in the middle 
 of the plan. But the fame effect is produced from each method ; for 
 drawing lines from all the divifions of the middle line B L to the eye A» 
 you will have the line of interfection B C, which is upon what may be 
 called the bafe line D E. 
 
 To put the geometrical plan in perfpective, transfer the whole length 
 of the terreftrial line D E to any place at pleafure, as D E in the 
 perfpective plan, and fet off the height of the eye A F ; then, putting 
 the line of interfection B C either in the middle, or on one fide, draw 
 parallels to the bafe line through all its divifions to the extreme rays 
 DA, E A, and fet the breadth of the pilafters D K on the bafe line j 
 then drawing a line from K to the point of fight A, the points wherein 
 it interfects the parallel lines will be the widths of the pilafters. 
 
RULES 
 
 F O R 
 
 ELEVATIONS. 
 
 PART III. 
 
4? 
 
 PRACTICAL 
 
 Part HI. 
 
 Preliminary infixuctions necejjary to the following methods. 
 
 rip H E reader is by this time fufficiently inftructed in what relates to Ichno- 
 J[ g r ^phy and Planigraphy, conlidered as the foundations of Orthography 
 and Scenography. 
 
 Orthography, I have already defined to be the elevation of the fore-right 
 plane or front of any object, the elevation of the face or front, &c. and Sceno- 
 graphy the elevation of all the parts. See the Definitions, page y. 
 
 To make myfelf more intelligible to fuch as are not verfed in the life of thofe 
 words, 1 purpofe, as already promifed, for the future to call fchnography the 
 Plan; the Orthography, the Upright or Elevation of the front ; and Sceno- 
 graphy, the Ekvaiim of the whole. 
 
 Here it is to be obferved, that elevations 1 never give the eye all the angles 
 of the plan, and that the quantity of fides, or angles which appear to the eye- 
 depends on the afpect or view the objecl: is taken in. Thus, if it be viewed 
 in front, as the figure A, it will only fhew one fide, though the plan hath four. 
 If it be viewed by the angle, it will fhew two, as B ; but never more, in what- 
 ever view it be taken. J fpeak of fquares for as to objects of many fides, 
 they may fhew three, four, five, and more. 
 
 "When objects decline ever fo little from the point of view, they are feen 
 by the angle, and of confequence muft fhew two fides. And ftill the farther 
 they are removed from the po;nt of fight, the more of the fide they fhew •, thus 
 the fide KE fhews more of itfelf than C L, though their thicknefs be equal. 
 
 Another thing to be obferved is, that the lines which are parallel to the hori- 
 zon whin the objecl is viewed in front, as C D E F of the door in Fig. 1. be- 
 come a vifual ray when the fame objecl: is viewed a little obliquely. Thus C D 
 E F, which in the upper figure ftands in front, becomes a vifual ray in that 
 underneath. And, on the contrary, the lines which are rays in the upper, be- 
 come parallel to the bafe in the under. As to perpendiculars, they always con- 
 tinue perpendiculars in whatever view the projected bodies are exhibited. 
 9 
 
43 
 
 PRACTICAL 
 
 Part III. 
 
 Of the Line 0/ Elevation, ferving to give the Heights of all 
 Kinds of Objects in all Parts of the Plan. 
 
 TH E ufe of this line is of the lad importance, infomuch, that whoever is 
 perfectly mafter thereof, will fcarce meet with any difficulty in raifing any 
 kind of elevation. 
 
 As^ in the putting planes in perfpeclive 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 objects in the plan. On this account 
 the line of elevation C D, is raifed perpendicularly on A B, as the other lines 
 in the plan mould be. Infomuch, that it is to be remembered as a rule, that 
 whenever, in the courfe of this work, mention is made of perpendiculars, it is 
 to be underftood of perpendiculars to the bafe. 
 
 Since this line of elevation is to receive and give the heights of all objects 
 to be raifed on the plan, it muft have the fame horizon with the plan. Therefore, 
 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, though what part does not matter, 
 the effect being the fame in all. In this figure, the line of elevation is C D, and 
 from C the line is drawn to the point of the horizon in E ; or it might 
 be drawn to the point of fight, if one pleafed. I have here put the line of 
 elevation on either fide, and the point different in each, to mew that it will 
 anfwer any where. 
 
 If from the point H, which is in the plan of the fecond figure, you would raife 
 a line of two feet 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 drawing a line to the 
 point E, you will have an elevation of two feet between the two lines C and F. 
 
 Now, to give the fame height of two feet to a line raifed from the point H, from 
 H draw an occult line parallel to the bafe line, till it meet the line C E in the point 
 I 5 then from the point I erect a perpendicular [ K ; this will be the height of the 
 line required, which is to be taken hence in the companies, and fet off from H to L. 
 
 If a line likewife two feet 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 QJl for the height of a line of two feet from the po nt P. 
 
 The fame rule will give a height of 3, 4, 5, 10 or 20 feet ; 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. 
 
PRACTICAL Part III. 
 
 To exhibit the El e v a ti on of a Cube in PerfpecYive. 
 
 1* J AVING projected the plan according to the preceding rules, and raifed 
 the line of elevation as F L, fet off the height of the cube thereon, namely 
 F M, and from the points F and M draw lines to the point of elevation E, 
 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 interfection F and H, 
 creel perpendiculars F M and H K ; then taking thofe meafures in your com- 
 paries, fet them perpendicularly upon the angles of the plan ; thus, taking the 
 height F M, fet it on the two perpendiculars raifed from A and B, which will 
 give you A G and B G 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 GO, O G, the cube will be raifed. 
 
 Or, if you draw parallels to the bafe line from M and K, their points of in- 
 terfection with the perpendiculars AG, B G, CO, DO, will be the altitude 
 of the cube, and thofe points connected by ftraight lines will complete its figure. 
 
 For the elevation of any figure whatever, always draw lines from the feveral 
 angles of its plan, parallel to the bafe line, till they cut the line drawn from 
 the foot of the line of elevation, and proceed in all refpeets as directed for the 
 cube, and you will find there is no figure however difficult and irregularly 
 formed, but will be thus brought into its perifpeclive. Examples of which I 
 mall give in the polygons following. 
 
 The fecond figure is another cube, raifed after a fomewhat different manner 
 from the firft. The procefs 1 fhall defcribe in few words, being nothing con^ 
 temptible. 
 
 Having difpa ched the plan the ordinary way, from the feveral angles thereof, 
 BCDE, erect perpendiculars j and on the firft of them, B C, fet off the given 
 height of the cube, namely B A, C A •, then from the points A A draw lines 
 to the point of fight F, or to the points of diftance G H, 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 1 ihali 
 have occafion to touch upon hereafter. 
 
45 
 
 PRACTICAL 
 
 Part III. 
 
 To find the Elevation of # Triangle. 
 
 I Now proceed to (hew with how much eafe all kinds of figures may be raifed 
 in perfpective. Of thefe, polygons, or figures of many fides, are the molt 
 difficult. I fhall therefore choofe to exemplify in thefe ; and, to obferve fome 
 order, will begin with the mod fim'ple, the Trian gle. 
 
 Having formed the plan, as already directed, page 21, where is fhewn the 
 method of drawing it with a ledge or lift ; the line of Elevation, as juft now 
 intimated, muft be fet on one fide, and of any height at pleafure, for example 
 B A, which we fuppofe to be three feet ; then from all the angles of the plan 
 drawing parallel lines, parallel to the bafe line, to the line B E, and from 
 the points of interferon erecting perpendiculars between the lines A E and B E, 
 fet off all their heights upon the feveral angles, whence the parallels proceed. 
 The height A B for inftance, on the angles C and D, which will give C R 
 and D S, the height N P on the angle Q, which will give Q_Y. Then for 
 the inner angles, fet F I on G and O which will give G T and O V, and N L 
 fet on K will give K K. Laftly, connecting the points R, S and Y, and 
 again the points T, V and X, by right lines, you will have the triangle in its 
 proper thicknefs, &c. 
 
 By drawing lines parallel to the bafe line, from the points A I L P, the 
 points of their interferon with the perpendiculars raifed from the angles of 
 the plan, will give the angles of its elevation. 
 
 To exhibit ^ Pentagon, or Five-angle, in perfpeSiive. 
 
 THE Pentagon, I have faid, is a figure with five fides, and as many 
 angles ; and have directed the method of forming its projection, page 22. 
 As to the making its elevation, I mould lofe time to defcribe it, the figure hereto 
 annexed, with the lines drawn from its angles, and from the perpendiculars of 
 its altitude, mewing abundantly that its method is the fame with that of the cube 
 and triangle. 
 
 To exhibit the elevation of a Hexagon, or Six-angle, in perfpeElive. 
 
 THE Hexagon is a figure with fix angles, and as many fides or faces, 
 as already obferved, pages 23, and 27. where I have given its diminution'. 
 The method of raifing it is obvious enough from the figure. 
 
PRACTICAL 
 
 Part III 
 
 The Heptagon, or Seven- Angle, in perfpeclive. 
 
 F | "1 HE Heptagon is a figure with feven fides and 
 jL angles ; the manner of defcribing it, and of putting 
 its plan in perfpeclive, I have already given in page 24. 
 Its elevation is performed after the fame manner as that of 
 the triangle, as appears from Fig, I. 
 
 'The Octagon, or Eight Angle, in perfpedive. 
 
 THE Octagon is a figure with eight fides and as 
 many angles, as reprefented in pages 25, 26. where 
 the reader will find different ways of putting the plan in 
 perfpedive. Its elevation is to be procured in the fame 
 manner as that of the preceding objecl:. 
 
47 PRACTICAL Part III. 
 
 A Double Crofs in perfpe&ive* 
 
 THIS and the following figure I add from the Sieur de Maralois, 
 who has given them a place in his works according to the me- 
 thod I have already laid down. The truth is, it would be fomewhat 
 difficult to put them in perfpe&ive any other way, by reafon of the 
 multiplicity of their angles ; but in this method all is eafy, by only 
 raiting the heights from all the angles of the plan, &c. as already ob- 
 ferved of polygons, and is evident from the figure. 
 
 A Stone fluted, or channeled ftar-wife, in perfpeElive. 
 
 NO T having given the plan of this figure among the other plans, 
 I have judged proper to add it underneath. The geometrical 
 plan is eafily made, as being only a circle whofe periphery i9 divided 
 into fix parts and the divifions joined by right lines, leaving a point 
 between each two j as, for example, between i and 3 , leaving 2 and 
 from 2 to 4, leaving 3 ; and fo of the other. The reft is obvious from 
 the fecond figure, 3 
 
4 8 
 
 PRACTICAL 
 
 Part III. 
 
 tfo exhibit Pilasters in perfpefiive. 
 
 IN the railing 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; it is fufficient to proceed as in 
 the fecond method for the cube, page 44, that is, having raifed perpendiculars from the 
 angles of the plan, as here from A B C D of Fig. 1. fet the height defired on the firft 
 or fecond perpendiculars, as A F or D E ; then drawing a line from E to the point of 
 fight F, to this line all the perpendiculars from the angles from the inner fide of the pilaf- 
 ters are to be raifed. In which cafe, the pilafters G and H will have equal altitudes to 
 the firft. 
 
 If one choofe not to make ufe of fquares in the plan, the meafures muft be laid on the 
 bafe line, and rays be drawn thence to the point of fight F, and other rays for the diminu- 
 tions to the point of diftance K. Thus, for example, L M being a fide of a pilafter, rays- 
 are to be drawn from the two points thereof, L and M, to the point of fight F, for the 
 breadths of all the pilafters ; and for the depth of each, as they are intended to be 
 fquare, the diftance L M is to be taken and fet off from L to N; then drawing a line to 
 K, it will give the depth of the pilafter in O; laftly, from the points L M O erect 
 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 P Q, 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 j. 
 and from S draw another ftiort parallel S T, cutting the ray MF; laftly, from the three 
 points R, S and T, erecting perpendiculars, proceed as in the former cafe. A third and 
 fourth pilafter, &c. are to be added after the fame manner, ftill obferving the fame meafures 
 on the bafe line as in the firft figure. 
 
 Tlo exhibit Pilasters viewed by the angle. 
 
 I HA VE already obferved, page 17, that the plan of fquares is formed by drawing 
 lines from the divifions of the bafe line to the point or 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 C D y 
 which will interfect and give the heights of the other perpendiculars raifed on each fide. 
 Then giving the diftances required between the two pilafters, which are two fquares, raife 
 the fecond ; and by the fame rule the third. Their heights will be found by drawing 
 a vifual ray from the point B to the point of fight E, the interferons whereof with the 
 firft perpendiculars in the points F and F, as alfo the interfections of other lines from F 
 and F to the points of diftance C and D with the other perpendiculars, will give the 
 heights required, as in the firft pilafter. 
 
 Thefe pilafters which are raifed 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 fight E, 
 which will give all the middle points, or diameters. Then fetting the fame breadth from 
 G to I, from the three points G H I draw lines to the points of diftance C D, which 
 form the firft plan. On this plan erect perpendiculars, on the firft whereof fet off the 
 height, as G K, and from the point K draw lines to the points of difiance, which will 
 give the (hortnings of the perp*endiculars of each fide. 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^, I 
 
49 
 
 PRACTICAL 
 
 Part III. 
 
 Effed of the Difference of Horizons, 
 
 T< HE higher a man is raifed above an object, the more he fees of 
 the 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 proportion is evident from Fig. I. the fecond from Fig. 2. 
 and the third from the laft. 
 
 The flrfl: and fecond cubes are formed after the manner already de- 
 livered. The third are alfo produced by the fame rules, though they 
 may appear fomewhat more difficult, by reafon the object is feen over- 
 head 3 but inverting the paper, or painting, and drawing lines to the 
 point of fight A, and points of dittance B and C, as in the former me- 
 thods, you will have the fame facility in exhibiting them. I fay no- 
 thing of objects viewed fide-wife, as having fo often repeated, that the 
 method is the fame as thofe in front. To render the practice of putting 
 them in perfpective more eafy, I have added in the next plate two figures, 
 the one a bare out-line, the other (hadowed farther. 
 
 Before we quit this third figure, it is to be obferved, that the lownefs 
 of the horizon is the reafon we fee the bottoms of objects, as DEF, 
 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 
 horizon j nor the bottom, becaufe they are the horizon itfelf. 
 
 There are abundance of painters faulty in this point, inconfiderately 
 (hewing the tops of objects, even where the horizon is very low. 
 
PRACTICAL 
 
 Part III. 
 
 Elevation of Objects viewed by the Angle. 
 
 I HAVE fhewn in pages 19, 20. that in the projection of oblique 
 plans, the lines are always to be drawn to the point of diftance, not 
 to the point of fight, unlefs for finding the diameter. The fame rule 
 is to be obferved in raifmg 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 the point of fight A. 
 
 The firft figure D mews that though there be a multiplicity of parts 
 in any object feen angle-wife, they are all to be^. drawn to the points of 
 diftance B and C. To perform the operation, the rule is this ; having 
 projected a plan, and raifed occult perpendiculars, as already directed, 
 let the given height on the firft angle, as E F, and from F draw lines 
 to the points of diftance B C, for the heights of the fecond and third 
 angles, in the points of interfection G G, then from G G draw lines 
 to B and C, and you will have the fourth angle of the platform. The 
 other lefter pieces are raifed after the fame manner, namely, 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 thicknefTes of all the IefTer pieces, and the 
 platform of the middle, by ftill continuing to draw lines to the points 
 B and C. The reft is evident from the figure, which may ferve for a 
 caftle defended with four fquare towers, or for a palace cantoned with four 
 pavilions. 
 
 The two other objects on each fide the great one are feen fide- wife; 
 the manner of drawing them is in all refpects like thofe viewed in front. 
 Thus, raifing 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 B C, you will have the fecond 
 and third angles in the points of interfection O O ; then drawing lines 
 from O to the points B C, you will have the fourth angle, 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 produced the fame way ; all the dif- 
 ference 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 ftiew the tops, the lines being drawn to the 
 points of diftance QJil in the horizontal line. 
 
PRACTICAL 
 
 Part III. 
 
 ( fo rai/e cfy'e&s of any heights and remove them to any 
 
 dijlance at pleajure. 
 
 SUPPOSE it be required to have an object two feet high, one foot broad, 
 and one foot deep •, and another three feet high, one foot broad, two feet 
 deep, and two feet diftant from the firft object and another a foot broad, five 
 feet deep, four feet high, and three feet diftant from the middle object your 
 method of proceeding will be thus. Having formed a plan of fquares, fuppofed 
 each equivalent to one foot, by means of the points of fight A, and diftance 
 B C ; from the firft angle D erect a perpendicular according to the fecond me- 
 thod, page 48, which perpendicular is to carry the proper meaiures to all the 
 objects, as here D E, wherein the meafure D F, is fet four times, by reaf >n the 
 higheft object is not to exceed four feet. From the feveral angles of the firft 
 Iquare F I G D erect occult perpendiculars ; and having fet the proper meafure, 
 namely two feet, on the firft of them, D, from the point 2 draw a line to the 
 point of fight A, and it will cut the perpendicular of the angle G in the point 
 H, through which a line is to be drawn parallel to the bafe, cutting the per- 
 pendicular of the angle I in K, and another parallel to be drawn through the 
 point 2, cutting the perpendicular of the angle F in the point L •, then connect- 
 ing the four points H K L and 2, by right lines, you will have the firft object. 
 Kow as you would have a fpace of two feet between the firft and fecond object, 
 two fquares are to be left vacant between them; and on the firft angles of the 
 third, perpendiculars are to be raifed, and the fame operation performed as to 
 the firft object, with this difference, that the height of the f.*cond is to be taken 
 from the third point of the line D E, by reafon it is to be three feet high, and 
 that it mu ft -take up two fquares, fince it is to be two feet deep. B tween this 
 fecond and the third object the fpace of three fquares is to be left, by reafon 
 there is to be three feet diflance from the one to the other. From the firft 
 angles of the fourth fquare perpendiculars are to be raifed as for the firft object, 
 and five fquares farther, another perpendicular for the line of the depth, and the 
 bound of the five feet, which is the depth of this third object. The fourth point 
 of the line D E gives its height, four feet, by cutting the perpendiculars, as in 
 the firft object. The objects on the other fide are railed in the fame manner, and 
 on the fame proportions as thefe •, but the wall in the middle is of an equal height 
 every where, namely, three feet, with an aperture of four feet in the middle. 
 
 In the fecond figure are three walls of equal height ; whereof that in the 
 middle is a fquare deeper than the two extreme ones. Between each is an aperture 
 of three feet, for doors or windows. On the other fide is a continued wall four- 
 teen feet long, and of an height anfwerable to the reft. The metho.i of elevat- 
 ing all thefe, is the fame with thofe above. What we call a wall may likewife 
 ftrve for a hedge, palifade, of a garden. 
 
52 PRACTICAL Part III. 
 
 Of W alls viewed in Front, 
 
 FROM what has been faid one may raife walls of all kinds in any oblique views ; 
 and (hough the fame method may ferve for the fame walls viewed in front, I have 
 thought proper to add this figure on two accounts : i/?, by reafon it is not always that 
 plans are made, and on fuch occafion a man would be a little to feek for the thicknefles. 
 2d/y, To give the thicknefles to gates and windows, which might occur in fuch walls. 
 
 To make walls parallel to the bafe line, or the horizon, on a plan, one may give them 
 any length at pleafure on the parallels to the horizon. To adjuft their breadth, you may 
 take that of a fquare, from the angles whereof A B, you are to erect perpendiculars to 
 any height, as C ; from C draw a ray to the point of fight D, and C D will give the di- 
 minution 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 j then from F a line is to be drawn to the 
 point of fight D, and from E, another to the point of diftance Gj and from the inter- 
 feron of the two in the point H, a perpendicular to be raifed, and another from the point 
 F. Then the height of the wall F I is to be taken, and from I a line to be drawn to the 
 point of fight D, the interferon whereof with the perpendicular H, will give the dimi- 
 nution of the wall. For the length, you may give it at pleafure on the firft parallel E F. 
 For the doors and windows, in the fame walls, mark the width and height as here PC L 
 M N, and fet the thicknefs required on a parallel, either above or below the doors or win- 
 dows, in the corner next the point of diftance, as here NO or L Oj laftly, from the 
 points L and N draw lines to the point of fight D, and from the points O to the point of 
 diftance G, and from the interferons of thofe lines in P, &fc. draw the thicknefles. 
 
 Other W|a'l ls viewed by the Angle. 
 
 WHEN the wall is to be raifed on a plan, you have nothing to do but erecT: per- 
 pendiculars from the angles already determined, and to mark the heights on the 
 perpendicular from the angle netft you, as on the line Q_R ; and from the point R, to 
 draw lines to the points of diftance ST; the interferons thofe lines make, with 
 the perpendiculars raifed from the angles of the plan, will give the length and thick- 
 nefs of the wall. If you have no plan, fet the meafures both of the breadth and depth 
 of doors and windows on the bafe line, as in this example, VX is the breadth, XY the 
 depth, and Z I the height of a window; then from all thefe points draw lines to the points 
 of diftance S T j 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 Y S will give it by its interfering with X T in the point 6 ; and Z 1 will 
 give the breadth of the windows in the points 7, 8; from which points X, 5, 6, 7, S 9 
 perpendiculars being raifed, and the height % being fet on the firft of them X, and from 
 the point 2 drawing lines to the points S T, the interferons with the perpendiculars will 
 give the height of them all. From the height of the window, marked 3, 4, draw lines 
 to T, and where thefe interfecl the perpendiculars 7, 8, lines are to be drawn ; and from 
 the corners 9 to S, for the depth 10, draw lines to T, and from the point of interfec- 
 tion 1 1, draw a perpendicular. This may alfo ferve for a palifade as well as a wall. 
 
 9 
 
53 
 
 PRACTICAL 
 
 Part III. 
 
 To place a Door in any part of a Wall at pleafure. 
 
 A WALL being raifed one, two, or three feet thick, on the points H I, and carried 
 on of the fame height, as already directed ; in order to place a door in any part 
 therepf, obferve the following method. Suppofe the door required is to be three feet wide, 
 and all its dimenfions to correfpond with that of the lower figure. To place this door in 
 the middle of the end wall, fet the breadth on the bafe line, as here in A B, and on thq 
 fide of A and B fet the breadth of the frame, or band, D and C, aad from A B C and D 
 draw lines to the point of fight K ; and where they cut the parallel M N in the points 
 O O, &c. ere& perpendiculars of any heights at pleafure. Thus is the width of the door 
 procured. For its height, D F E is to be transferred from the door underneath to the 
 corner of the wall I, and lines to be drawn from the points F E to K ; and where they 
 lnterfed the perpendicular M P in the point Q, draw Q_R parallel to M N, which will 
 give the height of the door, and the band or frame at 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 fight K, it will cut the perpendicular M P in the point S, through which 
 drawing S T parallel to Q^R, you- will have the thicknefs of the door V. 
 
 To make a door in a fide-wall, the inftru&ions given in page 17. are to be well re- 
 membered; importing, that all the meafures are to be put on the bafe line; and, that 
 lines being drawn from thefe meafures to the point of diftance, will give all the diminutions 
 defired. For an example, a door four feet broad is defired in a chamber. Set off four 
 equal diftances from I to C, and draw lines from the dimenfions of the door G A and 
 B D to the point of diftance L ; where the ray I M interfeds thofe lines, erect perpendi- 
 culars X Y, which will give the breadth of the door. For its height, draw lines from 
 the point E and F to the point of fight K, and the inter feclions with the perpendiculars 
 will give the height. As to the thicknefs of the top and bo tom, draw the thicknefs of 
 the wall, G H and F I, to the point of fight K ; then drawing a little parallel to the 
 terreftrial line, through the lower corner of the door X, and another through the upper 
 corner, you will have X Z, the thicknefs of the top and bottom, to be joined by a 
 perpendicular, as you fee in the figure. 
 
 If you would have a door on the other fide, you have nothing to do but draw parallels 
 to the bafe line from the pointX to the ray i N, and then raife them as already direded. 
 The reft is the fame as on the other fide. The gate is not here reprefented in the middle; 
 it is defignedly placed eNewhere, to obviate the error of fuch as without any other 
 meafures, draw two diagonals through their painting, though of ever fo great a fize, 
 and make all their object equally diftant from the interfe&ion of thofe lines, that is, from 
 the middle of the painting. So that, on their principle, a body mould always be mounted 
 to fhew their work in all its advantage; which is a palpable overfight. For though 
 painting fiiould be forty feet high, and it fhould be placed on the ground to be feen, the 
 horizon fhould never be above five feet high, but rather lefs than more; whereas in their 
 way the horizon fjiould be twenty feet high. 
 
54 
 
 PRACTICAL 
 
 Part III. 
 
 To draw Windows in PerJpeSfzve. 
 
 TH E method of defcribing a window is perfectly the fame with that of a door ; there- 
 fore by learning, to make a fingle and double crofs, you are a mafter of windows. 
 Suppofe now it be required to make a window in the wall A B, of any breadth at plea- 
 fure, lay down its breadth on the bafe line, as D E, and from the points D and E draw 
 lines to the point of diftance F, and from the interferons G G, of thofe lines with A K, 
 erect perpendiculars G H, G H giving the width of the window, which is here only two 
 fquares, or panes. As to the height, it is ufually raifed as near the ceiling as may be, 
 but the breaft-part mould not be above three feet and an half ; this meafure therefore is 
 to be fet on the perpendicular A B, as from A to I, and drawing a line from I to K, 
 where that line interfects the perpendiculars 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 fight K, its in- 
 terferon with G H, will be the top of the window ; by which means we fhall have a 
 long fquare, or parallelogram, to which a crofs being added, will form a window. To 
 make this crofs, the fpace D E muft be divided into two equal parts, each being about 
 half a foot; then drawing this breadth M to the point of diftance F, and from the inter- 
 ferons thereof with the ray A K, erect perpendiculars N O for the upright port, or 
 ilancher 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 upright piece; 
 therefore taking the meafure M, fet it off upon the perpendicular A B, as "is P, and 
 drawing lines from P to K, the points wherein they interfect the perpendiculars G H, 
 G H will give the crofs bars, and of confequence the window is finifhed. For its thick- 
 nefs, it is here only to be half that of the wall ; to accommodate which, occult lines muft 
 be drawn from the point Q_to K, and little parallels to the bafe being drawn from the 
 corners of the window S, the point wherein they cut the line Q,K will give the thick- 
 nefs 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 interferons 
 on the line A C fC, they muft here be taken in another line, re-entering into the wall 
 as much as the window is made 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 F, which is the laft. Laftly, when the win- 
 dow is finiftied, on the ray O K, and from the breadth of the wall O F, raife the per- 
 pendicular A, and draw it to the point K ; then from the lower corner of the window, 
 in the points P P, draw a little parallel cutting A K in Q, which will give the thicknefs 
 of the wall, covering the window a little, and mewing the thicknefs R P ; then from 
 the point R erecting the perpendicular R V, cutting the ray T K in E : which will be the 
 thicknefs of the top of the window. From the meafures here laid down, one may make 
 as many as one pleafes, ftill obferving the fame order. 
 
55 
 
 PRACTICAL 
 
 Part III. 
 
 Of ClELINGS. 
 
 IN forming perfpecTive repr, fentations, there are many inftances in which we 
 muft obferve a method, fomewhat analogous to the order pra&ifed by mafons 
 in raifing a building from the ground. The pavement, or ground-work, is 
 their foundation, whereon they raile walls, which they pierce in as many places 
 as they pleafe for doors, and windows. 
 
 Suppofe the walls A B raifed, on which beams are to be laid, and over them 
 joifts or quarters. Having meafured the fquare of one of the joifts (which we 
 here fuppofe a foot) it is to be carried to the top of the wall, as C D, and 
 from the points C and D occult lines to be drawn to the point of fight E, which 
 will give the rays C G D F. The fame meafure C D is likewife to be fet on a 
 parallel to the horizon D H, on which line the meafures of all the intended 
 joifts are to be difpofed, as will be (hewn prefently when I come to direct the 
 drawing them. The meafures of three joifts are here placed at I, K, L then 
 drawing lines from all thefe meafures to the point of diftance M, and from the 
 interferons with the line D F, in the points O, O, &c. letting fall perpendi- 
 culars, cutting the rays C G in the points P, P, &c. and laftly, drawing paral- 
 lels to the horizon through the points O and P, you will have the beams, or 
 girders, orderly laid : as in the firft figure. 
 
 Now, to lay the joifts upon the beams, or, more properly, to mortaife them 
 there, the line QJl, Fig. 2. is to ferve as a bafe line whereon to lay the joifts 
 in fuch number, and at fuch diftance from each other, as fhall be judged ex- 
 pedient ; the rule being ufually to be twice their thicknefs apart from each 
 other. To mortaife them, take their thicknefs within that of the beam QJ>, 
 fuch as T, and draw an occult line T V •, then between Q^R, and T V, 
 range the joifts X, X, and from all their angles that are vifible, draw lines 
 to the point of fight Y. And that they may not exceed the half of the further 
 beams, from the middle of the firft, which is the point T, draw an occult 
 line to the point of fight Y, which will cut the other two beams in the middle 
 of their depth, in the point Z ; laftly, from the point Z draw parallels to the 
 horizon, which terminating the lines drawn from the angles of XXX, 
 to the point of fight, will fhew the joifts mortaifed in thofe beams anfwerable 
 to the others, in drawing lines from the joifts to the point of fight. If you 
 do not care to take fo much pains, fet the joifts Z on the line QJl, as they are 
 underneath ; then draw lines boldly from one beam to another, from all the angles 
 of X 9 X, to the point Y, and you will have what you require. 
 
5 6 
 
 PRACTICAL 
 
 Part III* 
 
 Tthe Cielings of two Stories, fhewn in 
 
 Perfpe&ive. 
 
 ^Tp HIS Figure is only added to fhew the ef- 
 fect of the method juft now laid down ; 
 wherein it is obfervable, the number of ftories does 
 not render the pra£tice at all the more difficult. 
 
 The joifts are not mortaifed in the beams of 
 the upper ftory, - as they are in the lower. 
 
57 
 
 PRACTICAL 
 
 Part III. 
 
 Another Difpolition of Ci e l r n g s in PerfpeSlive. 
 
 np^ HIS method is performed in all refpe&s like that juft defcribed, only that 
 X the difpofition of the members and pieces that compofe the cieling is to 
 be changed ; that is, the beams are laid long-wife, tending towards the point of 
 light, and the joifts acrofs, 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 C D, and through the points C and D draw parallels 
 to the horizon C E and D F, between which you may put any number of beams 
 at pleafure, in the manner that three are placed in this figure, namely G H 
 and I, from all which, lines are to be drawn to the point of fight K j then 
 through the point P, wherein D P interfects the perpendicular L P, draw a line 
 parallel to the horizon P M, this will be the bound of all the other rays, as 
 GN, I M, &c. laftly, from the point N creel: a perpendicular N O : and fo 
 of the reft. Thus much for the beams. 
 
 To lay the joifts acrofs the beams, fet their thicknefs on the line Q^R, as 
 
 V V V, Fig. 2. and from the extremes of V draw lines to the point of diftance S ; 
 and through the points of interfe&ion with the ray QJT draw parallels to the 
 horizon, as far as the beam of the other fide. If you would mortaife them in 
 the beams, take the thicknefs of the rafters within the beam, asQX; and 
 from X draw a parallel to the bafe line, as far as the other fide X X ; and 
 between the two lines Q_R and X X fet the divifions V V, &c. which will form 
 
 Y Y, £s?f. And from all the points Y drawing lines to the point of diftance S, 
 you will have the thicknefles of the bottom and fides given by the interferons 
 with the ray X T in the points Z Z, &c. through which drawing parallels to 
 the horizon, the cielings will be finifhed ; as in the fecond figure. 
 
 Thus it is that fimple timber cielings are put in perfpeflive. If, after thefe, 
 or in lieu of thefe, you would have a handfome platform of painting, or enrich- 
 ments of other kinds, the inftructions given in page 35 for exhibiting the plan 
 of a garden, are applicable to thefe purpofes, for by making ufe of the line 
 QJ< for a bafe line, you will eafily fhew on the cieling the perfpective appear- 
 ance of any defign : and making ufe of the line QJR. for a bafe line, you may 
 do what you pleafe therein. 
 
 As to floors and pavements, fuch full inftructions have been given for them 
 in pages 30, 3r, 3?., 33, and 34, as to make the operation for fhewing them 
 very familiar and eafy, and to open the mind for inventing what variety of them 
 it pleafes. Thus far we have had to do with the rooms, as hall, chamber, or 
 the like, the feveral parts whereof are furficiently defcribed : the moveables therein 
 Ihall be fhewn hereafter. 2 
 
Part III. 
 
 PERSPECT I V E. 
 
53 
 
 PRACTICAL 
 
 Part III. 
 
 nr^HIS figure (hews the cieling juft now de- 
 fcribed, diftinft and clear of the lines where- 
 with the former was embarafled. 
 
 The conftru&ion of the gate {hall be fhewn 
 hereafter. 
 
59 
 
 PRACTICAL 
 
 Part III. 
 
 To defcribe Circular Gates and Arches viewed di- 
 reElly in the fronts or partly on the fide. 
 
 TJAVING given fufficient inftrudions for halls, cham- 
 JTX b ers > windows and fquare doors, or gates, we pro- 
 ceed to the practice of round ones. 
 
 Suppofe then ABCDEF to be pilafters on a plan, in or- 
 der to place arches thereon, divide the upper breadth G H 
 into equal parts, in the point I, on which fetting one leg 
 of your compaffes, with the other defcribe a femi-circle 
 G H, for the firft arch. 
 
 To make all the other arches of the fame height and 
 breadth, draw lines from the points GH to the point of 
 fight K, and through the two points L, L, where thofe 
 rays cut the perpendiculars C, D, draw parallels to G H. 
 Thefe parallels being divided into two, and femi-circles 
 ftruck from them, as in the firft, you will have the fecond 
 and third arch. To find the middle of thofe parallels M, 
 you have only to lay the ruler in the firft center I, and draw 
 a line to K, which will cut them all precifely in the middle 
 M M, and give the points for the femi-circles to be drawn 
 from. The arches viewed in front, and thofe by the fide, 
 are all performed the fame way ; as appears from the two 
 firft figures, and K is the point of fight both for the one 
 and the other. 
 
 If it be required to make an edge, or band about them, of 
 equal thicknefs, you are only to ufe one center as O, from 
 which the thickneffes N P of the lower figures are formed. 
 The reft is all performed as already direcled, by drawing lines 
 to the point of fight K. The laft figures mew how all kinds 
 of fimple vaults, only confuting of a femi-circle, are to be 
 formed. As to the enrichment thereof, we mall have oc- 
 cafion to fpeak hereafter. 
 
6o 
 
 PRACTICAL 
 
 Part III. 
 
 To defcribe Circular Arches over Pilafters viewed as 
 in the preceding plate. 
 
 TH E out-line of the laft plate readily direcls how to perform 
 this operation, the method being the fame in both. In the pre- 
 fent cafe there are a few more lines, but not any thing more of difficulty. 
 For, drawing parallels to the bafe line over the tops of the feveral pila- 
 fters, and dividing the firft of them into equal parts, from the middle 
 E as a center, defcribe the firft femi-circle A C, without removing the 
 compaffes, from the fame center defcribe the band or thickneffes A-GFC- 
 laftly, from the center E, drawing lines to the point of fight H, the 
 ray E H will give the middle points of all the parallels for defcribing 
 femi-circles over them all* from B D to the laft> I. The method is the 
 fame for that in the fide-view* 
 
 To defcribe the Gothic Arch, or Arch in the third Point. 
 
 THE drawing of this is as eafy as that of the circular arch. Having 
 laid down the breadth K L, fet one foot of your compaffes in K, 
 and directing the other to O, ftrike the arch L O ; then removing your 
 companies to L, defcribe the arch K O, and you will have an arch in 
 the third paint, KOL. Do the fame from M and N, and you will 
 have the fecond, or inner arch, M P N. The fecond figure, in the third 
 pointy has a band or lift all round it, which is defcribed from the fame 
 centers : thus, for example, from the center R the arches S X and T V 
 are fwept ; and from the point S the arches Q^V and R X. All the 
 reft is drawn to the point of fight Y. 
 
 Another third point, or terzo acuto, is reprefented in the figure -f ; the 
 diameter or chord whereof, a b, being divided into three equal parts, 
 and one foot of the compaffes fet in one of the drvifions, as c, and with 
 the other the aperture c b taken, the arch b e is ftruck therewith ; then 
 removing the compaffes to d, the arch da e is ftruck, which is an arch 
 in the third point, as well as the former j and either of them may be 
 ufed at difcretion. Thofe in old Gothic churches come neareft the for- 
 mer kind. 
 
PRACTICAL 
 
 Part III. 
 
 Sequel of the former Figure. 
 
 WE here add an arbour of a garden, the performance 
 whereof is in all refpe&s the fame as that of arches 
 viewed in front. 
 
 Sequel of the foregoing Rules. 
 
 r P HE rules g iven in the two former pages, are applicable 
 J- to a vaft variety of defigns. In this plate I fhew one 
 inftance thereof in the perfpedive reprefentation o£an arbour 
 compofed of five arches, of equal chords or diameters, and 
 placed at equal diftances behind each other. Thefe are exhi- 
 bited by the method laid down in pages 59 and 60. 
 
62 
 
 PRACTICAL 
 
 Part III. 
 
 To defcribe, and put in PerfpeEtive y femicircular Arches 
 
 and Doors. 
 
 THE circle being fomewhat difficult to put in perfpective, requires a num- 
 ber of previous lines and points : to mew the method of procuring them 
 is the defign of Fig. i. which ought to be well underllood. To dcfcribe a femi- 
 circle upon a diameter A B, there needs no more than to fet one foot of your 
 com panes in the middle thereof, in the point C, and with the other to fweep a 
 crooked line from A to B. And thus is the femi-circle to be upon the elevation 
 D E, Fig. II. for a circular gate or arch. 
 
 Now to put it in perfpedlive, it is to be divided into any number of parts, 
 and the more the better ; as already obferved in page 28. and as I (hall hereafter 
 have occafion to mew, when giving diredions for the exhibiting of crofs vaults. 
 The prefent femicircle I fhall only divide into four, and that by circumfcribing 
 it with a parallelogram, or long fquare, and drawing two diagona's interfering 
 each other in I, and the femicircle in K K, and laying a ruler over C I, bifect- 
 ing the arch in F j laftly draw the line K K, cutting the parallelogram in L, 
 which line L K is to be transferred to Fig, III. to put it in perlLective. 
 
 Firft then draw a line from the angle E to the point of fight M, fet off the 
 meafures of the diameter of arch D E on the bafe line as E N, N O, and from 
 the point N draw a line to the -point of diftance P ; which cutting the ray E M 
 in the point Q, Eq will be the widdi of the font arch D E & in perfpedtivse. 
 Then drawing a line from O to the point P, where it cuts the ray E M, in 
 the point R, will be the width of the iecond arch. As there is no more room 
 on the bafe line to take the third arch, a line muft be drawn from N to the point 
 of fight M ; and through the point R a parallel to the bafe lines R S. Now 
 as R S is under the fame angle with E N, it is the fame breadth in its proper 
 diminution, as has been already proved in the beginning of the book ; therefore 
 drawing a line from S to the point of diftance P, it will cut the ray E M in 
 the point T, which gives the third arch. 
 
 Proceed then to raife perpendiculars V V , &c. from the three points OR T, 
 which interfering the ray H M, will give the higheft of the arches ; then from 
 the ray B M, which gives the bottom of the femi-circle, draw diagonals B V, 
 H X, which interfering each other, give the place of the perpendicular Y F, 
 that divides the arch into two ; and drawing the ray L M, it will cut the dia- 
 gonals in two, and the arch in four j laftly, connecting the points B Z, F Z X, 
 with curve lines, you will have the firft arch: and this method will give you in- 
 finite others. The fame ferves not only for arches and doors, but alio for vaults, 
 bridges, and other things that require the femi-circle j 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 fatten the glafs to. 
 
Part III P £ R SPEC T I V B, 62 
 
6 3 
 
 PRACTICAL 
 
 Part IIP 
 
 To defcribe, and put in perfpeBive y double Arches 
 and Gates, that is^fuch as Jhew their thicknefles. 
 
 r'f^ H E former page only jfhews the formation of the out-line: I therefore 
 now proceed to the method of compleadng the fame and exhibiting the 
 breadths and thicknelTrs of . the arches, and their iupporters, by only connecting 
 the interfections of each by right lines : for example, 
 
 Having defcribed the firft line D E, and drawn lines from D and E to the 
 point of fight A, fet the breadth or thicknefs on the bafe line EC. From the 
 point C draw a line to the point of diftance B, and where it interfects the ray 
 E A in the point F, draw the line G F parallel to the bafe line, which will cut 
 the rays DA and E A in the points F G, and give the thicknefs required. Then 
 from F G erect perpendiculars, and from H draw a line to the point of fight A, 
 the interferon whereof with the perpendicular F I gives the height of that fide. 
 To find the chord or line of the center of the inner femi-circle, draw a line from 
 K, the extreme of the diameter of the femi-circle feen in front, to the point of 
 fight A, which gives the point L, a parallel drawn through which will have the 
 center of the hinder femi circle upon it, as N is the center of that before. This 
 line M L is to be divide \ into two equal parts, by drawing a line from N to A, 
 through O. Then fetting one leg of your compaflfes in O, with the other de- 
 fcribe a femi-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 femi-circle to the hind one, to connect the two into one >, as in the figure, 
 M is joined to P to R S, to TV, to X L, to K. 
 
 For circular arches, &c. viewed in front, as D E F G, there is no need of fa 
 many divifions, it being fufficient to find the line M L, in order for the deferr- 
 ing of the femi-circle, which refers to the firft NPQ^; but I have made them 
 defignedly to avoid confounding the letters with the lines of the lower figure, 
 whe°e the arches are viewed obliquely, tending all towards the point of fight Y. 
 Such arches would give their thickneffes by repeating the operation already laid 
 down for Fig. I. twice over, and joining the divifions of the one to the other, 
 as already obferved, and as is expreffed in the prefent figure, to which having 
 given the thicknefs E Z, 1 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 finifhed. 
 2 
 
64 
 
 PRACTICAL 
 
 Part III. 
 
 Another Method of defcribing Circular Arches. 
 
 rjA H E arches in front, which I have hitherto defcribed, are all performed 
 J[ to the lart exa&nefs •, but the procefs is a little long and tedious : I malt 
 now add another, equally juft, but much more expeditious. 
 
 Having defcribed a femi-circle, or a whole circle, B H I, from the center A r 
 from the fame center and the extreme of the diameter B, draw lines to the 
 point of fight C ; then fetting the breadth, or thicknefs required, 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 interfedt, 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 
 compafles in F, and in the other taking the diftance G, defcribe a femi-circle, 
 or circle, which will be the thicknefs of the arch, or fweep : as is feen in the 
 four different figures, which are all performed by this eafy procefs. All the lines 
 K K, &c, in the third and fourth figures are to be drawn to the center A, and 
 the others, L, to the point of fight C. The fame method may ferve for circu- 
 lar windows built of ftone, in which cafe the lines will reprefent the joints ; as 
 alfo for tons, vats, &c. 
 
 An expeditious method for Arches viewed obliquely 
 
 in perfpe&ive. 
 
 r~V\ HE following method may ferve'when a perfon is ftraitned, and does not 
 \ defire to be fo very exact ; as alfo to avoid a multiplicity of lines, which 
 in the preceding method is indilpenfible. 
 
 Having formed the fi ft arch N O as already directed, acrofs it draw little 
 parallels to the bafe in any number at pleafure, as here Q^Q^ £s?r. then with 
 your compares take the bread, h of the fpring of the arch, as P O, and fet it off 
 on the little parallels Q, by this means you will have the points R R ; through 
 which a curve line being drawn, will form the thicknefs of the arch. 
 
 It is certain, that, according to the rules of perfpe&ive, objects appear the 
 larger as they are the nearer to us-, of confequence, therefore, the line O F 
 mould be the fmalleft : but the difference is here fo very fmall, that it is not 
 worth the minding. Befide, I do not give this as a conftant rule, but only for 
 an expeditious fliift in cafes of neceflity.. 
 
PRACTICAL 
 
 Part HI. 
 
 To exhibit Elliptical or Flat ARCHES. 
 
 r-jT^ H E method of putting thefe arches in perfpective, is the fame 
 J. with that of the femi-circular, as appears from the figure A B, 
 Ail the difficulty is in finding the out-line, which is done two ways. 
 
 The firfl by two centers and a firing, the method already mentioned 
 page 4, for defcribing an oval 5 thefe flat arches being, in efTecl:, femi- 
 ovals. 
 
 The fecond method is thus : Suppofe the line C D given you to rai& 
 
 a flat arch upon of the height E F, from the center F defcribe a femi- 
 
 circle CGD, and divide it into anv number of equal parts at pleafure, 
 
 as is here done into twelve 5 and from all thefe divifions draw lines to 
 
 the center Fj then again, from all thefe divifions draw perpendiculars 
 
 to the diameter or chord C D, as are here the lines 01 j this done, 
 
 defcribe a femi-circle of the given height of the arch, as here HE K i 
 
 and through the interferon's made by this lefTer circle on the divifion- 
 
 lines of the greater, draw little parallels to meet the perpendiculars which 
 
 fall from the fame divifions, for inflance L O, L O, &c. and the feve- 
 
 ral points Q connected together, as is here done, will give you the arch 
 required. 
 
 The other figure makes the arch ftill flatter, and by the fame rules it 
 may be made of any lownefs at pleafure. 
 
 The figure underneath mews one of thefe arches in perfpecYive, fuch 
 as it mould appear, when finimed, in a front view. I fay nothing of 
 the method, as. having already intimated it to be the fame with that for 
 the femi-circle. 
 
I 
 
66 PRACTICAL * Part III, 
 
 T N the figure here reprefented, you have an inftance of 
 JL the fine effeft of Arches when they are well centered, 
 that is, when their juft rotundity is given them, in their 
 different perfpe&ive fituations. 
 
 As for the fteps and figures, I ihall have occafion to treat 
 very particularly of them hereafter. 
 
67 
 
 PRACTICAL 
 
 Part III. 
 
 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 piiafter between every two arches* 
 which is done by means of the plan, or bafe line ; as already directed 
 for circular arches. 
 
 Gothic Arches. 
 
 C "Gothic Arches and Vaults, called alfo arches in the third 
 "J point, fee page 60, are performed in the fame manner as the 
 femi-circular ; fo that having done one, you will do the other with eafe. 
 The figure fhews the reft. As to the out-line, I have already fhewn 
 that nothing is more eafy. The breadth A B being given to form an 
 arch of, open your comparles to the breadth, and fetting one leg in A, 
 with the other defcribe the arch B C ; then removing them to B, de- 
 scribe another arch A C ; and the point wherein the two interfecl:, will 
 be the point or apex of the arch C. 
 
 As the other arches feen on the fide view arc performed after the fame 
 manner as the femi-circular, page 62, I fhall 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 exemplify what I have already 
 laid, that all that is to be done is to draw lines from thefe divifions on 
 the bafe to the point of diftance O, which will cut the ray D E in the 
 points F F, &c. on which points perpendiculars are to be raifed; then 
 fetting off the thickneffes G, and drawing the ray G E for the breadth 
 of the pilafters H, from the fame point H erect perpendiculars, to be 
 connected to the other by the right lines, &c. as in the femi-circle. 
 
69 
 
 PRACTICAL 
 
 Part IK. 
 
 To find Cross Vaults in perfpeEtive. 
 
 TH E reader muft remember, or have recourfe to, what I have 
 faid in page 28. where, fpeaking of putting a circle into perfpec- 
 tive, I divided it, for the greater exaftnefs, into fixteea parts ; but as in 
 fuch a divifion there necefifarily occur a great number of lines, I have 
 here chofe to take up with a divifion of eight parts, which if it be the 
 lefs exaft, it will be the lefs confufed. The other divifion I mall refume 
 in the following page. 
 
 Having then formed a plan of a circle divided into eight parts, 1, 2, 
 %> 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 
 C C, &c. on which erecting perpendiculars CD, CD, &c. the firft of 
 them, B D, being the line of elevation, all the meafures of the femi- 
 circle' BEF muft 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 C D, you will have the fame 
 divifions as in the firft, fecond, third, fourth, and fifth Pl an s. For 
 a femi-circle, draw curve lines as in the arch of the firft fide, the divi- 
 fions whereof are to be transferred to the other, in order to have two 
 collateral arches from the center 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 diago- 
 nals, reftingon the corners G 5, KL, and pafling through K or the 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 femi-circle G K, 
 therefore, is to be divided into four parts, in the points G P QJl K, 
 which are to be drawn to the point of fight A, as far as the bottom of 
 the circle 5 L. Now what follows is the great fecret of the crofs, namely 
 that parallels to the horizon are to be drawn from all the interfecT-ions o£ 
 the circle on the fide 1, 2, 3, 4, 5, in fuch fort, as that G, which is the 
 firft divifion of the circle, touch the interfe&ion 1 in a point j 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 j laftly, connecting G S O T L with curve lines, you will; 
 have a diagonal j and doing as much for the other fide, you will have 
 the entire crofs, and the vault compleat.. 
 
PRACTICAL 
 
 Part III. 
 
 To draw the fame V au lt more accurately. 
 
 A MAN who has a good notion of the former method, 
 will find no great difficulty in managing this ; all that 
 is required being to double the lines, and take care of the 
 interferons, which are here more numerous, by reafon the 
 circle is divided into more parts* 
 
 How to form the plan is taught in page 28. Having pro- 
 duced the circle, and obtained the divifions on its peri- 
 phery, from thefe divifions draw parallels to the ray B A, 
 and their interfe&ions will give the points O, O, O, ftfc. 
 from which perpendiculars are to be raifed. The reft of the 
 procefs is the fame with the method laid down in the pre- 
 ceeding page, over which this has the advantage of exa<9> 
 nefs, and enabling you to draw the vault more eafily, becaufe 
 the divifions are clofer to each other, 
 
 3 
 
PRACTICAL Paft III. 
 
 To form narrow Vaults. 
 
 HERE are two procefTes in this figure \ the one for contra&ing or ftraitning fide* 
 vaults; the other for giving the thicknefs to the crofs. I (hall begin with the firlh 
 
 The two methods for vaults a 1 ready laid down, fuppofe them perfectly fquare, that is, 
 that their breadth and depth, or diftance, is equal j both in thofe reprefented in front, and 
 thofe in fide-views* But a perfon only inftructed in thefe, would find himfelf ftrangely 
 at a lofs were he put to conftrudr. a church, where the fide-arches are ufually much nar- 
 rower than thofe in the front or middle. 
 
 I proceed, therefore, to offer you an expedient whereby you will be enabled to make 
 the fide arches of what dimenfions you pleafe, and that by means of the bafe line A Q. 
 Suppofe then the front arch A Q^forty feet broad, and the fide-arches limited to fifteen or 
 twenty, you are now, according to the inftrudlions in page 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, A C being 
 fuppofed twenty feet, a line drawn from C to the point of diftance, (which here is fup- 
 pofed beyond the limits of the paper) cuts the depth twenty feet in the point E ; then re- 
 turning to the bafe line, an arch or femi-circle is to be ftruck on the line A C, and divided 
 into as many pans as the larger arch FG has divifions, namely, eight ; and from the 
 feveral divifions perpendiculars H H to be let fall on its diameter A C, and from the points 
 H, lines to be drawn to the point of diftance, interfering the ray A E in O, O, &c. 
 Perpendiculars O P, O P, &c. are to be raifed ; then the plan of the femi-circle F G is to 
 be made in fome feparate place, and the divifions thereof transferred from F to B. And 
 fince the plan of the preceding figure, fee plate 69, is equal to F G, take the divifions of 
 half of it, B C D E F, and transfer them upon the perpendicular A F ; and from the points 
 E F D C B draw lines to the point of fight D, and through the interferons which thefe 
 rays B CDEF make with the perpendiculars % 0 P, draw curve lines, which will form 
 the fide-arch. Then drawing parallels through the interfe&ions 1, 2» 3, 4, 5, 6, 7, 8, 
 9, to the divifions of the arch F G, you will have points FRST VXY-Z, to form 
 the crofs after the manner already mentioned. 
 
 For the thicknefs of the nerves, or branches, a little line of elevation muft be made, a b r 
 which I have here added at the top of the perpendicular raifed from This line A B, 
 being drawn to the point of fight D, cuts all the other perpendiculars in the point c d t 
 and this gives 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 
 firft elevation a b, for inftance, gives the firft perpendicular G e ; the fecond elevation c d 
 gives the fecond perpendicular F e ; and fo of all the reft in their order, which all give 
 points e e ; and which being connected by a crooked line, give the thicknefs of the nerves 
 or. reins of the vault : as is feen in half the adjoining figure. 
 
7 i PRACTICAL Part III. 
 
 a u l t on the Principles of the preceding Rules, 
 
 ^ | ^ H E feveral rules already dilivered, fuffice for the con- 
 JL flru&ing the various arches of a complete Vault, 
 as that hereto annexed. The rules for the columns, or im- 
 pofts, I fhall have occafion to fhew hereafter. 
 
PRACTICAL 
 
 Part III. 
 
 c /o exhibit Arches with three Sides. 
 
 r w <» HERE is another fprt of cieling which fometimes ferves for a 
 J 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 formed of a femi-circle divided 
 into parts. 
 
 Having raifed the walls A B, defcribe a femi-circle including the whole 
 breadth CD} then holding the compaffes open to the width of the 
 radius E C, and fixing one point in C, with the other ftrike an arch 
 upwards, cutting the femi-circle in G, and another arch E H from the 
 point D ; then connecting the four letters C D G H by right lines, you 
 will have a femUhexagonal arch. A femi-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 fight F j 
 at the interferons of thefe rays with the lower femi-circle, right lines 
 being drawn, will form the arch I L M K. 
 
 To exhibit an Arch with five Sides. 
 
 THIS arch is performed after the fame manner as the former > all 
 the difference lies in the divifion of the circle, the nrft being into 
 three, and this into five. Accordingly the femi-circle L M being divided 
 into five parts, NOPQ, and lines drawn from all thefe points to the 
 point of fight R» the reft is performed after the manner already laid 
 down. 
 
73 
 
 PRACTICAL 
 
 Part 11L 
 
 To exhibit the Elevations of Round Objects. 
 
 TH E defire I have of enabling my reader to put all kind of objeds 
 in perfpedive with the utmoft eafe, has induced me to mew the 
 method for raifing circular figures to any height at pleafure; and the 
 fame rule may ferve for exhibiting all other rotundo's, as cupola's of 
 churches, amphitheatres, towers, &c. &c'. 
 
 Having put the plan of the round in perfpedive, as already direded, 
 and raifed the line of elevation A B by the fide thereof, from the feve- 
 ral angles of the plan, which are here the feveral points whereof the 
 round cwfifts, namely, i, 2, 3, 4, 5, 6, 7, 8, 9, & c . parallels are to be 
 drawn to the ground line, and from their interfedions with the line A O 
 perpendiculars are to be raifed thereon, as already taught, and the lengths 
 of thofe perpendiculars transferred upon other perpendiculars, raifed from 
 the points 1, 2, 3, 4, 5, 6, 7, 8, 9, &c. 
 
 The front part of the femi-circle has but half the height of the hinder 
 part, and both the one and the other are mere out lines without any 
 thick nefs. 
 
 There is no round figure but may be put in perfpe-dive by this me- 
 thod. Round figures, I mean, that are parallel to the horizon : for as 
 to fuch as are perpendicular thereto, they are already taught in the rules 
 for vaults. 
 
 For the Elevation of Pilasters. 
 
 rp HE circle muft be drawn in the plan double, as already fhewn in 
 X page 29. and between the two circular lines muft be placed the 
 plan of the parts or members to be raifed, as thofe here marked A B 
 C D, which all tend towards the center E 5 then perpendiculars are to be 
 raifed from all the angles of thefe plans, and their proper heights fet off 
 from the line of elevation FGj as already fhewn in the firft figure. 
 
 3 
 
74 PRACTICAL Part HI. 
 
 A Vault in form of a Shell, in Perfpective. 
 
 THIS figure, with little variations, will either ferve 
 for the hollow of a church, or grotto, a mc6 9 or 
 the like. The elevation is performed after the manner 
 already directed. 
 
 To draw the plat -band, or border A B, which might ferve 
 for a cornifli, its diminution is to be taken on the line of 
 elevation in C D, and transferred thence to the pilafters. 
 
 For the vault, take the firft arch E F, as before taught, 
 and in the middle of the infide defcribe a femi-circle O, to 
 which draw curve lines fpringing from the pilafters, an^ you 
 will have the ribs or reins of the vault, as in GHI K. The 
 heights of the windows muft be taken on the line of eleva- 
 tion between L and M. For the reft, fee the figure. 
 
Part III. 
 
 PERSPECTIVE* 
 
 A a 
 
75 
 
 PRACTICAL 
 
 Part IIL 
 
 To exhibit open Domes, Vaults, w Perfpe&ive. 
 
 HAVING made the plan of a double circle according 
 to page 29, and marked the places of the pilafters 
 between the two circles, the lines of all of them tending to 
 the center A, fet off the height intended from the ground 
 to the cavity of the dome, as the line D E, which is to ferve 
 for a bafe line, upon which the meafures already laid down 
 on B C drawn parallel to the ground line to touch the circle, 
 are to be placed. Then from the fame point of fight G make 
 another plan at the top, like that at bottom, all the places 
 of the pilafters tending towards the center H. To form the 
 pilafters, all required is to draw lines from the places oppo- 
 fite to each other, which will thus give the breadth and 
 thicknefs. I have drawn no lines for the three front pilaf- 
 ters, both for the conveniency of fhewing thofe behind, and 
 to inftance that the plan of them muft be drawn both at top 
 and bottom. 
 
 To give the thicknefs of the rotundo from 1 to H, and 
 from K to L, fet the intended height on the line of elevation 
 D M, from whence draw lines to the horizon in the point 
 F ; and from the feveral points of the upper circle draw pa- 
 rallels to the line D F, at their interfedions erecl perpendi- 
 culars, as D M, which are to be transferred thence, with 
 the compaffes, to the perpendiculars raifedYrom the points 
 K L, N O, P Q ; and fo of the reft. 
 
 If inftead of a round you require a fquare, or polygon*, 
 the fame method is to be obferved, 
 
7 6 
 
 PRACTICAL 
 
 Part HI. 
 
 That a Number ^Objects, and Plurality ^Stories, 
 only admit of one Point of Sight. 
 
 IT has already been obferved, that only one point of light 
 is ever to be ufed in a pi&ure, and that the ignorance of 
 certain painters is publifhed to all the world* by their making 
 as many points of fight, and horizons, as they make lines. 
 
 It is 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 fight ; and yet the painter 
 wonderfully efteemed his performance. The prefent figure 
 may ferve to correct this error, and to fhew, that there 
 fhould only be one fingle point of fight, to which all the 
 objects, and all the rooms, though they were a hundred 
 over or afide of one another, are to tend* As the three 
 apartments do all here tend ta the point A, The reft k 
 performed by the rules heretofore directed. 
 
77 
 
 PRACTICAL 
 
 Part III. 
 
 7*0 put Chimneys in perfpe&ive, either in the front 
 
 or fide- view* 
 
 TH E 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 ac- 
 counted 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 feet 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 A E in the 
 point F, gives a depth of three feet. 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 H. Then fet the 
 breadth, of the chimney from G to I, four feet and a half j and half a 
 foot; namely, from I to K, for the thicknefs of the jaumb j then draw- 
 ing lines from I and K to the point of diftance D, you will have their 
 meafures on the ray A E, in the points L M : and from the four points 
 F H L M draw little parallels to the bafe line, as FN, HO, LP, MQ^ 
 For the breadth of the jaumbs take a foot and a half, namely, A R, 
 and the ray R E will cut the little parallels in the points NOP from 
 which, and from F L raife perpendiculars. For the height of the mantle- 
 tree, take five feet on the bafe line, and fet them off on the corner of 
 the wall from A to S j and from S to T fet off the cornifh. 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 occasionally 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, which are a foot and an half, draw a line from 7 to the point 
 of fight, 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 paral- 
 lel, cutting the four rays 1, 2, 3, 4, in the points 9, 6, 9, 9: from 
 which perpendiculars are to be caifed, and the reft conducted, as above. 
 
 The fecond figure reprefcnts what I have been fpeaking of free and 
 unembarrafled with lines. 
 7 
 
Part III. 
 
 PERSPECTIVE. 
 
 77 
 
7'S 
 
 PRACTICAL 
 
 Part III. 
 
 To exhibit Steps or Stairs in PerfpeElive. 
 
 THERE is nothing gives a perfpective fo much grace, or deceives 
 the eye fo eafily, as a number of returns and breaks; by reafon 
 thefe introduce a number of different lights and fhadows, which give 
 the objects fuch a force, that they feem to project or ftand out from the 
 ground. Now flairs have this advantage, that what way foever you 
 place them, they have always a variety of (hades, and of confequence 
 are agreeable to the fight. I mall add a few inftances of fteps in different 
 pofitions by way of fpecimen. 
 
 If you make ufe of fquares, there will be the lefs difficulty, all re- 
 quired being to raife perpendiculars of as many fquares as you would 
 have fteps ; then to fet the line of elevation, divided into any number of 
 parts, on the firft: fquare, and from the divifions to draw lines to the 
 point of fight, which will interfect the perpendiculars in the places where 
 the fteps are to be. 
 
 It is defired, for inftance, to conftruct a ftair-cafe of eight fteps, the 
 laft of which to be the breadth of three feet. Take the number of 
 fquares 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 B D, in manner following. 
 
 The firft divifion, which, fuppofing the fquare 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 ftep ; and fo of the reft. The fteps you 
 may make as long as you pleafe, by fuppofing the fquare a foot. Ac- 
 cordingly the uppermoft here, taking three divifions, is three feet. Per- 
 pendiculars fhould likewife be raifed, as in this inftance, on the fide B : 
 but that trouble may be faved, by taking the height of the laft ftep h] 
 and that of the firft I, and drawing the line H I, raifing the angles on 
 the fide I, as E K does on the fide B ; for this done, you need only 
 to draw parallels to the bafe line from all the flairs from the fide B, to cut 
 the line H I in L M N O P &fr. 
 
 One might likewife do without making fquares } 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, this much being fufficient for 
 the underftanding and executing them all. 
 
79 
 
 PRACTICAL 
 
 Part IIL 
 
 Stairs open or perforated underneath. 
 
 THE method of managing thefe ftairs is the fame with that already 
 defcribed. 
 
 As to the aperture, a bare fight of the figure is fufficient to (hew how 
 it is to be put in perfpective. Thefe two may give occafion to the in- 
 venting many others* 
 
 Steps or Stairs viewed in Front. 
 
 THIS method is founded on the ufe of the line of elevation : the 
 fame number of perpendiculars are to be raifed from the angles of 
 the fquares of the plan, as there are required fteps, for example, C I> 
 EFj and from the fame angles parallels are to be drawn to the ground 
 line meeting the line of elevation A, the interfections whereof give the 
 points OOOO, from which perpendiculars are to be raifed till they cut 
 the occult rays of the divilions of the line of elevation. Thefe meafure* 
 are to be taken in your compaffes, and fet off on the perpendiculars raifed 
 from the angles of the plan, each in its order y the firft for the firft ftep., 
 tl*e fecond for the fecond, &c. 
 
 To find the returns P P, &c. from the fame- angles P, &:ic. lines are to 
 be drawn to the point of diftance Q^and notice taken where they cut 
 the line of the plan,, or the bottom of the ftep ; for inftance, over the 
 fourth ftep is the plan of the fifth : now to find its return P, from the 
 point P draw a line to Q^_and the point S, wherein it interfec~fo the par 
 rallel R R, will be the line of return S T j and fo of the reft. 
 
8o 
 
 PRACTICAL 
 
 Part HI. 
 
 To exhibit Steps that pew four Sides* 
 
 THERE are various manners of ordering fuch fteps, two of the eafiefir 
 of them follow. Take the length of the ftrft flep, and fet the number 
 of fteps required upon the fame ; as on the line A B are here fet the points C C 
 C C, for four fteps. From thefe points draw rays to the point of fight D, which 
 rays are to be cut by the diagonals A F and B E in the points III, from which 
 perpendiculars are to be raifed, and parallels to the ground line drawn to the line 
 of elevation G, which give the points H, to be raifed as H K. 
 
 On this line of elevation G, as many equal parts muft be marked as there are 
 fteps defired, for example, four, here marked i, 2, 3, 4. From thefe four 
 points of divifion rays are to be drawn to the point of fight D, to. cut the per- 
 pendiculars H K, and give each its proper height. 
 
 Thefe meafures muft be taken in your compafles, and transferred one after 
 another, beginning with the firft G, which is to be fet on the firft perpendicular 
 en the angle A, namely AL-, then a parallel to be drawn to the other fide B, 
 (though here I only give half of it, to have room for the plan in the other.) For 
 fche fecond ftair the fecond meafure H 2 is to be taken, and fet off on the fecond. 
 perpendicular a .d a parallel is to be drawn as before \ and fo of the reft,. 
 
 Another Manner 
 
 THE fide MN being given, make a parallel O P over the fame, for the- 
 thicknefs or height of the firft ftep. From the two points O P draw two rays 
 to the point of fight Q, and again other lines to the points of diftance R S ; 
 which laft will give a fquare after the ufual way, and form the firft ftep. For 
 the fecond, fet the intended breadth on the line O P, for example, O T, and* 
 from T draw a ray to the point of fight Qj which line or ray T Q^will cut the 
 diagonal O in the point V, the place where the fecond ftep muft be raifed. The 
 height of this fecond degree muft be half of VX, as MO is half of O T. The 
 point Y thus gained, 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 fight and diftance, to form the fquare, as for the firft ftair. For the 
 third, fet the meafure V X on the line Y Z, extending, for example, from Y 
 to A; and from the point A draw a ray to the point of fight Q, which inter- 
 fering the diagonal of the point Y, will give the point B for the third ftep.- Its 
 height will be half of B C, which is always that- of* O T iu perfpeclive. The 
 reft the fame as in the firft and fecond. 
 
 The third figure Ihews thefe flairs free of all the confufion of lines and letters. 
 
Part III. PERSPECTIVE. 80 
 
8i 
 
 PRACTICAL 
 
 Part III, 
 
 Stairs or Steps viewed Jtdewife in Perfpe&ive. 
 
 TH E number of flairs is fir ft to be laid down on the bafe line, that is, fo 
 many points are to be made thereon at equal diftance as you intend fteps ; 
 as in the prefent cafe ABC. From thefe points lines are to be drawn to the 
 point of fight 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 
 ftairs, by its interferon with the rays B D, CD in the points I; and by its in- 
 terferon 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 ftairs. From G a line is to be drawn to 
 the other point of diftance H, which gives the angle of the laft flair in the point 
 K, and the place of all the reft in the points I I. Laftly, from all the points I 
 erect perpendiculars. 
 
 Now to give the heights ; from the points A B C on the bafe line ered little 
 lines, ferving for a line of elevation ; on thefe lay the heights according to their 
 number.^ The perpendicular A, for inftance, which is the firft, will only have i ; 
 B, the fecond, will have 2 ; and C, the third, will have 3. From all thefe 
 pints i, 2, and 3, draw lines to the point of fight D, and you will cut the 
 perpendiculars railed from the plan in the points O, which will ai ve the height 
 of each flep. 0 
 
 The draught on the other fide mews the fteps free of points and lines. The 
 " fame method may ferve for divers purpofes ; as for the fteps of an altar, a throne, 
 the front of a church, a gate, &V. 
 
 Stairs in a Wall in PerfpeBive. 
 
 MA K E as many divifions at the end of the bafe line as you intend ftairs, 
 as in this cafe, three between A and B, and from A and B draw lines to 
 the point of fight C ; then, having determined the fpace the ftairs 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 interferons of lines drawn from the points G H to the point of 
 fight C ; and from the fame points I ?, perpendiculars IK, I K are to be ere&ed, 
 to receive the heights of the ftairs, by drawing points 1, 2, 3, to the point of 
 fight C, as appears from the figure. 
 
PRACTICAL 
 
 Part IH, 
 
 exhibit a Stair-Case with Landing Peaces in 
 
 Perjpeftive. 
 
 DO bat recoiled the preceding methods, and you will find it exceeding eafy 
 to conftruct fuch ftair-cafes. However, to fave the trouble of too irkfomc 
 a retrofpect, I fhall explain the whole here. , 
 
 By reafon ftair-cafts of this figure ufually run over a fpace equal to twice their 
 width, to raife one of them in perfpe&ive, the horizon muft firft be difpofed at 
 pleafure % then a fquare to be made according to the common rules, and this 
 to be doubled, as directed in page 16; then divided by an unequal number of 
 fmall fquares, that the wall, which is fuppofed in the middle, may be the meafure 
 •of a fquare. 
 
 In this figure each fquare has nine fides, or fquares, on either hand, which 
 being doubled, give eighteen ; of thefe, four being left at each end for the land- 
 ing-places, remain ten fquares, or flairs, each whereof we fuppofe equal to a 
 foot every way. 
 
 At the diftance of four fquares from the point A, erect the perpendicular B 
 pretty high, then a fecond perpendicular C at the other angle of that fquare, and 
 ,a third D and fo onwards on the other angles of the fquares, to the number of 
 ten. This done on one fide, the fame mult be repeated on the other ; and fuch 
 perpendiculars will give the depths or breadths of the ft eps. 
 
 For the heights, if they be a foot broad, they muft be half a foot high, or 
 half the little fquare A O ; which height being taken in your compafTes, fet it 
 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 divi lions thereon as you intend 
 flairs, namely ten, from the bottom to the firft landing-place where you begin to 
 mount up the oppofite fide, and the feries of numbers is continued to twenty-three. 
 
 From all thefe twenty-three points, lines are to be drawn to the point of fight 
 :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 fight, crofs the firft perpendicular 
 B to C with a little ftroke, for the firft ftep. For the fecond ftep, from the 
 fecond 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 ftrokes between the perpendiculars draw 
 parallels to the horizon, as far as the wall F erected in the middle ; fuch are 
 the lines 1 1 II, which I have only added on one fide, to avoid confufion : It is 
 thefe parallels alone that form the flairs. All the other lines hitherto drawn 
 mould be occult, and not to be feen when the figure is finifhed. 
 
 The landing-places fhould contain all the vacant fpaces between the laft per- 
 pendicular and the wall, as from G to H. Their height, or thicknefs A K, is 
 half a foot, the fame as that of a ftair. 
 
 The lower figure is the fame with the upper, only that one has the apparatus 
 of lines, neceffary for the performance, which the other is without 
 
 6 
 
§3 
 
 PRACTICAL 
 
 Part IIL 
 
 To exhibit Winding or Spiral Stairs in PerfpeBfoe. 
 
 O N E fide of the flight, or afcent, is to be fet on the bafe line, and divided 
 into as many parts as you require flairs. Suppofe, for inftance, A B the 
 fide of the (lair cafe, and fixteen fteps required in the whole circuit of the fquare ; 
 each fide, in this cafe, will contain four ; confequently A B being divided into 
 four, a fquare is to be formed thereof, as here reprefented, divided "into fixteen 
 according to the ufual rules. 
 
 From all the divifions on the fides of the plan, perpendiculars muft be raifed 
 to give the bounds of the flairs. Suppofe then the perpendiculars A A, B B 
 C C, D D, E E. Thus E E Hands for three of the perpendiculars, by reafoa 
 the point is in the middle, and ferves as a newel, * or common center of them 
 all. On the fir ft perpendicular A, which is to ferve for a line of elevation, the 
 height of a ftair QA muft be fet, and from the point Q^a line be drawn to the 
 point of fight X, which by its inter lections with the perpendiculars QRSTV 
 gives the dimenfions of all the ftairs. Thus A QJs.the height of the firftv F R 
 of the fecond, G S of the third, H T of the fourth, and I V of the* fifth 
 This laft is the height of all thofe at the bottom, as A Q is of thofe in the 
 front. 
 
 Since G S is the meafure of the third, which is that in the middle of the fide, 
 it muft likewife be the meafure of the center, and of the newel of the flight: 
 for this reafon, having taken the meafure G S in your compafles, fet itolfin 
 the center of the fquare or the newel as many times as you would have ftairs in 
 the flight; for example, eighteen times for eighteen ftairs. 
 
 All things thus difpofed, the reft is eafy. For the firft ftep you are to take 
 the divifion A Q, and fet it off upon the perpendicular D in the point i, and 
 from i to draw a parallel to the perpendicular B ; then from the two points 
 
 1 i draw lir.es to the third i at the newel or center of the fquare. Thefe 
 three i i i will form the firft ftair. For the fecond, fince its angle reaches 
 to the perpendicular B, which is on the fore-fide, it muft have the fame meafure 
 A Q, which will be i, 2; then from the point 2 a line is to be drawn to the 
 point of fight X, cutting the perpendicular P in the point 2 ; from which points 
 
 2 and 2, lines are to be drawn to the 2 at the newel. Thus will you have formed 
 the fecond ftair. For the third, fince it is found on the perpendicular P, the 
 meafure FR muft be taken for hs height; and the fame procefs obferved as in 
 the former. 
 
 If you would have them round withal, the fquare muft be reduced to a circle ; 
 according to the preceding rules : and for the reft, the fame method will fctve 
 for both. 
 
 • The newt«l is the upright poft which a pair of winding ftairs earns aboit. 
 
 6' 
 
CC 2 
 
PRACTICAL 
 
 Part III. 
 
 Winding-Stairs. 
 
 f"T~"1 HIS figure is the fame with the preceding one, which 
 JL was not fhaded, that the method of the operation 
 might be the more confpicuous. For the fame reafon the 
 newel of the flair cafe was referred for this figure* It is 
 formed by affuming the point A as a center, and thence de- 
 ferring a circle ; or rather a fe mi- circle, as B C, becaufe 
 only half of it is to be feen. To the center of this femi- 
 circle lines muft be drawn from all the divifions of the fquare 
 of the firft plan, as DEFGHIK, which will cut the arch 
 B C into eight parts ; and from the interferons O O, &c. 
 perpendiculars are to be raifed ; taking care they cut precifely 
 in the points, where the fteps are placed ; the ftep I, for 
 inftance, to be cut by the perpendicular raifed from its point 
 in the femi-circle, as in A ; the fecond ftep to be cut by 
 the perpendicular raifed from the point which K gives in 
 the femi-circle : and fo of the reft. 
 
 The doors, windows, &C in the figure, are all con- 
 ftrucled according to the rules already laid down. 
 
Si PRACTICAL PartHl. 
 
 ♦ 
 
 To exhibit Round Stairs in Perfpeilhe. 
 
 TO raife thefe three round flairs or fteps, in a front 
 view, make a plan of three circles within each other, 
 after the manner already directed in page 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 elevations, which are to be 
 taken thence with the compaffes, and fet off on perpendi- 
 culars raifed from the feveral points of the plan. 
 
 Round Steps viewed Jide-moife. 
 
 THE rules for object viewed by the fides I have often 
 obferved are the fame with thofe for objedh in front. 
 However to mew we are not always obliged to obferve the 
 dwifion of the circle into fixteen, thefe of the fide-view we 
 have divided into eight. For the reft, it i s the fame as in 
 the preceding cafes, the line of elevation is CD, drawn to 
 the point of fight E. 
 
86 
 
 PRACTICAL 
 
 Part nr. 
 
 To exhibit Squares, with Circles therein^ in PerfpeBive. 
 
 npHE method for this procefs, is the fame with that delivered for 
 ± putting planes in perfpedive. The circle, for in fiance, is to be 
 divided into eight parts, as in figure A, wherein the circle on the front 
 of the cube, gives the diminution of that on the top ; and that in the 
 front, with that at top, give the diminutions of all the other fides ; as 
 in figure B, where the circle is alfo diminiflied on the fide, and in 'the 
 figure C, where it is diminithed on three fides of the cube, I mean both 
 on the outer and inner fides. 
 
 The three figures D E F are perforated each on two fides, according 
 to the plan of tbe circle A. Thus the cube D is pierced through its 
 fore-fide ; and through that perforation the bottom is feen. Thus alfo 
 E is perforated on the fides, and F through the top and bottom, though 
 the latter perforation be not diftinguifhable, by reafon the objecT: 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 I out of F. 
 
 Upon the whole, the method of difpofmg fquare figures in circles ap- 
 pears very eafy ; nor can the attentive reader find any difficulty in placing 
 columns under any difpofition whatever. The reafon why I have yet 
 given no directions for them, is, that I chofe to render the raifing of 
 elevations as eafy to conceive, and the practice as little embarrafled as 
 pofTible. Thus much may ferve for the beginning of columns j how 
 to carry on and -finilh them fhall be mewn hereafter. 
 
Part III. PERSPECTIVE. 86 
 
 H (y I 
 
 D d 
 
8 7 
 
 PRACTICAL 
 
 Part III. 
 
 To exhibit Columns in PerfpeSlive. 
 
 HAT has been juft obferved is not confined to the cube, but 
 
 V V extends equally to any object which is to be rounded. For in- 
 ftence, if from the fquare, A, you would raife a column A B, defcribe 
 a circle within the fquare, according to the common rules j and at the 
 intended height defcribe another fquare with a circle within it, B. Now 
 to get the two lines D E, which make the thicknefs, or diameter of 
 the column, obferve where the circle cuts the diagonal of the fquare, 
 and on thofe points raife the lines which form the fides of the elevation. 
 Thus C is formed by perpendiculars raifed from the interferons D E of 
 the circle with the diagonal of the fquare. 
 
 Thus much regards the column in fide-views. As to thofe in front, 
 for example, the figure F, they always mew the femi-circle G H I, and 
 for this purpofe the perpendiculars are to be raifed from the extremes of 
 the diameter G H ; and in both thofe in front, and thofe in fide-views, 
 perpendiculars to be raifed from the center, to give the diminutions. 
 
 As to the three columns underneath, as they mew the former in- 
 ftances more clearly, and with the addition of lliadowing, they likewife 
 ferve to point out the manner of proceeding to finim the columns. The 
 middle figure, K, is quite round, without any ornament at all, and 
 being viewed in front, is raifed by perpendiculars from the extremes of 
 the diameter. The fecond, marked L, (hews, that when a bafeis requir- 
 ed, a double circle muft be defcribed on the fquare that ferves as a plinth, 
 whofe upper part is MN; the interval between the circles to be the 
 projecture 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; taking care the abacus anfwer, as it ought, 
 to the plinth. Thefe two columns L and O being feen fidewife are raifed 
 by perpendiculars from the points where the circle cuts the diagonals of 
 the fquare. 
 
D d 2 
 
88 
 
 PR ACTICAL 
 
 Part III. 
 
 Cornices and Mouldings in PerfpeSiive. 
 
 AFTER the columns, which are the chief ornaments of architecture, we proceed to 
 the cornices, or mouldings, with their projectures j which have hitherto been omitted, 
 for fear of rendering our elevations perplexed. 
 
 There is fcarce any building but has fome moulding or projecture by way of enrichment, 
 and to render it pleafing to the eye : for this reafon, it is proper to give the rules for thefe ; 
 not the rules for their conftruction, nor their meafures and proportions, for in that cafe I 
 fiiould be obliged to give all the orders of architecture, and a thoufand other inftances,* 
 which the reader will find elfewhere : but rules to put them in perfpective, when any parti- 
 cular ornament or order is pitched upon. 
 
 To put the pilafter A B, with its ornaments or members in perfpective : its breadth 
 being taken, and a fquare plan made as ufual, erect perpendiculars from all the angles 
 thereof, and you will have the body, or ftiaft, of the pilafter. 
 
 Proceed now to take the prefectures, or jettings, as for example, the bafe of the pilafter 
 C, and lay down the feveral meafures thereof in D E. To put this in perfpective all round 
 the pilafter, from the point of diftance F draw a diagonal to the point E, and farther at 
 random, as to G j then from the point of fight A draw a line to the bottom of the pro- 
 jecture H, and in the point I, where this cuts the diagonal, will be the jet, or prefecture, 
 of the whole bafe. The fame line A H gives the prefecture of the bottom, by its in- 
 terferon with the other diagonal in K. For the proje&ure of the front, from the point I 
 draw a parallel to the bafe line, till it cuts the diagonal in L : this gives the other corner 
 of the projecture 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 fhew the reft, and even the effect of what is faid, free of con- 
 fufion. For the pilafter O, regard muft be had to that above in P, where the line D H 
 has upon it all the interferons of the bafe. For this reafon lines are to be drawn from 
 the point of fight A, which pafling through the divifions of D H, will exprefs the fame 
 on the lines D I and N K ; then parallels being drawn from- the points D I to M L, no- 
 thing remains but to draw the outlines. When there happens fquares, or fillets, either 
 at top or bottom, they are formed by perpendiculars. Thus, for the plinth, perpendiculars 
 muft be raifed from the points LI K, and from the point of fight A a line to be drawn 
 through the angle of the plinth to Qj this will give the height of the 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 iines. They are all broke 
 in the middle, that there might be room to exprefs both the bafe and the capital \ the page 
 not allowing them to be reprefented whole. 
 
8 9 
 
 PRACTICAL 
 
 Part HI, 
 
 To exhibit a large Cornice above the Horizon, in 
 
 Perfpe&ive. 
 
 "\ H E method is the fame as that juft delivered ; but being fomewhat trouble- 
 ^ fome by reafon of the number of lines, I have judged proper to repeat it 
 again here, in order to avoid confufion. 
 
 ; To the purpofe then : having taken the profile of the cornice, and its pro- 
 jefture, you are to transfer it to the place where the draught is to be made as 
 here the profile C, is at the corner of a wail A B. To find what height 
 it mult, have, and to make it mew its bottom, from the point of fight D draw a 
 line through the extreme of the profile E, as the line D F ; then draw a dia- 
 gonal from the point of diftanee H, patting through the corner of the wall B 
 and prolonged till it cut the ray D E in the point F ; from which draw the line 
 F Cj, which is to reprefent the angle in perfpedtive, and to receive all the mea- 
 sures of E G. The corner of the other end of the wall, K L, is to be drawn 
 to the point of diitance I, as being the other diagonal. 
 
 In Fig. II. it is fhewn, that all the figures which are on the line M N, are to 
 be transferred, by means of vifual rays drawn from the point of fight D upon 
 the line N O ; 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 fquares are formed by per' 
 pendiculars. Thus, for inftance, to form the large fquare of the cornice, havine 
 made the doucine, and the fillet ; from the bottom of the fillet which is the 
 top of the fquare, let fall the perpendicular P Qj then, to find the place it is 
 to be cut in, to mew the bottom, a line muft be drawn from the point of di 
 tance I, through the point at top of the quarter round R, to the perpendicu- 
 
 lij and y0U Wl11 have y° ur defire - What has been faid ^ the large fquare 
 holds equally of the lelfcr ones; as the denticles, fillets, which are all to 
 fhew their bottoms. 
 
 The third figure fiiews, that having found all the points, and drawn lines on 
 the line of the angie S T proportional mouldings muft be drawn thereon I 
 mean, that when they project much, as is here the cafe, by reafon the point of 
 diitance 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 enlarged • and 
 the fame done at one end as the other ; for example, the fame on V X as on S T. 
 
 This done, all that remains is, to draw parallels to the bafe line to form the 
 rront-lide of the cornice. 
 
 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 wa'l is 
 made to pals over -the cornice, to (hew that we are at liberty in fuch matters • 
 and that the rule is general. * * 
 
90 
 
 PRACTICAL 
 
 Part III, 
 
 c fo find the Bottoms of large Projectures, 
 
 y | ^ O find the projecture of the corona of the wall A; on 
 JL the angle of the quarter round B, make a line equal 
 to the length of the intended projecture, as B C ; then from 
 the point of fight D, draw a ray E, pa fling to the extreme 
 of the meafure C. This done, draw a diagonal from the 
 point of diftance F, pafling through the quarter round B ; 
 and the point G, wherein it interfects the ray D E, will give 
 the bottom on both fides, B H : as is more clearly expreffed 
 in the oppofite figure K. 
 
 The projecture of the wall L, is formed after the fame 
 manner as that of the former A. All the difference is, the 
 projecture M N 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 little as one pleafes. 
 
 It is likewife obfervable in the fame wall, 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 C D will be a point, through 
 which a little parallel to the horizon R QJbeing drawn, will 
 give the return required. 
 
 The fame method may ferve for all fquares on cornices 
 and mouldings both great and fmall. 
 
 The wall S fhews all the mouldings on that of L, more 
 diftindly. 2 
 
9* 
 
 PRACTICAL 
 
 Part III. 
 
 To exhibit Cornices and Mouldings below the Horizon. 
 
 f I ^ H E rules that obtain here are the fame with thofe of 
 JL the preceding cafes ; though through an accident 
 which fometimes falls out, namely, a diverfity of horizons, 
 there arifes a little variation, which fuch as are unacquainted 
 therewith might chance to be puzzled withal. 
 
 I obferve then that in viewing a cornice below the eye, 
 and of confequence below the horizon, the projeclures hide 
 fometimes half, fometimes more ; more or lefs of them being 
 feen, according as the eye is more or lefs elevated. 
 
 To find precifely how much of the projection is to be co- 
 vered, and how much not ; fet the profile of the moulding 
 on the corner of the body to be enriched therewith ; and 
 having found the line of the angle, after the manner already 
 directed, draw the divilions of the profile upon the fame. 
 Thus* will you find that the fquare, or plat-band, covers the 
 whole aftragal underneath, and only lets half the fillet be 
 feen. For, drawing a line from the point of fight A, through 
 the profile B C, it cuts the perpendicular from the line of 
 angle in D, and fhews how much is to be covered. For the 
 moulding at bottom the fame method ferves as for that at 
 top. 
 
E e a 
 
92 
 
 PRACTICAL 
 
 Part III. 
 
 To exhibit 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 point of diftance. Thus, having drawn 
 
 rays, A and B, to the point of fight 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 bottom or projecture of the fquare ; as already 
 
 fhewn in page 90, 
 
 I would willingly have made a much bigger cornice ; as 
 that would not have been a whit the more difficult : but the 
 compafs of the page obliged me to be contented with this. 
 
 If you would have returns on the ground, in the manner 
 as thefe are above the horizon ; the fame method is to be 
 obferved. For proof of this, invert the paper, and you will 
 find it have the fame effeft. 
 
93 
 
 PRACTICAL 
 
 Part III. 
 
 *Ib exhibit the Apertures of Doors in Perfpe&ive> 
 
 I N my inftrucYtons, I have kept pretty clofe to the order obferved in the actual erecting 
 of buildings of all kinds. I now proceed to fhew how to furnifh and difpofe them for 
 the reception of inhabitants. I begin with wooden doors ; and hereafter fhall find occafion 
 to fpeak of other apertures, as windows, cupboards, &c. then of moveables, as tables, 
 •beds, chairs, chefts, benches, cffr. 
 
 All doors are to open and fhut far or little at the pleafure of the perfon who opens them. 
 For this reafon I fhall {hew an eafy method of putting them in perfpective, at any degree of 
 width or aperture at difcretion. 
 
 Now it is obfervable, that doors, windows, cabinets, chefts, and, in fine, every thing 
 intended to open and fhut, always defcribe a femi-circle in opening. The reafon is, that 
 the fide hung by hinges keeps its place, like the fixed leg of a pair of compaffes, while the 
 other fide, like the other leg of the compaffes, fweeps its arch. Thus in the plan under- 
 neath the oppofite figure, the fixed fide A extending to B, if you open the door quite, 
 the fide B muff, defcribe the femi circle BCD, whofe center is A. Hence it follows, 
 that if the door be three feet broad, as in the prefent cafe, the radius A C will likewife 
 be three feet, and the whole chord or diameter of the femi-circle B A D fix feet. Of thefe 
 fix feet in length, and three in breadth, a plan muft be made, confiding of eighteen 
 fquares, wherein the femi-circle A B C D is to be defcribed, this method is directed to 
 render the making of the fame femi-circles in perfpective the more eafy. Always ob- 
 ferving where the femi circle of the plan cuts the fquares, that thofe in the perfpective 
 may be cut after the fame manner, and a femi-circle be drawn, taking up the fame fpace, 
 traveriing as many fquares, and cutting them in the fame places. An inftance of which 
 you have in the door E, where the interferons are marked the fame as in the plan under- 
 neath, i, 2, 3, 4, 5, 6, 7. 
 
 When a door is to be reprefented open in perfpective, a femi-circle muft be ftruck on 
 its plan, and the point of aperture placed on any part thereof at pleafure. Thus for the 
 door E the point of aperture is fixed at 2. From this point 2 a perpendicular muft be 
 raifed, as 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 horizon 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 per- 
 pendicular raifed from the point 2, in the point H. Thus will you have the door 
 open F I H 2. 
 
 All apertures are performed by the fame rules as is farther feen in the doors K and L. 
 The door K fnews its outfide, and that of L its inlide ; yet both are performed after the 
 fame manner as the firft. The accidental point of K is drawn from the point M in the 
 horizon, and that of the door L from the point of diftance O. If bolts, locks, or the 
 like, be added on the doors, they muft all be drawn from the fame accidental point ; as' 
 the bolts and lock of L tend towards O. What accidental points are, has been explained, 
 page 12. 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 
 fight. The other, when its pofition is parallel to the horizon j by reafon the parallels, in 
 lhat cafe, never interfecl: : as in the door N. 
 
94 
 
 PRACTICAL 
 
 Part III. 
 
 jTo exhibit Apertures of Cafements in Perfpe&ive. 
 
 AL L the difference between the apertures of cafement s> and thofe of doors % 
 lies in this, that doors have their femi-circle of aperture on the plan, and 
 cafements in the air •, by reafon windows are raifed, and doors ufually turn on the 
 ground. On this account, the femi circles of cafements may be either over or un- 
 derneath them. And in fuch femi-circles is the point of aperture to be placed. 
 
 Thus, for inftance, if a cafement be two fquares, or panes, broad, as A B, 
 and it be made quite open, it will then take up twa fquares more C A, whereof 
 A is the middle, and the center of the lemi circle ABC. But by reafon the 
 window is raifed above the ground, the femi-circle muft alfo be raifed; as is here 
 actually done in the femi-circles of the windows D and E : whereof the fame D 
 and E are the centers and which are eafily formed by erecting perpendiculars 
 from the intermediate fquares, till fuch time as they interfect the rays drawn from 
 the corners of the cafements D, E. From tjiefe interferons, lines muft be 
 drawn to the bafe line, and the meafures of the fquares of the plan i, 2, 3, be 
 let thereon. From the fame points 1, 2, 3, lines are to be drawn to the point 
 of fight F ; which cutting the parallels, will give fquares 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 femi-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, for example, 
 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 KEGH. 
 The fame is to be obferved with regard to all the reft ; and the point ftill to be 
 taken in the horizon. Thus, L is the point for the 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 performed 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 manner 
 already directed ; and the cafements according to the method laft delivered. 
 
 Apertures of Cafements with Embrafures. 
 
 TH E rules for thefe are the fame as for thofe that range even with the wall, 
 excepting that thefe are not capable of being quite opened, by reafon of 
 the thicknefs of the chamfraining, or embrafure. On this account we never give 
 them a whole femi-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 Q^and R ; that below is parallel to the horizon, 
 4 
 
Part ill. 
 
 PERSPECTI V ■ E, 
 
 04 
 
 F f 
 
95 
 
 PRACTICAL 
 
 Part. Ill, 
 
 Divers other Ape rt u re s. 
 
 r-yr^llE openings of cupboards, prejfes and chefts, are at leaft as necef- 
 fary as thole of doors and windows j nor bad the omiffion of the 
 ■one been a whit more excuiable than that of the other. Their doctrine 
 will be difpatched in two figures. 
 
 The cupboards or prefies A A* are opened according to the rules de- 
 livered for cafements, which it would be need lefs here to repeat. I ihaJi 
 only add, that the uppermoft is parallel to the horizon \ and that the 
 latter tends to the point of diftance B. 
 
 The flop on the other fide is opened by two . leaves, one of them rif- 
 ing upwards, and the other falling downwards. Each of them defcribes 
 its femi-circle from the centers C and D j which being drawn with the 
 compaffes, the apertures are fixed at any point at pleafure j as here in 
 the point E ; from which a ray is drawn to the point of fight F, till it 
 ^interfecT: the femi-circles at the other ends in the points G. .From thefe 
 points E and G, lines being drawn to the centers CD, give the leaves 
 ■opened in that pofitioa. 
 
 In fhe lower figure there are three chefts? differently opened. To open 
 the firft, H, the quadrant M is put in perfpecYive, according 'to the 
 irneafures of the fquares of the plan. Thus, obferving the width of the 
 cheft, which is two fquares, perpendiculars are to be raifed thence, and 
 •a femi-circle, or quadrant, defcribed for the opening, which is here fixed 
 at the point N j and from this a parallel k to be drawn to the other qua- 
 drant O ; and from N and O lines to be drawn to the centers PP. -If a 
 greater aperture is required j a femi-circle is to be drawn in lieu of a 
 ^quadrant. 
 
 The chefl I in that pofition has the eafieft of all openings, for hav- 
 ing taken the breadth QJR* from the center R defcribe the femi-circle 
 Q^S^ then take any aperture at pleafure, as T, and draw a line to the 
 point of fight V, cutting the other femi-circle in X j and, laftly, from 
 the points T and X, draw lines to the corners R, and you have the lid 
 farmed with that aperture. 
 
 If it is required to ©pen the cherts farther, you have only to fix the 
 pomt of aperture high in the femi-circle ; as Y is in the cheft K. The 
 reft .of the jprocefsis the fame as in the firft cheft. 
 
Ff 2 
 
9 6 
 
 Practical 
 
 Part III. 
 
 Plans and firft Elevations of Moveables 
 
 THESE plans I fhould have placed in their order among the reft, but for 
 this confideration ; that bad I treated of them at the beginning of the 
 work, without mewing the neceflity thereof, they would have paffed for ufe- 
 lefs, and accordingly have readily dropt out of remembrance. They now come 
 in feafon, and cannot fail of being well received and learnt with pleafure ; inaf- 
 much as numerous forts of moveables or houjbold goods have a dependance upon 
 them. 
 
 The firft plan, A r may ferve for beds, tables, chairs, Jlools, Sec. The other 
 B, which is twice as long as it is broad, ferves for long tables, cupboards, buffets,, 
 cheftsy trunks, &c. The third, C, which is long and narrow, ferves for benches* 
 or forms, couches, and other pieces of furniture with fix legs or feet.. 
 
 The acquaintance the reader is fuppofed to have with the other plans already 
 treated of, 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, for example, for the firft plan A, the two meafures of E and D muft 
 be fet on the bafe, and lines be drawn thence to the point of fight F. Then 
 ^rom one of the points of diftance, a line is to be drawn to one of thofe meafures, 
 as from G to E ; and through the points H and I, wherein it interfects the rays, 
 parallels are to be drawn ; by this means four little fquares will be formed, whofe 
 meafure you may account as much or as little as you pleafe. For a table they* 
 muft be more than for a ftool, that is they muft have more breadth ^ the latter 
 being ufually 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 interfect in M, and give a whole fquare whereas, we only want half 
 of it. Parallels then muft be drawn from K to the points of interfeclion with 
 the ray ; and from the corner L, a line muft likewife be drawn to the point of 
 diftance G, interfering the ray : Thus will you have the four little fquares. 
 
 The third plan, C, needs no explanation ; it being evident that it is formed 
 like the firft A ; and that the fquares muft be doubled to get the fix little fquares. 
 
 The figures underneath are intended to fhew that perpendiculars muft be raifed 
 from all the angles of the aforefaid fquares, to begin to form the moveable pieces 
 of furniture hereafter fhewn. 
 
 6 
 
Part III* PERSPECTIVE. 96 
 
 i lm 
 
97 
 
 PRACTICAL 
 
 Part III. 
 
 Elevations of Moveables. 
 
 HA V TN G raifed perpendiculars from the plan, as already intimated *, a line 
 of elevation muft be made in fome part of the painting, on which the 
 heights, crois pieces* &c. are to be laid. 
 
 Thus the line C D being a line of elevation, and C E and D F breadths or 
 depths of the crofs pieces ; from thefe four points draw lines to fome place 
 in the horizon, as to the point G. Then having erected perpendiculars from all 
 the angles of the plan, as in A and B-, from the angles draw parallels to the 
 bafe line, till they cut the line C G. Thus will you have the points i, 2, 3, 4 ; 
 from which perpendiculars are to be raifed, and the interfections thofe perpen - 
 diculars make with the line D G, will be the points to cut the perpendiculars of 
 the plans, as (hewn 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 fight H, the other perpendiculars of the plans will 
 be cut in the points P P, &c. And doing the like from the point F, &c. you 
 will at length have a cube perforated on all its fides. Which procefs being well 
 underftood, all the other pieces that follow, and even all that can be conceived, 
 will be readily performed. 
 
 Inftead of parallels from the points on the line D G, to cut the perpendiculars 
 of the plan, the meafures of them taken with the comparTes and transferred to 
 thofe perpendiculars will anfwer the fame purpofe, as has been Ihewn elfewhere. 
 
 It is eafily obferved, that the two frames or ftands 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 in the 
 former. In the latter, for inftance, we find it in the line L, which gives M M. 
 The feet of the ftands or that part of the perpendiculars which are beneath the 
 crofs bars, one may either leave them fquare, or round them into bowls. 
 
 As to the laft frames, N and Q^, there is nothing in them more than in I and 
 K only that they are viewed by the angle, and the other in front. The plans 
 of thofe ftands, I and K, are drawn to the point of fight R ; and thefe latter to 
 the points of diftance S T. 
 
 The figures in this plate, with little variation, may be adapted to divers forts 
 of moveables. Thus, for inftance, to make a bedftead of Fig, I or 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 ftool, or the like. For a table 
 you have only a top to add. For a joint-ftool, befide the top, it muft be made 
 more in height than width, but the conftruction thereof with four legs, and the 
 four crofs bars, is the fame as in this figure. 
 
P RACTICAL 
 
 Part III. 
 
 "To exhibit the upper Part of Tables, Stools, &*c. 
 
 If AVING raifed perpendiculars from the plan, as di- 
 ~j[ reded in the foregoing page, and fixed the proper 
 height thereon, the frame will be complete. Now to make 
 a cover to it perfectly on a level, and which (hall not extend 
 beyond the frame, there needs nothing more than to leave 
 the top of the cube plain, without expreffing any other lines 
 but thofe which bound the four fides, which will make the 
 upper part of a table, ftool, or the like. 
 
 But if it is defired the upper part or cover flhall have a 
 prefecture, or ledge ; from one of the angles of the frame 
 a parallel mull be drawn, as A B ; and on this parallel the 
 meafure or quantity of the intended projeclure rauft be fet, 
 as here AB. Then from the points of diftanceC and D, occult 
 lines AE, AE, &*c. muft be drawn through the angles of the 
 fquare of the frame here exprefled by dotted lines. And to 
 make the meafure A B give the proper breadth to all the 
 fides and angles of the table ; draw a line from the point of 
 fight F, through 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 fight F, the 
 other diagonals will be interfered in I and K; which will 
 give the upper part of the table, with the proje&ure that 
 was 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 
 objects, whether in front or in fide- views below the horizon, 
 and for the bottom of thofe that are above the horizon, as 
 particularly fliewa in pages 49 and 50. 
 
99 
 
 PRACTICAL 
 
 Part lit. 
 
 To exhibit the Elevation of Buffets, Preffes, and Cup-boards, 
 
 H AVING made the plan, and raifed perpendiculars from all the 
 angles, as already taught 5 upon the line A B, which is here to* 
 ferve for a line of elevation, the meafures or proportions of the diftances 
 of the (helves, with their thicknefTes, &c. as hereCDE, muft be laid: 
 down. Then from the points C D E, draw parallels to the bafe line, as- 
 far as the upright poft G F ; and from the points thus marked on G F, 
 draw lines to the point of fight H; as far as the other port 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 F L is laid down j and from the point L, 
 a line is drawn to the point of diftance M ; and the point I wherein it 
 interfects the ray F H, is the place of the laft poft. 
 
 The buffet on the oppofite fide 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 Q^N, or of the breadth of the buftet ; and drawing 
 lines thence to the point of diftance G, where the ray N H is interfered 
 thereby, draw parallels to the bafe line, cutting the ray T H 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. IE are performed after the 
 fame manner as the buffets above; only that in the middle being viewed 
 in front, needs a little explanation to determine its depth. I obferve, then 
 that its plan muft be formed, as already directed, and as one half of it 
 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 per- 
 pendicular of the depth S ; and from the points of interfe&ion draw 
 little parallels to the bafe. The reft of the operation is plain. 
 
ICO 
 
 PRACTICAL 
 
 Part nr. 
 
 ^Elevations of Chairs, Forms, and Couches. 
 
 raije a chair \ from the dimenfions ABC, erect 
 J. perpendiculars, and proceed in the fame method al- 
 ready direded for table- feet, or frames without tops. All 
 that is to be done farther, is to procure the back of the chair; 
 which may be made of any height at pleafure. In the pre- 
 fent cafe the height of the back is equal to that from the 
 foot A to the feat 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 AE; and from the point E to 
 draw a line to the point of fight G ; which cutting the per- 
 pendicular or port 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 raife the perpen- 
 diculars of the front legs higher, as the hind ones are for the 
 back, and to draw a crofs piece, or bar, in the fliape you 
 would have the elbow. 
 
 In the figure underneath, you fee a form, or bench, co- 
 vered with cloth, and two couches. The head of one is 
 turned back in the front of the pidure, and the other is 
 viewed 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, mamely, 
 by making a plan, railing perpendiculars, 
 
not 
 
 P R A C T I C A L 
 
 Part III. 
 
 Another Method of putting Moveables in Verfpe&ive. 
 
 *-pHERE are (ovat moveables' that fold, or flmt down and that 
 t .l ferve for tables, feats, beds, flfc. very eafy to be put in ptf^! 
 
 th l? 1 f v ? t ' 10 ". >.t* performed as that of a cube as /hewn ;„ 
 ABCD, which s viewed in front- or FFPH T J ' s !. ewn m 
 a p . d p. , 111 llo nc, orfir OH. Then two diaponak 
 
 F H f C u° be , made for that in ,he middle of the front or 
 
 ff^heT FG / ortha , t . Gf th ^>de : and thefe will ferve fo the drawing 
 
 OK 5^.1^ 5 J^ ,ng C3re th2t ° ne enter ^'f through the othe^ af 
 ?ol%:tA HI -> 3ndb0th ° f ^ be faftenel by thf^ddle 
 
 Jfwnlh^eS^ 
 
 E draw hnes from the fame to the point of di(W F ™? kr 
 where they interfe<2 the r,„ jr cmtance and obferve 
 
 -aw ..^y hi", t^l' w di ?* r " * 
 
102 
 
 PRACTICAL 
 
 Part HI, 
 
 To exhibit M oveables placed without any Order* 
 
 ^TZHEN moveables are placed orderly along the fide of a wall, or 
 YV in f he direction of the rays and the bafe line, it is eafy to put 
 th em in perfpective by the rules already delivered ; but if they be irre- 
 gularly placed, as in this figure, you are to proceed as I (hall now direct. 
 Draw the geometrical plans, R, S, and T, for plans of three chairs • 
 which are to be diminished or put in perfpective by the rule delivered 
 for the irregular figure, page 40, and the plans will be found fituated 
 like the chairs, or rather the chairs like the plans. Now the plans being 
 in perfpective, lay a ruler along one of the fides, to fee what accidental 
 point it gives in the horizon; thus, laying a ruler along the fide A B, 
 you have the point C in the horizon for an accidental point, to which 
 all the lines of that and the oppofite fide muft be drawn. In this man- 
 ner you fee that A and D are drawn to the fame point C. It is true 
 each plan placed irregularly fhould have two accidental points, but they 
 are frequently fo far off in the horizon, that it is doubtful whether you 
 find, them both. The prefent plans have each of them one ; as A B 
 has C 3 and A D, the other fide, would have another, if our paper were 
 broad enough. E F gives G for its accidental point, and I H gives K. 
 As to the little fquares 1, 2, 3, 4, they are the plans of the fee? of the 
 fame chairs, as may be made broader and narrower at pleafure. 
 
 Proceed then to erect perpendiculars from all the angles of the plan, 
 and on the fide of the picture add a line of elevation M N, whereon to 
 lay the dimenfions of the crofs pieces ; as O, for the lower bars ; P for 
 the bars of the feat ; and QJbr 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 per- 
 pendiculars. Thefe will give the dimenfions, as already obferved of the 
 former figures. 
 
 All the lines of the fides are to be drawn to the accidental point of 
 the plan. Thus, in the middle chair, all the fides are drawn to the 
 point G, which is the point of the plan, as appears from the figure. 
 
 3 
 
103 
 
 PRACTICAL 
 
 Part HI, 
 
 To exhibit Moveables laid or tumbled on the Ground. 
 
 FROM the fame plan, which has been given for chairs ftanding on 
 their feet, it is eafy to form thefe which are laid on the ground. 
 
 At the feveral angles of the plan erect perpendiculars, and give the 
 fide on the ground the fame dimenfions as when it was ftanding above it. 
 For example, having eredted perpendiculars from the angles, you will 
 have the breadth M in the chair laid on its fide, which is drawn to the 
 point K. This meafure M, being doubled, gives O for the bar at the 
 bottom of the chair ; and the perpendiculars raifed from the plan, give 
 the bar of the feat P: from which points, lines drawn to K, will cut the 
 other perpendiculars of the front in the places required to (hew the fame 
 bars on all the fides they are vifible on. As to the height of 'the back of, 
 the chair, make it the fame with the height of the feat ; but for the back 
 of that in the middle, you are to draw a double diagonal, and obferve 
 where it cuts the rays, or fides, R S. The reft is obvious. 
 
 The two other figures underneath, with their feet aloft, are eafily per- 
 formed. One of them is drawn to the point of fight T, the other to the 
 point of diftance Y, X. -The line of elevation is Y Z. 
 
 The method of raifing them, is the fame as for elevating thofe upon 
 their feet : that is, perpendiculars muft be raifed from the angles of the 
 plan i and from the fame angles, lines be drawn to the line of elevation s 
 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. 
 
PRACTICAL Part III. 
 
 To exhibit Altars in perfpeSlive. 
 
 THE method for railing altars is the fame as that for frames of long tables, all that is farther 
 to be done, relates to the circle in the middle, the edges of the cloth and the laces ; of each 
 whereof in its place. 
 
 In raifing 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 fight E ; and from the interferons thofe lines make with the bottom of the altar, 
 ereft perpendiculars, which being joined by a parallel at the proper height, give the front, and 
 rays drawn to the point of fight E form the fides. As to the circle in the middle it is {truck, with 
 compafles. The reft is obvious. 
 
 For a fide-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 rhe figure. Then, from B, D, and C, draw lines to 
 the point of fight E : and fince B F on the bafe line 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 is interfe&s the ray BE; 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 HI. For the two orna- 
 ments that are on each fide 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, 
 I need not repeat what has been already faid of the method of putting it in perfpeclive. I fhall 
 only here obferve, that lines muft be drawn from all the divifions thereof on the bafe line to the 
 point of diftance G ; and in the interferons with the ray B, perpendiculars to be raifed. Then, 
 the fame dimenfions to be taken and fet off between O and B ; as PPP, and from thofe three 
 points rays to be drawn to the point of fight E , obferving where they cut the perpendiculars raifed 
 from the other divifions of the circle, and connecting thofe points with a circular line, which gives 
 the circle in perfpeclive. The method of diminifhing 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 muft be pro- 
 longed, as Q_R. Then, from the point of diftance G, a line to be drawn through the corner of 
 the altar T, and continued till it cut QJR ; 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 candlefticks be laid ; for 
 example, V for the crofs and S S, tiff, 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 QJS, little 
 parallels to be drawn j which cutting the ray S E, give fquares upon the altar, XX, dsV. for the 
 crucifix, and candlefticks. This fquare muft be left for the foot of the crucifix; and from the 
 middle of the fquare, the crucifix is to be raifed. For the proportions of the arms of the crucifix, 
 erect occult perpendiculars from the angles of the fquare, as here Y Y ; and draw lines to the 
 point of fight E, for the candlefticks. Then turn the fquares, for their feet, into circles, and 
 obferve where they interfedt the diagonal : For perpendiculars erected from the points of interferon, 
 give the breadth of the bafons or ftands ; and lines drawn to the point of fight, the height. Laftly, 
 from the middle of the foot erect a perpendicular for the body of the candleftick, and the taper 
 therein, which is to be made high or iow at pleafure. To proportion them, draw a line from the 
 top of the firft to the point of fight E. The reft as already faid. The figure will call to mind 
 the methods. 
 
PRACTICAL 
 
 Part HI, 
 
 Th exhibit the Fixtures o/Shops in Perfpe&ive. 
 
 TRADESMEN'S (hops are ufaally encompafied with (helves, 
 boxes or drawers, wherein their goods are difpofed. 
 
 The rule for defigning boxes, preffes or (helves, is much the fame as 
 that already laid down for doors and windows ; for example, in lieu of 
 the thicknefs of the wall ufed in making a window, you are here to put 
 the board A B, and from the point B, to draw a line to the point of fight 
 C. Then, for the width of the (helves or prefles, having laid down the 
 diftances on the bafe line in E FG, from thefe points draw lines to the 
 points of diftance D. Thefe make intersections H I K, with the ray B : 
 from which inter feci: ions, perpendiculars being raifed, will give you the 
 upright divifions. 
 
 For the crofs boards, fet any number thereof at pleafure on A B, or 
 only on the firft perpendicular B O • fuch are here LMNO: from all 
 which draw rays to the point of fight C, and at their interferons with 
 the perpendiculars in the points P P, draw little parallels to the bafe line, 
 which will mew the. top and bottom of each (helf, and Separate them 
 from the fides. 
 
 As to the front divifions and (helves, there only needs to draw rays 
 from the points of meafures E F, and in the points of their interferons 
 with the lines QJS, to erect perpendiculars R and S. The crofs pieces 
 are had, by drawing parallels from all the divifions on the perpendicular 
 K; as here, P i, P 2, P 3, P 4. 
 
 As to the divifions on the oppofite fide, where there are fquare upright 
 pods to fuftain the (helves, their depth is had by drawing lines or rays 
 from the meafures T, G, to the point of fight C. And to get their plan, 
 or fquare, lines are to be drawn from the meafures AEFon the bafe line 
 to the point of diftance V, which give the interferon XYQ^on the ray 
 T C. Through thefe interferons little parallels mud be drawn till they 
 cut the ray C G in Z ; and from the angles of thefe little fquares, per- 
 pendiculars are to be erected, which give the upright ports, as in the figure. 
 
 The figure underneath (hews a (hop quite fitted up, and ready to receive 
 goods of any fort : for a bookfeller, it muft be (locked with books ; for 
 an apothecary, with drawers and gallipots } for a draper, with pieces of 
 cloth, (tuff, &c. 2 
 
io6 
 
 PRACTICAL 
 
 Part III. 
 
 Buildings viewed on' the Outfide. 
 
 -rjAVING now confidered every thing relating to the interior parts of buildings, I 
 J fl_ proceed to gve rules for the exterior. 
 
 Many of the methods already laid down for the infides may likewife ferve for the out- 
 fides ; the procefs for the doors and windows is the fame in both cafes, and as thefe are 
 very material, and diftinguifhtng parts of every jtruaure, the reader is already in great 
 meafure qualified for the elevation of buildings. It they be adorned with orders of columns 
 or jpilafters, inftruftions have alfo been given for thefe. 
 
 Suppofe there' be windows in front, as A, and it is defired to have others in the fame 
 proportions on the other fide, the proportions AAA muft be transferred to the bafj line, 
 as here BBB, and lines be drawn thence to the point of diftance C : and in the points 
 F FF, where they interfect the ray D E, perpendiculars to be raifed for the uprights in the 
 window. 
 
 For the crofs pieces ; thofe in the front window muft be continued to the perpendicular D, 
 by which means you will have the points 1 1 ; from which lines are to be drawn to the point 
 of fight E, which cutting the perpendiculars F, give the crofs bars in the fide-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 fide, which has two windows 
 from the fame rays. As to the breadth or thicknefs of the pofts or 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 l nebe drawn to the point of fight E ; and from the point H, another to the 
 point of diftance C, for the window A, and to the point of diftance L, for the window on 
 the other fide ; and in the point, where thofe two latt lines interfeft, a perpendicular, H M, 
 muft be raifed. Then, from all the corners of the window lines to be drawn to the point of 
 fight, and from the points Q,Q., &c. where they interfeft the perpendicular, H M, parallels 
 muft be drawn to give the thicknefs 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 fight; and in the 
 points Q^Q,, where it cuts the thicknefles of the crofs bars, ereding perpendiculars Q.R, 
 
 QR. 
 
 To fix the thicknefs of the windows on the other fide, it muft be fet in the corner of 
 the wall, on the perpendicular D, as the diftance IO; and from the points O O, lines 
 muft be drawn to the point of fight E. Laftly, little parallels to be drawn from all the 
 corners of the windows, as S T ; which, interfeaing the ray O, give the thicknefs in the 
 point S. Thefe rules may ferve for all kinds of windows, both high and low. 
 
 In the figure underneath is (hewn a door diminifJhed according to the rules delivered here- 
 tofore. As, in efFec"t, every thing belonging thereto is very eafily underftood, and readily 
 pra&ifed, on fome or other of the preceding methods, 
 
Part III, PERSPECTIVE. 106 
 
 fo6 
 
 — l00 
 
 * 
 
 li 
 
PRACTICAL 
 
 Part III, 
 
 To exhi&it Roofs qfHaufes hi Perfpetfive. 
 
 ROOFS are made of different heights according to the materials they are covered with. Thofe 
 of Jlate are the moft upright of all. Their ufual meafure is an equilateral triangle ; that is, 
 their flope, or the declivity of the roof, is equal to the width of the houfe. Thus, in the little 
 figure at the bottom of the prefent 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 
 flate, or the width of the houfe, as in A E B. For thatch, the height is ufually but half the width ; 
 and for fan-tiles, only one third j as A 9 B. 
 
 Before we go any farther it is to be obferved, that what we call punchion, or middle top, is a 
 timber raifed 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 flays, and are ufually longer than 
 rafters, as H K. 
 
 There are three kinds of roofs in ufe ; pavilions, pinnacles, and pent-hoofe-form. The firft have 
 four fides, the fecond only two, and the laft but one. 
 
 To put a pavilion or turret, in perfpettive, the place of the middle top muft be known, that the 
 flays may be drawn to the fame. For this reafon it was that I made the geometrical plan LMNOj. 
 to fhew, that a fquare, LMN P, is to be made of the breadth of the houfe L N, and two diagonals 
 drawn through the fame, interfering in Q. Some put the punchion in but that advances it too 
 far, and renders the end of the declivity too fquat. It has a much better grace when more upright. 
 With this view, it fhould be approached towards the wall LNa third part of the diftance QJl, 
 which will bring it to the point S ; from which point a perpendicular, S, muft be drawn upon the 
 line N P. Then the meafures L T and T M are to be fet on the bafe line, and lines drawn from 
 them to the point of diftance, which is here more remote than ufual ; and from the points, where- 
 in they interfeel the ray V, perpendiculars to be erected to the top of the wall, which will give 
 the points XX; from which, parallels to the bafe line are to be drawn as far as the other ray J„ 
 Then, from the middle of the wall Y, a line to be diawn to the point of fight, cutting the paral- 
 lels in the point Z, Z, cifr. from which points the punchions are to be raifed. To give them the 
 proper height retard muft be had to the materials intended for the covering, and the height to be 
 adjufted thereby, according to the proportions already fixed. Thus, fuppofe the covering flate, an 
 equilateral triangle, 1, 2, 3, muft be made of the breadth of the wall ; and from 3, a line be 
 drawn to the point of fight, cutting the punchion in the point 4. To which point, lines being 
 drawn from the corners of the houfe, will give the form of the pavilion. 
 
 For pinnacle roofs 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 fide fhew the fame thing unembarrafTed with lines. The projedlure 
 {landing beyond the roof is made at difcrecion. 
 
 The front houfe is covered with a pavilion, performed after the fame manner as that on the fide. 
 
 In the prefent figure, where the letters are, the horizon is placed very high, to fhew the tops of 
 the honfes, and render the practice more eafy and conceivable. But, as it is not often fuch a cafe 
 happens, I have added the other figure at the top, wherein the horizon is as low as ufual. Though 
 the rule in itfelf is the fame as that already delivered. 
 
 2 
 
PRACTICAL 
 
 Part HI. 
 
 Sequel of the Roofs in Perfpe&ive. 
 
 IN the preceding figure the pinnacle roofs are viewed in front, in this 
 plate they are (hewn laterally ; the method for conftrucYmg them 
 wkh their returns in the fide-views is now to be given. 
 
 The width of the houfe muft be fet on the bafe line, as here A B ; 
 and of this width a triangle is to be formed with the dimensions of the 
 fides according to the fo*rm of the roof. The prefent is an equilateral 
 triangle, whereof C D 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 
 half the breadth of the houfe is to be laid down in C, which is the 
 middle of A B j and from thence a line to be drawn to the point of 
 diftance ; and in the point G, where it interfects the ray A, a perpen- 
 dicular mull: be raifed. Laftly, from F, a line is to be drawn to the 
 point of fight Xj the interfection 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 I. If you would have eaves, they 
 are eafily added, as is feen in the figure K on the other fide. 
 
 For the conftru&ing of pentices ) you have only to draw a line to 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 M N, 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 fight X, the perpendiculars of the depth 
 will be cut in the points P and Qj which being connected by a right 
 line will form the roof. The figures on the oppofite fide fhew houfes 
 covered after fuch manners. 
 
 The uppermoft figures are only intended to fhew that the fame rule 
 is to be obferved, though the horizon be changed. 
 
 A church is feen in the middle, which is covered or roofed with pin^ 
 nacles 5 and the wings with pentices. 
 
 There is alfo a pavilion viewed end-wife ; mention whereof has been 
 made in the preceding page. 
 
log PRACTICAL Part III. 
 
 To exhibit Rows of Buildings, or Streets in Perfpe&ive, 
 
 A Bare fight of the figure muft fuffice to fliew the me* 
 thod, which is exceeding eafy. All you have to do 
 is to make a plan of fimple fquares, the common way ; and 
 to take one, or two, or three of the fquares for the breadth 
 or length of each houfe ; and on fuch breadth, ftfc. to fet 
 off the meafures of the doors, and windows ; and to get the 
 diminutions by drawing lines from the feveral meafures to the 
 point of diftance ; as here from BCDE and F, the lines are 
 fuppofed to be drawn to the point of diftance A. 
 
 The firft angle of each houfe may ferve for a line of eleva- 
 tion, as the angle G for the firft houfe. As to the roofs, I 
 have already faid how they are to be managed. 
 
 If you require any crofs ftreets, one, two, or three fquares 
 are to be left vacant, and nothing upon them, as here H 
 and I. 
 
 The figure underneath is to fliew, that where houfes are 
 to advance beyond others, or fall further back, you have 
 only to put their elevations forwarder or backwarder on the 
 plan of fquares. Thus L advances a fquare farther than K, 
 and M farther than L ; and fo of the reft. 
 
no 
 
 PRACTICAL 
 
 Pare III. 
 
 A Demonjlration that remote Objects do not pew 
 
 their Thicknefs. 
 
 T T rauft be here remembered, that obje&s near the hori- 
 J[ zon, that is, fuch as are extremely remote, are not to 
 fhew any thicknefs when viewed in front. Thus, for example, 
 the windows and doors of the houfes A, B, C, D, fliould 
 not have any thickneffes fhewn, but be expreft only by mere 
 lines. The reafon is, that the vifual rays proceeding from 
 the front parts of the objed become united in the eye with 
 the collateral ones. 
 
 I fhould have given a Ariel demonftration hereof, had I 
 apprehended it any way neceffary. But as I do not fee of 
 what ufe it would be, and as I ftand engaged from the be- 
 ginning of the book not to enter into fuch demonflrations, 
 by reafon I fuppofe I have to do with people who are but 
 indifferently prepared to underftand them, I decline it. 
 
iii PRACTICAL Part III. 
 
 To exhibit Buildings viewed by the Angle. 
 
 OF thefe two buildings feen angle-wife, the firft is performed after 
 the manner already delivered for fquares viewed by the angle, and 
 elevations of other obje&s in fide-views. However, to fave the trouble 
 of recurring to the one and the other, I mail here obferve, that to per- 
 form fuch buildings the meafures muft be fet on the bafe line, and from 
 each of them, lines be drawn to the po'int of diftance, and from the 
 points of interferon perpendiculars to be raifed ; the perpendicular 
 raifed on the firft angle ferving for a line of elevation. Thus, in the 
 prefent building, the breadth being A B, and the length, B C, double 
 its breadth j 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 inter- 
 ferons BF 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 BD or 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 irregularly, fee page 102; that is, having made the plan, put it 
 in perfpective as irregular objects are put. Then, laying a ruler along 
 each fide of the plan, obferve where it cuts the horizon, and marking 
 thofe accidental points, draw lines to them from each part of that fide 
 of the building. Every fide or face of a building has its particular point. 
 Thus the plan being put in perfpective, the fide H I, gives the point K 
 on the horizon, to which all the rays on that fide muft be drawn. The 
 other fide I L, mould 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 fide of 
 the building parallel upon the plan to that which gave the point in the 
 horizon, and continued to the bafe line j as from R, through L toM; 
 and from the other point continue an occult line through H to N. Then 
 fettine the number of windows of the fide H I, between N and I ; and 
 between I and M, fetting the number of windows on tw fide 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. 
 
112 
 
 PRACTICAL 
 
 Part III 
 
 "To exhibit Walks, with Rows of Trees y in PerfpeBive. 
 
 THOUGH the preceding rules might furnifh fufficient inftruc- 
 tions for putting walks with trees in perfpe&ive ; I have judged 
 it not amifs to add a particular rule which may render the method ftill 
 more eafy. 
 
 If only a fingle row of trees on each fide be required, there is no need 
 for making a plan of fquares, or chequers : what is directed in page 17, 
 will fuffice. 
 
 But where a number of walks are to be fhewn, I think it advifeable 
 to form a plan in occult lines, as already taught in page 31, and from 
 the diagonals of the little fquares, to erect perpendiculars, as is fhewn in 
 A B. If you defire to have the trees farther or lefs apart, increafe or 
 diminim the diftances of the fquares on the bafe line. 
 
 When you have given the ftem of the firft tree its proper height, as 
 A C, draw a line from C to the point of fight D, which ray C D is to 
 bound the ftems of all the other trees. The firft tree, A B, mews that 
 you may give what turn or form you pleafe to the body of it .be- 
 tween the two perpendiculars A B, for it mould not be drawn with the 
 ftraightnefs of a ruler. 
 
 The figure underneath is performed as that above, all the difference is, 
 that the fquares of the upper are direct, or in front j and thofe of the 
 under are viewed angle- wife : whence the meafures on the bafe line, in 
 the latter eafe, muft be all drawn to the points of diftance E and Fi v i 'Per- 
 pendiculars are to be raifed from the angles of the little fquares ; 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 point of fight ? Thus the 
 middle walk tends to the point G, which is the point of fight ; and the 
 others to the points E F, which are thofe of diftance. 
 
n 3 PRACTICAL 'Part .III. 
 
 To put Gardens in Perjpe&ive. 
 
 T N the doctrine of plans was (hewn, page 35, the manner of dimi- 
 I niftiing, or putting the plan of a garden in perfpecYive, by an eafy 
 rule 3 fuppofing that you have the plan thereof. But, as I always en- 
 deavour to avoid geometrical plans, by reafon it takes up too much time 
 to make them, I have added the prefent figures j whereby it appears, 
 that having made a chequer, or plan of fquares, 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 fquares every way j the reft ierving 
 for walks, as C C. If you would have compartments, or knots in the 
 beds, you are to ufe the little fq iares or divifions of each bed ; cutting 
 them, and forming them into the figure required ; as is fhewn in the 
 fquares of A and B; and thofe of the other fide, D and E. The pali- 
 fades and arbours are cut through the breadth of the walks. 
 
 To exhibit Beds with Borders^ Arbour s> and Groves. 
 
 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 muft be drawn to the point of fight. 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 fquare F and G, to the point 
 of fight I ; and go on with the reft, as abovefaid. 
 
 To exhibit arbours, raife upright pofts, or perpendiculars, O O, from 
 the angles of the fquares of the walk, and perform the reft as already 
 dire&ed for arches viewed fide-wife, in page 60. 
 
 The grove in the middle is performed by erecting perpendiculars from 
 all the angles of a chequer, &c. 
 
1 14 
 
 P R A C T I C A L 
 
 Part III, 
 
 c fo put Fortifications in Perfpetlive. 
 
 I Need not here repeat the method of diminifhing, or pitt- 
 ing in perfpe&ive, the plans of all forts of fortifications : 
 what has already been faid in page 39, is clear enough. 
 
 There is no more difficulty in raifing them than in th e 
 elevation of 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 ; 
 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. From 3 
 to 4 is the height of the parapet of the rampart', and from 
 5 to 1 , the depth of the ditch. 
 
Part III. 
 
ii5 PRACTICAL Part III. 
 
 To make Defigns in PerfpeEtive* 
 
 THERE is no matter fo excellent, but he makes defigns of the works he 
 would fucceed in. If this be ufual in mod arts, it is necefiary in this by 
 realon of the great number of points and lines to be ftridly obferved, and nicely 
 managed, without which nothing is to be done corre&ly, or in any wife pleafine 
 to a perfon that has tafte or fkill. 
 
 Since then there is a neceffity of making defigns, we are to look out for what 
 may be affiftant therein. And as every body knows that the length and tedious- 
 jiefs of fuch works lie in the drawing of parallels and perpendiculars, I have 
 fought, both in authors and in experience, for a method of doino- the fame as 
 expeditioufly as poffible. The refult is, that nothing of this kind°has appeared 
 to me worth the recommending, but the plate and fquare, which Viator has left 
 us in his writings j which are inftruments fuch people as have occafion to 
 fpend much time in defigning will find a deal of eafe and benefit from. 
 
 The figure gives a tolerable notion of the inftrument, and the method of ufin» 
 it, but it may be convenient to give fome defcription thereof. The plan A B 
 CD, then, is to be perfedly on the fquare, a foot and 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 meet of paper may be ftruck'on it. 
 
 The fquare E F 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 G H, ei^ht 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 ABCD, in which cafe the other 
 ruler E F, is certainly parallel to the bafe line, provided the board and ruler be 
 exactly formed. 
 
 When you go to work, faften the meet of paper I K L M, on the board 
 with four htde pieces of wax, N OPQj then may you draw lines from any 
 point, fecure that they are right. And for raifing perpendiculars, you have only 
 to lay the handle of the ruler, G H, on the fide G D, in which cafe E F will be 
 perpendicular to C D. 
 
 For myfelf, I find a wonderful eafe herefrom. The truth is, without" fuch a 
 contrivance, a man muft never be without the compafies in his hand. 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 fight. But this 
 is to run into a trouble greater than what you would avoid. The'common ruler 
 does every whit as well. 
 
 S R is a common ruler. T a pair of compafes. V another pair of compoffts 
 with a drawing pen therein ; for circular lines. * 
 Thefe are all the inftruments neceffary for making of defigns in perfpeclive. 
 
 6 
 
■ . PRACTICAL Part IIR 
 
 The Method of enlarging perfpettive Draughts out of Small into Great ; 
 and of reducing great Ones, into leffer, 
 
 AS^gnsare more eafily made of a frml!, than of a large fize, it is but reafonable they, 
 mould always be fo made. This has put me on giving a method of enlarging fmall defigns 
 on the canvas. & & 6 
 
 The method commonly ufed by the painters is to divide their little defign,. and the canvas they, 
 intend the large ones to be on, into an equal number of little fquares, and to transfer what is in the 
 lquares of the defign, into the correfpondent fquares of the canvas. This way Tome greatly approve of.. 
 
 ^ H r S f0 } l °r WS ano ' her ' * hich > in m y °P inion > eafier and furer. Provide a.fcale proportionate to 
 the little defign, and another proportionate to the canvas. To make a defign the firft thing to be de-' 
 
 A I' °iV Vh } C } 13 10 k tl ? e T eafures of a11 the P arts of che work - Thus > ^ the little de- 
 iign A, the fcale B C of five parts, which we may call feet, is the firft thing made. From thi, icale 
 are taken the horizon, the height and diftance of the trees, the breadths of the walks,. cifc. 
 
 To enlarge this defign the method is this. Confider whether or no the draught is to have its na- 
 
 S a V S L Whether ,'. w l . hen J* b ° ttom of the Panting is on the ground, the horizontal 
 line be the height of the eye, which is about five feec. Then,, of the five divifions between B and C,. 
 make a fcale of five feet F G, that thtw, having taken all the meafures and proportions in the fmall 
 one, you miy transfer them to the great one, after the following manner. 
 
 The two fcales th u S fix d> the m thing tQ be dong h> tQ ^ Jn ^ ^ ^ 
 tween the bafe line D and the horizon E, and to apply the compaffes thus opened, to the little fcale 
 
 S n ° tin S *hat number of parts it. includes, as here it does five. Take therefore five divifions 
 on the large fcale FG in your compafies, and fet them on each. fide the painting, or large defign 
 beginning at the bottom o the cloth H H, and ending in 1 1. From the points ft, ftrike? or (clrl 
 a line with a chalked or blackened packthread. This line I I, will mark the horiz ,n in the large 
 draught Then take the diftance or depth, K L, of the little defign, which gives the bottom of 
 the houfe, note how many divifions it includes, and take the fame number from the large fcale 
 and fet them on the edges of the canvas, H M, H M, which you muit ftrike with a pack thread for 
 the bottom of the houfe. Proceed to take the diftance N O, which includes two pares of the little 
 icale; accordingly two parts are to be taken on the great one, and fet off from H to P, which muft 
 be ftruck as before, for the depth of the fecond tree. Do the fame for all the parallels to the bale 
 line, as the other trees, windows, roofs, P Da,e 
 
 The method is the fame for the perpendiculars as for parallels only that they are to be ftruck 
 or fcored not from the fide, but from the top and bottom. Thus, for the two corners of the houfe 
 he .n erval between them and the fide of the draught being taken.in the comoafies, and found on' 
 the li tie fcale equivalent to feven divifions and a half, as many divifions muft be taken from the- 
 great fcale, by which you wdl have H S, T S, to be ftruck as before. And the like muft be re- 
 peated for all the other perpendiculars, as buildings, trees, palifades,. &rV. 
 
 To find the vifual rays, which are the lines- proceeding to the point of fight V, fallen a pack 
 thread to this point V, of the length, of the painting, and with tins ftnke or fcore all the rays very 
 exaftly Thus, for the two rays D X, which give the breadth of the trees in the httle defign 
 take the diftance DX, fet it one the little fcale B C, and take an equal number of divilions from 
 the great fcale, this will g.ve you H Y ; to which points H and Y, lines are to be flruck with the 
 pack-thread, from the point V. For the ray of the paiifades, take the diftance D Z, and fet it on 
 the little Icale, and take as many divifions from the large fcale j by this means you will have H + 
 which are to be ftruck from the point V, as before. f 
 
 Every thing in a perfpeaive ordinarily comes under one or other of thefe three forts of line* 
 parallels, perpendiculars, and vifual rays : and having ftiewn how to defcribe thefe with a good" 
 deal of eafe on the canvas, there remains nothing difficult in the procefs of enlarging a fmall defign. 
 
 As to the reducing ^/ J»jo liu/e, you have only to invert the procefs » that is, take the meafures. 
 firft on the large fcale, and dimimfli them proportionably on the fmall one. Thus, if the horizon 
 of the large defign were five divifions of the large fcale, five divifions of the fmall fcale were toLe 
 taken for the height of the horizon of the fmall: defign. And fo of the reft. 
 
ii7 PRACTICAL Part III. 
 
 Apparatus to the univerfal Method of the Sieur G. D. L. 
 
 AS feveral, for whofe benefit I intend this work, may not be fufficiently Ikilful to fee clearly into 
 . th » meth0d , of f he L Sieur G D - ^ the author, I believe will allow m to mak fit « 
 
 •eafy as I can, that they may be the better enabled to reap the benefit thereof. For this eafon I have 
 added the two following figures which will call to mind what has been already touched upon ia the 
 fecond third, fourth and fifth obfervations, pages ,6, 17. The defign wherJriTto tof^E&h 
 method, and accordingly in them is Ihewn how to take all the meafures on the bafe i e ' and M*a a 
 many rays as cut the diagonal C F, fo many fquares are formed in the depth of the draught which 
 fquares may be made of any magnitude at pleafure. ur<tugnc » vvnicn 
 
 1 N ° W ; *f t0 have £&f back to feek view the firft figure, where the bafe line is A B, the point of fieht 
 C, and the points of diftance E, F This bafe line 1 divide into twelve equal parts, whS I fCofe 
 equivalent each to one foot, from all thefe divifions draw lines, or rays, to the^o nt of fight where 
 of A and B are the lad Now, ,f a line mould be required that is funk a foot deep in the drauphT 
 draw a line from the firft divifion B D, to the point of diftance F ; and where thl lie D F cutsfhe 
 ray B G, will be the po.nt for a line to be drawn through, that is funk a foot. If another three feet 
 deep were reqmred, take three of thefe parts on the bafe line, and from the third draw a InTto the 
 pom of diftance F, and the point where it inters B G, will be the place for thaUine Confe 
 gently, if from C a line be drawn to F, the point where C F cuts B G will be a line fix feet deep 
 
 If of the other fix parts remaining of A C, you make twenty four, by dividing each into fk„r 
 yet account each divifion a foot, you will have twenty four feet between A a„| C? fo that" a Ime 
 Aouldberequ.r.de.ghteenfeetdeepinthe 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 inter flion with 
 A G would give a point for that line. If a line were required twenty four feet* deep, he wholeXe 
 
 £ PlineH fih H * ^ * ^7 t0 , E ' a " d fr0m H > " he ^ -here^ C E cut A G 
 
 the Ime H I muft be drawn, to appear twenty four feet deep in the draught. " 
 
 In perfpeaive, the line H I is equal to that of A C, that is, contains as many parts, or feet So that 
 if from I, a line be drawn to E, the interferon of I E with A G will give the line K L fnrr A! 
 
 wfth th e : P ' ap ^ fr ° m .n e POltt l U a ,ine b£ drawn t0 Che ^ cfiitanceE, bytes' imerfedfon 
 with the ray A G, you w.ll have a line twenty four feet farther off than the other. Y '"Election 
 
 ♦vA y tV 0uM r haVe a , 3ine . th:rty feet dee P' ff0m the P^>nt A reckon fix fmall divifions and from 
 the fixth draw a hne to the point of fight G, obferving where it cuts the line H I, as 1 Ire in the pS 
 M Then from M draw a line to the point of diftance E, and the Ime M E Will interfeft the Z 
 A G m the point N, through which the line'required muft be drawn. If a depth of forty feet were 
 required, from A fixteen divifions were to be reckoned, and the reft to be done as before. If fix y 
 feet be required, twelve divifions muft be taken, and from the twelfth a line be drawn to he point of 
 ight G, as far as the Ime K L, which will give the point O. Then from O, a line o be drawn to 
 the point of diftance, and its interferon 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 diftanrv .t 
 pleafure. It remains to (hew how the fame is found within or without the rays A Gar BG In order 
 to this, the Ime B C is to ferve as a fcale of fix feet, one of which we divide into twelve inches thaT 
 we may Jiave the half, third, fourth, &c. of a foot. Things thus difpofed, if it be equTred o fW 
 a point feventeeo feet diftant, and a foot and half within the ray AG, a line muft beTawn t 
 the feventeenth divifion of the bafe line, to the point of diftance E, and whereThe ray A G is inter^ 
 feQed theieby m P, the Ime P be drawn. Now fince a foot and half is required wkh in the ray 
 Inr R Is h 6 CXtent - 0n i the J ame . ]l » e N Q> my compaffes, and fet it off from P to R, which 
 a p i 15 !he P^\^ed If a point twenty nine feet diftant, and feven and a half within t£ ray 
 A G beared, a Ime muft be drawn from C to the point of diftance E, and through the P oL wVe'e 
 t cuts A o, a hne being drawn, gives twenty four feet. Then, from A taking five leffer pa«s a 
 line muft be drawn from their extent to the point of fight G, till it cut that line in the pointS [ and 
 from S a line is to be drawn to the point of diftance E, and from the point wherein it cuts the ray 
 
 77 r mUft b t dr / Wn ' And fmCe feven feet and an half are rs ^d beyond the ray A 
 hatfpace muft be let 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 PRACTICAL p art m. 
 
 An tmverfd method of per failing Perfpecli-ve without b*<vm<> the point of di fiance out of the paintin? 
 or Ground of the work ; made public by the Sieur G. D L. 
 
 IN this method a geometrical plan is required, or at lead a fcale of meafures both for the plan 
 ard the e evation, in order for the one or the other to be put in perfpedive. 
 . For an °. b ' ta or &b J eft » vve fo^ 1 tak « the author's own example, which is a'fquare cage-, terminat- 
 ing at top in a point, or a bailding with a pavilion roof. The meafures whereof ftall be given by a fcale 
 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 diltance the object is to appear at in the draught, as here the line a b 
 H ™\ wh *»* t0 L be the bale llRe > or boicom of the piece, and to be placed accordingly to the 
 lhe j ob J cd 15 10 b ~ viewed Then » < f ' roin the two extremes of the line a b, two indefinite lines 
 muft be drawn parallel to each other, as the line ^ and b g. On one of which lines, tsar, VM 
 are to dr.,w l. tlc parallels to the bafe line, proceeding from the angles of the plan, and by means 
 of the kale fee how f ir each angle of the plan is removed from this line a z% and maik the lame 
 on each line. 1 hen, from the place the painting is intended to be viewed from, which is here the 
 point c, five feet diftant from ,n, defcribe a perpendicular to a b, namely, the line et; and to this line 
 allow as many little parts of the !ca!e, as the fpedator is to be diftant to view the painting, namely 
 24 feet. At the extreme of which 24 feet, which is the point /, ered a little perpendicular of the 
 height of tne eye, namely, the line t J] equal to four feet and an hif. 
 
 The doth, wall or paper thus difpofed for putting the plan in perfpeclive, and making the e'evation 
 on the F lan, divide the bafe line A B, in o as many parts as a b in the plan is dividedinto, namely twelve 
 each accounted a foot; and over the points A and B, fet the height of the line //, namely four feet and a 
 half ; that Making in your compass four and a halfofthedivifionsof A B, fet them perpendicularly over 
 Cjfc points A B, by which means you will have the points E and F. Draw the line E F, therefore piralH 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 divihons diitantfrom b, you are to reckon as many parts from B ; and from the fifth 
 C, ered a perpendicular to A B, which cutting the horizon in the point G, gives the point of fight G, to 
 which ah the rays AG and B G, reprefenting the parallels of the plan ag and b g, muft be drawn. 
 
 As to the point of diltance, it will be the point F, and as the line <t is 24 feet long, 6 divisions 
 muft be taken from the line A B, namely, from A to D, and each fubdivided into 4 : which 24 parts 
 are to ferve as a fcale for the depths ordiftances, being fufficent for the fame; though they were infinite 
 And the 6 parts remaining between B and D, will be a fcale for the feet, according as the lines drawn 
 from the points found for the plan, fhall cut the rays drawn to the point of fight G. For as this 
 icale is a pyramid, whereof B D is the bafe ; 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 fcale of diftances, the points of the plan are found, and by the fcale of meafures the lengths 
 of the lines both of the plan and elevation. 
 
 Now to put the plan in perfpedive, all the meafures of the geometrical plan muft be obferved. The 
 firft angle of the plan r m is 17 feet diftant from the point a, on the line a g. 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 point m 
 is within the ray a g, by a foot and an half, therefore, on the fide B D of the line R, muft a divifion 
 and an half be take n, 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 /, which is 26 feet diftant from the point a, a line mult be 
 drawn from the point D, which is 26 feet fom A, to the point F ; and where the ray A G is inter- 
 ledted tnereby, namely, in the point jy, a parallel is to be drawn. Now as the point y is not remote enough 
 by 2 feet, a line muft be drawn from the fecond divifion of the fcale to the point G, and where this 
 ray cuts the parallel y, namely in the point Q, the line QJ 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 fide B D of the 
 fame line H, muft the div;fions for 14 feet and an half be taken, namely, from the point H to L 
 
 Fqr the point k, which is 29 feet diftant from A, a line muft be drawn from the fifth part of the 
 fcale AD, to the point G, and where this ray interfeds the parallel y, namely in the Doint O, the line OF 
 muft oe drawn, which gives the po nt N on the line A G. Then from N draw a parallel, the fide where- 
 of B D, 7 feet and an half, muft betaken, to be fet off without the ray A G, namely, from N to K 
 
 For the point i, which is 38 feet from a, take 14 divifions on the fcale A D, 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 m T, which is 38 feet from the point A, inafmuch as the parallel y is 24 ; 
 to which, 14 being added, gives the whole 38. And fince the angle / is 4 feet and an half within the 
 ray A G, that extent muft be fet on the fide D B of the parallel T, namely, from T to I 
 
 To fcTrm the plan, tbofe four points MLKI muft be connected by right lines, and 'perpendiculars 
 ceded from their angle-, as My/, hff, K/r, and \fp x each of which will be feventeen feet as is 
 expreffed 111 tne plan of the line X. Then, from the extremes of thefe perpendiculars, draw two dia- 
 gonals./? jp nndj.fr, which mterfeding in Z, from the fame point Z ereft a perpendicular Z JE 
 tmteen feet and an half. Laftly, drawing lines from all the four angles/?, f t fp and ft; to the poinJ 
 A, the cage will be formed in perfpedive. ff you would have it funk a foot under ground, add a 
 foot underneath, each point of the plan, and conned them by lines. 
 
PRACTICAL 
 
 Part III; 
 
 To give any precife dijiance required^ without removing the point of fight 
 
 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 figures are put two points of diftance, the one 
 fix, the other twelve feet, which have an eafy ratio to each other ; inafmuch as the fix parts being 
 each divided into two, you have twelve. 
 
 Suppofe then the line A B divided into twelve- parts, and from each divifion lines drawn to the 
 point of fight C ; take half thefe divifions A D, and from D to the point E, which is the diftance of 
 fix feet, draw D E. It is certain its interferon with the ray A C will give the diminution of the 
 fquares viewed at fix feet diftance. And if from D a 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 fquares, viewed at 
 twelve feet. And if the diminution of twelve fquares, viewed at twelve feet diftance were 
 required, from the point B, which is the whole bafe line, a line muft be drawn to F, and its in- 
 terferon with the ray A C, in the point H, wilf give the thing required. Or from I a line I F 
 is to be drawn, which will give the fame point H, the line H K, in each cafe, being the depth of 
 twelve fquares, viewed at twelve feet diftance. Hence we obferve, that twelve fquares, viewed at 
 twelve feet diftance, meet in the fame line H K with fix fquares viewed fix feet off, and that all the 
 lines of the fix fquares, given by the interfe&ion of the diagonal D G, have a relation two by two 
 to thofe given by the diagonal D F. The reafon why the diagonal D F gives two lines for one of 
 thofe D G, is, that the diftance is double. If it were triple, it would give three, and four if qua- 
 druple. Now, to find the fame interferons, and the fame number of fquares on the fide 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 fight C, and drawing parallels to the bafe 
 line through all the interfeftions the diagonals make with all thofe rays, you will have twelve fquares 
 depth in the fame line as if the diftance were twelve feet, though in reality G be but fix. The 
 reafon is, that in multiplying the rays you multiply the fquares, and multiplying the fquares you 
 remove the diftance farther. Such is the reafon why having made twelve parts of the fix that were 
 between B D, there are procured twelve fquares, 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 interfetts 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 the fame depth and diftance on the fide M N, as on the fide A D, which gives the line H K * 
 to fhew, that if a line were drawn from the fifth part, as QjG, 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 QG 
 would fink too much ; even though 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, 15 V. the diftance 5 may 
 ferve for 10, 15, 20, 25, 30, &c. and the diftance 8 for 16, 24, 32, 40, 48, CsV. In this way you 
 cannot fail ; for fuppofing the point of diftance cannot be nearer the point of fight than G is to C 
 it follows, that if G be fix, feven, eight, or ten feet from C, that then half the bafe line will have 
 the fame number, which p to be divided proportionally to the diftance intended. For inftance, if 
 there be eight feet from N to L, and I require a diftance of thirty two feet, without moving G out 
 of its plae ; I divide each of the eight parts, or halves of the bafe lines, as L N, into four, accord- 
 ingly, four times eight makes thirty-two rays. So that the diminutions of the fquares will be thirty 
 two feet diftant. 
 
 Thefe little divifions do none of them remain after the painting is finifhed, only the principal 
 divifions of feet, which are drawn to the point of fight, and the diminutions, that is, the parallels 
 to the bafe line, which ftill ftand. 
 
1 20 
 
 PRACTICAL 
 
 Part III. 
 
 A very curious Method of drawing all Perfpe&ives in the mqft natu- 
 ral Manner \ without obferving the rules. 
 
 TTA VING given you all the neceffary rules for drawing perfpectives in the exacteft 
 _£~j[ manner, I have thought fit to add this and the following method of drawing very 
 correctly after nature, without being tied to the procefs of any one rule- 
 Many lovers of painting, and who entertain themfelves in drawing after nature, would 
 willingly be excufed the trouble of opening the companies, or taking up-the ruler, and in 
 this method neither the one nor the other are required j and yet the proportions and diftances 
 of objects will be exactly preferved. 
 
 Before I come to the method of performance, I muft defcribe the inftrument ufed there- 
 in. The principal requifite is a large piece of fine clear glafs, fitted in a wooden frame, 
 exprefled 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, that is, about a foot broad, as (hewn in B C, the cheeks 
 are groved to receive the frame A. In the middle of the board 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 very thin, being made 
 of tin, or the like, and having a little aperture about the fize of a pea in the middle. The 
 whole is reprefented put together in G. 
 
 The figure of the inftrument fhews the application, yet I (hall defcribe the method of 
 proceeding. Place the inftrument G before the object you would draw, look through the 
 little hole or fight F, and if you fee all the propofed objects reprefented on the glafs, the 
 inftrument is rightly fixed, otherwife bring the fight nearear the glafs, till you fee the whole 
 of what is required. The piece thus rectified, draw on the glafs every thing that you fee 
 thereon through the hole F ; which has the fame effect here, as the point of fight in the 
 other methods. And it is certain, every thing thus drawn on the glafs, the eye being fixed 
 to th,e little hole, will be according to the ftrict rules of perfpective. 
 
 It is well known how to take off" or copy what is thus defigned on the glafs. One me- 
 thod is to draw on the glafs with pen and ink, then wetting the backfide of the glafs a little, 
 and laying a moift Iheet of paper on the fide that has the defign, rub or prefs the paper 
 gently thereon with the hand, and the whole draught will be imprefled or transferred from 
 the glafs upon the paper. 
 
 Some advife to make ufe of a hair pencil and colours* but every body is left to his 
 own difcretion. It is enough to know the method in general. The draught of a palace 
 is as eafily taken this way as a landfkip, and a church as a houfe or chamber. All re- 
 quired in any of them being to pitch on a fituation where the whole object intended to be 
 reprefented, may be feen, and to bring the fight to a proper nearnefs to the glafs. 
 
 A painter may ufe the fame method for the drawing of figures or poftures, from nature, 
 ftatues, relievo's, and every thing elfe. It being certain, that a little practice will render 
 the method exceeding eafy. 
 
Part III. PERSPECTIVE. 1 20 
 
 12,0 
 
121 
 
 PRACTICAL 
 
 Part III. 
 
 Another curious Manner of praBifing Perfpetlive f with- 
 out under/landing the Rules. 
 
 TH I S method is as curious as the former, and fome even prefer it, 
 becaufe a double draught is required in that, one on the glafs^ 
 and a fecond copied or imprinted from it. Whereas in the prefent me- 
 thod only a fingle draught is made, and that as exactly as the former. 
 
 I (hall not defcribe the ftructure of this inftrument, 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 fquares by fine 
 threads, drawn at equal diftances from each fide of the frame, acrofs 
 each other, forming what we call a reticula or lettice. As to the num- 
 ber of fquares, it is left to difcretion. But they muft not be too lar<*e 
 that you may work the more exactly, nor too fmall for fear of being 
 confufed. 
 
 For the practice, place the inftrument H in fuch manner as that you 
 may fee all the objects you intend to draw, through the hole of the fight 
 % If your draught is to be larger than the compafs of the frame or 
 reticula, fquares muft be made on the cloth or paper, larger than thofe 
 of the frame. If your drawing be intended fmaller than the frame, 
 make the fquares lefs. But in all cafes make the fame number of fquares 
 on your paper or cloth, as you fee in the frame when you look through 
 the fight I. Then, transferring proportionally from the fquares in the 
 one, to the correfponding fquares in the other, the perfpective will be 
 as juft as if you had gone by the ftrict rules, and ufed the compafs and 
 ruler. 
 
 The two figures (hew how the inftrument H is to be placed, in order 
 to draw on a table. The expedient is of excellent ufe in painting, and 
 ferves to draw very exactly any perfpective from nature, or to copy from 
 paintings. 
 
 Some people will be apt to urge, that the method is not new ; there 
 being few painters but what know how to enlarge or diminifti paintings 
 by means of the chequer, or fquares. All this I allow, but muft take 
 the liberty to fay, that I do not know of any that ever yet ufed the fight- 
 hole, which, however, is of very great advantage to the artift. 
 
E A S U R E S 
 
 AND 
 
 ROPORTIONS 
 
 O F 
 
 I G U R E S 
 
 FOR 
 
 Perfpeaive Draughts, Paintings, and 
 
 Relievos. 
 
 PART IV. 
 
 N n 
 
122 
 
 PRACTICAL 
 
 Part IV. 
 
 Figures in perfpeftfoe. 
 
 HAVING ftiewn how to draw all kind of views in perfpective, I proceed to give directions 
 for adjufting the height of figures. 
 
 I would here make one obfervation concerning the altitudes of figures. Thofe which are placed 
 at the end of a gallery, hall, or in a garden at the termination of a walk, with a defign to deceive 
 the eye, and appear at a diftance to be real life, are beft reprefented in attitudes which do not fup« 
 pofe a progreffive motion. Whereas thofe figures which are introdaced as part of the compofition 
 of a picture, admit of every kind of attitude to the defign of the piece. 
 
 ■p^ w ' ■ • 
 
 The number of horizons which our painters frequently introduce in the fame piece, leads them 
 into innumerable faults, in not being able to give the figures their proper heights, proportionate to 
 their horizons. I fhall therefore here give a fingle rule, which may prevent their failing, be the 
 horizon what it will. 
 
 For Figures that have the Eye in the Horizon* 
 
 IN perfpective draughts placed at the end of a gallery, hall, or walk, to deceive the eye the 
 horizon Ihould always be its natural height, that is, five feet, which is that of an ordinary fize. 
 
 And figures intended to appear there the fize of life muft have the eye in the horizon. For, hav- 
 ing the eyes in the fame horizon with ourfelves, they will be of our own height. This might pafs 
 as fufficient inftruclion ; but to make the point more clear and obvious, I lhall inftance in thefe 
 three figures, inftead of twenty others which might be brought. 
 
 The firft figure A is the natural height, and has its eye 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 
 appear of the fame height with the former. If you require a third at C, let his eye likewife be in 
 the horizon, and he will be the fame height with the reft, in appearance. In effect, though there 
 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 proportion to the 
 large figures, according to the discretion of the painter. 
 
 For Figures that have a low Horizon, 
 
 IN painting for halls, which are ufually hung pretty high, the horizon muft be lower, to bring 
 it as near the eye as poflible. 
 
 Now, to give each figure its juft height and proportion in whatever part of the painting it be, 
 fome one muft be drawn of any height at pleafure, in any part of the piece, as 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 he/id and feet of this figure D F, to a point in the intended horizon, as E, 
 and within this triangle D E F, will be found the heights of all the reft. Thus, for example, if 
 the height of a figure injhe point G be required, from that point G draw a parallel to the bafe G H, 
 till it interfedb the line or ray F E in the point H, and the perpendicular H I gives the height of the 
 figure, which is to be taken in the compafles, and fet off in the point G. If another be required 
 1 in the point K, the fame operation is to be repeated, and we fhall have the perpendicular M N for 
 the juft height. Andfo of whatever number of figures you pleafe. 
 
N n -a 
 
! 2 3 PRACTICAL Part IV. 
 
 To exhibit Figures that have a high Horizon. 
 
 WHEN the horizon is high, as it necefiarily is when objects are viewed 
 from an eminence, the fame rule already laid down for the remote figures 
 in a low horizon, muft be obferved * as in that cafe, the hindermoft figures- 
 are placed higheft, and are moft diminiftied, fo in the prefent cafe, their diftance 
 is exprefied by raifing them further off from the bale line* and diminilhing them 
 in proportion to their diftance- 
 
 Having drawn the fkft figure AB, draw a Fine from the top of its head* 
 and another from 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 tri- 
 angle A CB. 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 ray 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 a figure in the point D. 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 » 
 
 For Figures that have their feet m the horizon, 
 
 IT is but rare that figures are made above the horizon,, but where there is a 
 necefiity for it, thole intended to appear the foremoft muft be made the 
 laro-eft; 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 
 fio-ure K L is here the biggeft and the neareft, and M. N the remoteft. All the 
 fecret here, is the painter's finifhing the front figures more than thofe behind, 
 and ftill the farther off they are, the fainter and lefs perfect muft they be. 
 
 The rule for thefe figures, and for thofe which have their eyes in the hori- 
 zon, is no other than reducing their height, and making them fmaller and 
 fainter, as they are thrown farther behind,. 
 
PRACTICAL 
 
 Part 1^ 
 
 To exhibit Figures raifed a fmall Matter above the Plan. 
 
 THERE are fome who plead, that obje&s raifed above 
 the ground are more diminiflied than if they were 
 on the plan ; and, of confequence, a figure mounted four 
 or five feet mould therefore be fmaller than if placed on the 
 earth. The rule is good for figures at a great height, as 
 mall be (hewn in its place : but an elevation fo fmall as that 
 juft mentioned, can only make an infenfible diminution. 
 For fuppofing fuch an object or figure may be feen at one 
 fingle view, that is, without railing the eye, it muft: be the 
 fame height when fo inconfiderably raifed, as when ftanding 
 on the level ground. Thus, the figure A muft be the fame 
 height as B, and the figure C as D, and F equal to G. 
 
 The fame reafon holds for figures a little below the plan, 
 which are to be reprefented of the fame height as thofe above 
 it, as as fhewn in figure E, which is equal in height with 
 H ; and I is as big as K. Thefe two examples may ferve 
 for all cafes, where the variation of the figures is as fmall 
 as in thefe inftances, the diminution of figures occafione4 by 
 high elevations will be the fubjecl: of future inftruclions. 
 
PRACTICAL 
 
 Part IV. 
 
 1he Poftures of Figures in Perfpe&ive, 
 
 THERE mud be a judicious choice in the poftures, or attitudes of figures, 
 when intended to deceive the eye. For all of them are not proper, as I 
 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, fitting j the fecond is reading an advertifement 
 polled on the wall •, the third plays on a lute ; the fourth is afleep ; the fifth is 
 lolling againd the banifters; the group of two figures marked 6, are looking on 
 a draught on paper-, the remoter, marked 7, are in earned difcourfe. One 
 might add others, playing, fpeaking, or difcourfing at table, writing, praying, 
 &c. In effect, you have a choice of numberlefs poftures, provided they be 
 fuch as that a man may continue in them for a time. But never ufe fuch as are 
 much in action ; for you can never be deceived in feeing a leg or an arm in the 
 air, or a perfon running without (hiding his place. 
 
 ©©®®®®@@@®@@®@®®@®®®®@@®®®®@®®® 
 
 Beasts and Birds in PerfpeElive. 
 
 THE 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 from 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 paral- 
 lel 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 fize. 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 H I 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 active, as a dog deeping or gnawing a bone, a cat 
 watching a moufe, a parrot, 65V. 
 
 2 
 
126 
 
 PRACTICAL 
 
 Part V, 
 
 To find the Height of remote Figures •, whereof the firjl 
 is on a Mountain near the Eye. 
 
 IT gives great fatisfaction to the mind, when a perfon knows what he does to 
 be right: on which account, no doubt, the reader will be pleafed to have 
 the following rule, with which but few practitioners are acquainted. 
 
 When figures are to be made, determine the hight, that is, the fpace of the 
 ground you would have it raifed ; and at that diftance put another figure un- 
 derneath, of the fame height as the firft ; and from the feet and head thereof 
 draw lines to the horizon ; by which yon will have the height of the other 
 figures in the champain. To explain my felf: 
 
 The figure A, for example, which is at the top of a mountain, is five feet 
 high, which is the natural height-, and I fuppofe the mountain twenty-five feet 
 high : If now a man be raifed twenty feet, as is the piece in the middle, where- 
 on the fpe&ator is mounted (who himfelf is fuppofed five feet high) the hori- 
 zon will be twenty-five feet as well as the mountain ; and confequently will 
 reach the top of the mountain : as is exprelfed in the figure. 
 
 Now to find the height of the little people in the champain, make a figure 
 twenty-five feet 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 in the 
 horizon, as the point O •, and between thofe two lines, B and C, drawn to O, 
 take the height of the little figures, in the manner 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 raifed, 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 compaffes, and fet off in the points G and H. The fame you are to do 
 for any other figures, ftill diminilhing, till at length you come to a mere 
 point. 
 
 This is all I have to fay as to the meafures of figures in perfpective. But 
 as I have ingaged myfelf to give all the meafures of this kind, the following 
 rules come in my way, though they have no ftrict relation to that art. 
 
O o ?. 
 
1 2 7 PRACTICAL Part V. 
 
 To give the natural or any other Height to Figures much elevated. 
 
 TO omit nothing relating to the heights of figures, I add the two following rules. The firft 
 given by Albert Purer, Seriio, and others, for adjufting the fize of letters in infcriptions fo 
 as they may appear of the feme fize as others below. Which rule may be applied to find the 
 meafures and magnitude of figures placed at different heights to appear equal when viewed by 
 the fpedlator placed at any height. 
 
 Thus in B there is a man five feet high, and fifty diftant from the tower A, viewing the firft figure 
 C, which there appears of thetiatural fize ; and thirty feet higher another figure is to be placed, 
 which (hall appear of the fame fize as the other when viewed from the fame place. Now, to find 
 its dimenfions defcribe a quadrant of a circle, or a leffer arch, on a paper to be placed before 
 the eye ; then looking at 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 obCerve what point it gives in the quadrant, namely G. And from this point G fet off 
 the fame diftance or angle, as that of the figure C, that is to fay, E F, which being removed to G 
 gives G H. Then looking through the point H, note what part of the perpendicular raifed from 
 D is cut thereby, namely, the point I ; then will the interval D I, be the height required for the 
 figure to be placed there. If you would have another ft ill higher, the fame operation muft be re- 
 peated, and they will all appear of the natural bignefs to the fpe&ator, B, 
 
 If you require the reafon thereof, you muft recolleft the principles already laid down, or recur to 
 them again ; and you will find that all objetts viewed under equal angles appear equal. Now it is cer- 
 tain, that the angle G H is equal toEF; confequently the figure D I mufit appear equal to the figure C, 
 
 To find in what Proportion equal Figures grow lefs to the Eye, when placed 
 
 over one another, 
 
 THE fpe&ator K having a quadrant or part of a circle, like that of the former fpeclator B, 
 looks towards the firft figure M of the tower L ; which there appears of the natural fize. 
 Then taking its meafure from head to foot he marks the diftance thereof on the quadrant, namely, 
 N O. After thi?, 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 Q_R. And if there be others ftill higher, he fhould 
 t >ke 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 compaffes, and you will find that the higheft gives the fmalleft angle, and of confequence 
 appears the fmalleft to the eyt ; the figme P only appears half the fize of the figure M, though 
 in reality both figures are of equal magnitude. If you afk the reafon of this different appearance, 
 I anfwer that the angle of the higheft figure P, is only half that of the lower figure M ; as you fee 
 that QR is only half of N O, or nearly fo. 
 
 By the knowledge of this rule 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 appear to be only half of M, we may 
 fecurely fay, that to make P appear as big as M, it muft be twice its prefent magnitude. 
 The fame may be faid of the upper figure, where D, which is double to C, appears of the fa-ne 
 fize to a fpeclator in B. It might be added, that if the figure C was removed to D it would only 
 appear half as big ; fo that one rule is the reverfe of the other. Boih the firft and fecond rules are 
 btft put in practice by the little foot, as the figures hitherto have been ; by which we come to tkc 
 difference and proportion of figures as fec»rely as if they were taken from the life by a quadrant. 
 
 2 
 
128 
 
 PRACTICAL 
 
 Part V. 
 
 Meafures for elevated Figures* 
 
 F 
 
 ROM what hzsbeen faid concerning the diminution of figures when placed on high, we are 
 to take our meafures in proportion, for fuch as are to be raifed in paintings, whether 'they be 
 placed on mountains, the tops of houfes, or above the clouds in the air. The t*o rules I fhall now 
 give, will render the method extremely eafy. 
 
 For the firft. Suppofe the man A to be fix feet ; which height fet off feveral times on the per- 
 pendicular B, and from the feveral divifions 6, 12, 18, t3V. draw lines to the head of the figure 
 A. Then fetting one leg of the compafles in the point A, with the other defcribe the arch C D 
 and the interferons that arch makes with the rays, are the meafures to be given the figures at 
 thofe feveral heights or perpendiculars B. Thus, if you would have a figure appear forty two feet 
 high ; take E D, which cuts the two lad rays, and fet it off to F, which is forty two feet above 
 the bafe line AB. If another be required thirty feet high, the diftance G H muft be taken 
 which cuts the ray 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 
 ipedlator and the objeft, namely here, thirty feet, or thereabout. 
 
 For the fecond rule. Inftead of the perpendicular B ufed in the firft figure, I here put the divi. 
 fion 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 fight K. Thus between the two rays I K, and 6 K, we have the meafures of fix feet 
 which is the height to be given the figures. Tnen from all the other divifions 12, 18, 24, 30, £jf/ 
 draw lines to the point of diftance L, and in the interfe&ions 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 
 iigures of equal magnitude, but at different diftances. Which may be proved by comparing the 
 meafures of the firft method with thofe of the fecond. 
 
 If it be afked how much each figure is diminilhed from the firft, which is fix feet high, you need 
 only to take the height of the figure required in your compafles, and fet it off on the little fcale M, 
 and the queftion is folved. Thus having taken the height of the figure B, and fet it on the fcaleM' 
 it gives four feet ; which fhew-s that a figure fix feet high, raifed thirty feet, will only appear to 
 be four feet. The heights or diminutions of the reft are found by the fame operation ; provided the 
 diftance be the fame with that of thefe. If the diftance be changed the procefs muft be begun anew. 
 
 The figures V, X, Y, placed in the clouds are of the fame height and proportion as the figures 
 in the uppermoft draught. They are only here added to {hew, that though the method be different 
 the effects are the fame. 
 
 What has been faid as to the diminutions of figures elevated over the bafe line A B in the firft 
 method, and I T in the fecond, muft be obferved in proportion between thofe figures which are 
 funk farther behind. Thofe of them which are placed on an elevation muft have the fame relative 
 magnitude according to their heighth with the figure on the ground, on the fame line with them, 
 as F and P have to A. Thus, in the fecond rule, if over-againft the laft figure N, another figure 
 C, be placed on a tower foity eight feet high, its magnitude muft be in the fame proportion to N, 
 as the figure at N has to that at I. And inafmuch as the figure at N contains only two and a half 
 of the fix parts which I contains, this at 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 feet 
 high oppofke the figure I take two parts and a half of the figure Q_ for the height of the 
 figure. If another were required in S, which is thirty feet high, in the fame tower, he muft take 
 four of the fix parts of the figure G^. that is, four feet j as already mentioned in the firft method 
 between the rays G and H. 
 
 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 in all cafes ; and he would render them fo familiar, that in a little 
 time he would tell you offhand, that if you are thirty-five feet diftant, and the figure fix feet, or fix 
 parts high, when on the ground, another, that fhall be of the fame fize, will only appear five and 
 a half when raifed to the height of twelve feet ; only five, if raifed eighteen feet ; only four and 
 a half, if twenty four feet ; only four, if thirty; only three, if thirty-fix; and only two and a 
 half, if forty-two : and fo on, by fix and fix, to any number at pleafure. 
 
METHODS 
 
 Of finding according to the Laws of perspective, the 
 
 NATURAL SUA DO W S 
 
 O F 
 
 » 
 
 OBJECTS 
 
 Both by the 
 
 Sun, Candle, Torch, and Lamp. 
 
 PART V. 
 
129 
 
 PRACTICAL 
 
 Part V. 
 
 The Origin ^/Shadows, with the Laws of their Projec~ 
 tion from opaque Bodies. 
 
 TO define a natural Jhadow y we do not call it an abfolute privation 
 of all light, for this would be to form a perfect obfcurity, where- 
 in objects would be no more feen than their fhadows : but by Jhadow is 
 meant diminution of light, occasioned by the interpofition of fome opaque 
 body, which receiving and intercepting the light that mould be caft on 
 the plane, gives there its own fhadow. For the rays of light diverge, and 
 diffufe themfelves on every thing not hid therefrom, particularly on every 
 plain and fmooth fubftance, but where there happens the leaft elevation, 
 a fhadow is produced, which exhibits the figure of the illumined part on 
 the plan. 
 
 The diverfity of luminaries occafions a difference of madows j for if the 
 body that illumines be larger than the body illumined, the fhadow will 
 be lefs than the body. If they be equal, the madow will be equal to 
 the illumined, and if the luminary be lefs than the object, the fhadow 
 will be continually enlarging as it goes farther off. 
 
 The better to comprehend this, I here add three figures, which may 
 ferve as a foundation for all the rules to be advanced hereafter. 
 
 The firft mews, that the luminous body A B, being larger than the 
 illumined fphere CD, enlightens more than half the object, and gives 
 a pointed or conical fhadow, whereof the luminary is the bafe. This 
 truth is evinced in an eclipfe of the moon, which is rarely quite covered 
 by the fhadow of the earth, though the latter be above forty times bigger 
 than the former. The reafon is, that the fun, which is the luminary, 
 is one hundred times bigger in diameter than the earth, which therefore 
 it illumines more than half, and of confequence makes its fhadow ter- 
 minate in a point. 
 
 In the fecond figure, the luminous body F G is equal to the illumined 
 fphere H I, therefore half of the object is enlightened, and its fhadow 
 projected parallel, HIKL, and it will be propagated in that form to 
 whatever diftance the luminary is capable of acting. 
 
 The third figure fhews, that the luminary or light M, being lefs than 
 the illumined N O, that object is not half enlightened. And of con- 
 fequence the fhadow NOP (^enlarging as it recedes farther from the 
 object, makes a pyramid, whereof the luminary is the point or vertex. 
 
«'-3° PRACTICAL Part V. 
 
 Of the Difference of Shadows. 
 
 FROM what has been obferved in the preceding page we draw this 
 conclufion, that the fame object may project fhadows of divers 
 forms, though flill illumined on the fame fide; the fun giving one form, 
 the torch another, and the day-light no precife form at all. 
 
 The Sun always makes the Jhadow of breadth equal to the opaque ohjett> 
 that is, projects it parallel- wife, as in the firft figure. 
 
 How this method is to be put in practice, and every object have its 
 natural fhadow, mail be fhewn hereafter. It is certainly of confequence 
 to all painters, engravers, &c. to obferve thefe rules precifely, and not 
 indifferently to ufe the fame method for fhadows produced by the fun 
 and by artificial luminaries, as is too frequently done. 
 
 The fhadow produced by a torch or flambeau is not projected in paral- 
 lels, but in rays proceeding from a center ; whence the fhadow is always 
 bigger than the opaque body, and grows bigger as it recedes the farther, 
 this is mewn in the fecond figure, where the fhadow is larger than in 
 the firft, though the cube of the one and the other be of equal breadth 
 and height. It appears, therefore, agrofsabufe, to reprefent the fhadow 
 of a torch like that of the fun, and the fhadow of the fun like that of 
 a candle, when the difference is fo confiderable. 
 
 There is a third kind of Jhadow, neither produced by the fun nor a 
 torch, but only a fine clear day, which wanting flrength 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 conducts it at 
 difcretion. 
 
 All thefe fhadows, both thofe of the fun, of the torch, and of the 
 day-light, muft appear darker than the parts of objects not illumined. 
 Thus A is lefs dark than B, by reafon A receives the reflection of the 
 brightnefs around it, and B has no reflection but from A, which itfelf 
 is in obfcurity. It muft be obferved by the way, that the part of the 
 fhadow mod remote from the object is flill darker than that neareft it ; 
 as G is darker than H, by reafon A cannot communicate the little reflexion 
 it receives, as far as G, though it does to H. 
 
PRACTICAL 
 
 Part V, 
 
 To find the Form of the Shadows. 
 
 IT maybe remembered, at the entrance^of this work, perspective 
 was defined the art of reprefenting objects which are on the ground 
 or horizontal plane, upon a plane perpendicular to the horizon. But 
 in the bufinefs of fhadows it is quite the reverfe, fince we there conceive 
 a body raifed over the plan, which being illumined, cafts its own fhadow 
 on the plan ; as the body A gives a fhadow B, on the plan. 
 
 To produce a fhadow, two things are fuppofed, namely, light and an 
 opaque body. Light, though quite contrary to fhadow, gives it its being, 
 as the opaque objed gives its f >rm and figure. What we have here to con- 
 Jider is thejhadows, the reader has been already injlrutted in what relates to 
 putting the bodies in perfpeclive. 
 
 To conceive the nature of fhadows more clearly, and render the prac- 
 tice more eafy, it muft be obferved, there are two points to be made ufe 
 of. One of them is the foot of the light, which is always taken on the 
 plan the object is placed upon ; the other is the luminary. The rule being 
 common to the fun, torch, or any other light, with this difference, that 
 the fun projects the fhadow in parallels, and the torch in rays, from the 
 iame center. I begin with the fhadow produced by the torch, as leading 
 to a more eafy understanding of that by the fun. 
 
 Suppofe then, for example, it is defired to have the fhadow of the 
 cube A here reprefented in B, lines n^uft be drawn from O, the foot of 
 the luminary, through all the angles of the plan of the cube, as here 
 O D, O E, O F, O G. Then other lines are to be drawn from the point 
 of the light of the torch C, through ajl the raifed angles, till they in- 
 terfect the lines from the point O. 'jThus having drawn a line from O 
 through the angle D, another muft be drawn from C through the raifed 
 angle, interfering the former in H, which point H will be the fhadow 
 of that angle. And if from the fame point C, the fame be done through 
 all the raifed angles, the lines of the plan will be cut in the points HIKL, 
 thefe points being connected together by right lines, you will have the 
 fhadow of the cube, as is fhewn in the uppermofl figure of interferon, 
 and more diftinctly in that below. 2 
 
J 32 PRACTICAL p ar t V, 
 
 Shadows from the Sun. 
 
 THE fun that magnificent luminary, being va% larger than the 
 terreftnal globe, as has been already intimated, muft give the 
 fliaddw of that fphere pointed, by reafon it always illumines more than 
 half thereof. 
 
 In confequence of this demonftration we might conclude, that all the 
 fun s rtiadows muft be lefs than the bodies that project them, and dimi- 
 mQi more and more as they recede farther. Now this would be true 
 were there any conceivable relation of magnitude between the illumined 
 body and the illuminer; but as all objects on the earth are fo fmall, either 
 in companfon of that ftar or of the earth, the diminution of their madows 
 is imperceptible to the eye, which fees them always of equal breadth to 
 the body that forms them. On this account all the fhadows caufed by 
 the iun are made in parallels, as is fhewn in page 130. 
 
 From the whole it appears, that to find the fhadow of any body what- 
 ever oppofed to the fun, a line muft be drawn from that luminary per- 
 pendicu ar to the place where, according to former directions, the foot 
 of the light is to be taken, and from this point an occult line is to be 
 drawn through one of the angles of the plan of the object, and another 
 from the fun through the raifed angle; the interferon of the two lines 
 will expreis how far the fhadow is to go. The other line muft be drawn 
 parallel hereto. 
 
 For example, to find the fhadow of the cube A, the fun being in B. 
 From the bottom of the fun C, which is, as it were, the foot of the 
 light, draw a line through one of the angles of the plan, as C D. Then 
 rom the other angle E, draw a parallel to this line. The breadth of 
 he fhadow being thus finimed, to find the extreme thereof, draw a line 
 from the fun B, through the raifed angle F, cutting the line CD in G. 
 Then drawing a' parallel to this line through the angle H, it will cut the 
 line h in the point I 5 thefe two points G and I being connected by a 
 ltrait line compleats the fhadow of the cube D G I. 
 
 If you defire to have the fhadows caft forward, or any other way, you 
 have only to determine the place of the fun, and the point beneath 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 
 repeated. The figure mews the reft. 
 
«33 
 
 PRACTICAL 
 
 Part V. 
 
 The Shadows produced hy the Sun are equal in all Ohje&s of 
 
 fame Height \ though at a Difance from each other. 
 
 I 
 
 EXPERIENCE teaches us, that feveral elevations of the fame 
 height, removed to a diftance from each other, do yet project equal 
 Shadows at the fame time. I fay in the fame time, for the fhadows are 
 lengthening and ftibrtning, in proportion as the fun comes nearer or re- 
 cedes farther off; one or other of which he is continually doing. 
 
 For this reafon, when the fhadow of an object is to be produced, you 
 muft determine the place of the fun, and the point underneath which I 
 call the foot of the luminary, and draw two occult lines from them, for 
 thre extremity of the fhadow; as here the palifade A gives the extreme 
 of its fhadow in B. And if from this point B, you draw a line to the 
 point of fight C, this line B C will be the fhadow of the palifade D, 
 as well as of that of A, and of all others of equal height in the fame 
 line to the very point of fight. In effect, it muft be held for a certain 
 maxim, that fhadows always retain the fame point of fight as the objects. 
 
 ^ On the footing of this obfervation, that objects of the fame height 
 give equal fhadows, if you would give the fhadow of the palifades E, 1% 
 which are the fame height as A, D 5 take in your compaffes the diftance 
 A B, and fet it on the foot of the palifade E, by which you will have 
 E G ; then from G draw a .line to the point of fight C. And thus you 
 are to proceed, be the walks ever fo numerous. 
 
 If the light come from the fore-part, as in the figure underneath, the 
 method muft not be altered ; but only the foot, or bottom of the fun, 
 is to be brought nearer or farther off according to the fun's place, and 
 lines drawn from the center and foot of the luminary through the upper 
 and lower angles. Thus the lines from H and I give the extreme of the 
 fhadow of the palifade K, in the point L ; and from L a line drawn to 
 the point of fight M limits the fide fhadow. From the remote angles 
 of the plan of the palifade, a parallel to the line H drawn as far as the 
 ray L M, will give the extreme end of the fhadow, and the whole will 
 appear natural. 3 
 
Q q * 
 
*34 
 
 PRACTICAL 
 
 Part V. 
 
 Of Shadows, when the Sun is direSlly oppofed to the Eye. 
 
 AS often as the fun is before the eye, that is, directly over the point of 
 fight, the fides of the fhadow it produces will be parallels, as all the 
 vifual rays are. For this reafon, the point of fight is always to ferve for the 
 foot of the light when in that altitude, and the other ray, that is to determine 
 the fhadow, will be taken from the center of the fun. 
 
 Thus the fhadow of the cube A being required, draw lines through the an- 
 gles of its plan B C, to the point of fight D, as the lines B E and C F. Then, 
 from the center of the fun G, draw two rays cutting the former in the points 
 K and L, and paffing through the raifed angles H and I. By this means the 
 fhadow of the cube will be found in B K L C. 
 
 The fhadows of the two other objects, M and N, are found by the fame rule, 
 and fo might the fhadow of any object whatever. 
 
 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 fun, paffing through its vertex or point, only make 
 one line ; and of confluence cannot terminate any thing for the fhadow of the 
 vertex of that pyramid. 
 
 When this happens, draw a line from the point of fight P, through one of 
 the angles of the plan ; by which means you will have O Q^. Then from O 
 erect a perpendicular O S, and from the point of the pyramid T draw a paral- 
 lel to the bafe, till it cut the perpendicular O S in the point V. Draw the ray 
 of the fun through this point, and continue it till it cut the ray O QJn the 
 point X ; from X draw a parallel to the bafe, as far as the ray of the middle of 
 the pyramid, which will be cut thereby in the point Y, the extreme of the 
 fhadow. To Y draw lines from the angles Z and O ; and the triangles Z Y O 
 will be the fhadow 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 center of the plan, draw a line from the fame center 
 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 fight, and proceed as before. 
 Wnich will be a ftanding rule, whether the pyramid be viewed 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 fhadows as already taught 
 in that of the cube A. 4. 
 
135 
 
 PRACTICAL 
 
 Part V. 
 
 For the Shadows of perforated Objects* 
 
 WHEN the object is fquare or rectilinear, aline muft be drawn 
 from the foot of the luminary through the angles of the plan 
 for one fide of the fhadow, and parallels thereto for the other fides ; then 
 from the middle of the fun B, draw a line through the raifed angle C, 
 which will cut the line from A, in the point D; through which point 
 a line mufl: be drawn to the point of fight, till it meet the remoteft line 
 from the plan F. To find the reft of the fhadows ; draw parallels to the 
 line BCD, through the angles GHI; and inafmuch as the fun illumi- 
 nates two fides of the object, and makes the fhadow broader, as is 
 {hewn in the figure, where G C and H I are the diagonal of the fquare 
 pieces; where thefe lines drawn through G C and H I cut the line A, a 
 line muft be drawn to the point of fight E ; and you will have the whole 
 projection, or fhadow of the object. 
 
 If it be a round object, as reprefented in the fecond figure, a circle 
 muft be defcribed, according to the rule given for arches in pages 62, 63, 
 by erecting of perpendiculars, &c. And when the circle is formed' and 
 its thicknefies given, from the bottom of thofe perpendiculars, parallels 
 to the bafe muft be drawn ; as here K, L. Then taking L, which is 
 the parallel of the middle of the circle, for the foot of the luminary, 
 from the middle t>£ the fun M, draw a line paffing over the circle 
 and continue it till it cuts the parallel L in the point O ; which will be 
 the extremity of the madow. The vacuity or aperture of the rotundo 
 is found by drawing a parallel to N O from the point P, which is the 
 top of the object oppofite to the fun, till it cut the line L 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 line ; as is here done for that of the middle L O. I could 
 eafily mark them all with points, but I forbear it to avoid confufion, 
 
i3 6 
 
 PRACTICAL 
 
 Part V. 
 
 Shadows ajfume the Form of the Planes they are caji 'upon. 
 
 HITHERTO I have confidered fhadows on the horizontal plane ; 
 being certain that a perfon who underftands fuch, will find no 
 difficulty in the practice of the reft which follow. For the rule is the 
 fame in all ; and one fingle inftruction will fuffice to mew how fhadows 
 fmk and rife according to the planes on which they are caft. 
 
 To {hew that thefe fhadows are formed by the fame rule as thofe pre- 
 ceding, draw a line from the foot of the luminary A, through the plan 
 of the door B ; and another from the fun C, over the top of the fame 
 door at D j thefe lines will interfect each other, though without the 
 limits of our page, and give the extremity of the fhadow ; as already is 
 obferved of the others on the horizontal plane. But the wall E prevent- 
 ing the line A B from being continued as it mould be if the plane was 
 horizontal, obliges it to rife, as we fee in F G. For this reafon the 
 fun's rays, which mould proceed to meet the line A B, cuts it on the 
 wall in the point G, and there marks the form or fhadow of the door ; 
 the top whereof is drawn to the point of fight H. 
 
 The fhadow of the object K is caft in all its length K I, and pafles 
 over that other L. And it is to be obferved, that the fhadow ftill pre- 
 ferves its length, though it meets with a raifed object in the way : and 
 that the fhadow. which pafles over any thing aflumes the fame figure, as 
 here the fhadow M and N takes the form of the object L, or rather is 
 loft: in the fhadow of L. 
 
 Though I have made the fun to appear in all my figures, it muft not 
 be imagined that he is fo near the objects. My intention was to fhew 
 that the rays proceed from him when at fuch a height, though far with- 
 out the limits of the paper, as in this fecond figure, which yet has the 
 line for the foot of the fun A B, and that of the rays of the fun C j by 
 reafon thofe are always required for finding the extremities of the fhadow. 
 
 The fhadow of the object O is found by continuing the line A B, and 
 making it rite over the fteps, and againft the wall, till cut by the ray in 
 the- point S, by the rays pafiing over the corner of the object and from 
 S drawing a line to the point of fight T. 
 
 To find the fhadow of the object P, it muft be remembered (as already 
 obferved) that the foot of the light is always fuppofed on the plan where 
 the object is placed. Accordingly the ray C cutting the little line A B, 
 thews how far the fhadow of the little object P muft go, to be thence 
 drawn to the point of fight T. 
 
 The object V cafts it fhadow the ufual length, though in its way it 
 defcends into a pit and rifes again. 
 
 The fhadow of the wall R, is found by the fame rule as the reft; as 
 appears from the lines A B and the ray C. 
 
"137 
 
 PRACTICAL 
 
 Part V. 
 
 To find the Shadows of Ohje&s broader at Top than at Bottom. 
 
 WHEN the projection or fhadow of a figure is requir- 
 ed, 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, B A, from 
 the fame. The plan finifhed, a line muft be drawn under- 
 neath the fun, as already mentioned, and parallels to this 
 line be drawn from all the angles of the plan. Then a line 
 is to be drawn from the fun C, through one of the angles 
 of the object, as D, till it cut the line'of the plan of the 
 fame angle at F. Another line is to be drawn over the angle 
 A, till it interfe&s the line B A in the point F. Then draw- 
 ing lines from E and F to the point of fight, you will have 
 the fhadow of the fquare of the top of the object Laftly, 
 drawing lines from the point of the figure H, to the points 
 F and L, you will have the fhadow of the whole figure^ 
 which is a pyramid inverted. 
 
 It is evident that the projection or fhadow of the crofs un- 
 derneath is performed after the fame manner, w T hich it i s 
 unneceflary to repeat. 
 
Part V. PERSPECTIVE. 137 
 
 *7 
 
t 3 8 PRACTICAL 
 
 Part V, 
 
 To fnd the Shadows of Obje&s fufpended from the Ground, 
 
 rTTlHE method of finding the fhadows of objects fufpended frojn the 
 j[ ground is rendered very eafy by the preceding rule : all you have 
 to do is to find the plan, and from the angles thereof to draw parallels 
 to meet the perpendicular line under the fun, and then, from the fame 
 angles of the objects fufpended in the air, to draw other lines, cutting 
 thofe drawn from the plan j by which means you will find the extremes 
 of the fhadows, as already mentioned under the preceding figures. 
 
 I am clearly perfuaded, that my reader would eafily conceive the me- 
 thod of thefe, or any fhadows made by the fun, without farther expla- 
 nation of the figures here annexed, they being all intelligible, and per- 
 formed by the rules already taught. 
 
 However, as every inftanee has fomething particular therein, it may 
 not be improper to take notice thereof, that there may be nothing but 
 what is eafily underftood. 
 
 I obferve then, thrat in the firft figure the plan AB CD is alone made 
 ufe of, to find the fhadows of the objects E F, by reafon they are both 
 on the fame line, and of the fame height. 
 
 In the fecond, it mutt be obferved, that the piece of wood G cafting 
 its fhadow on the wall H, the fhadow makes that fame figure at the cor- 
 nice I underneath. And the lame is obfervable of the flick K, raifed 
 againft the wall H. 
 
 To find the fhadow of the board L, the rule already delivered for ob- 
 jects broader at top than at bottom, mu ft be remembered ; for having 
 drawn the perpendicular M, where it cuts the ray N O, you muft draw 
 the line from underneath the fun M P. Then from the board L, draw- 
 ing a line to cut the line MP, the point of interfe&ion will be the extre- 
 mity of the fhadow. 
 
 The fhadow of the globe or ball Qms 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 fun R, and a tan- 
 gent from the fun, as C^S, 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 fhadow of the ball,. 
 
139 
 
 PRACTICAL 
 
 Part V. 
 
 To find the Shadows" of human Figures , caufed by the Light 
 
 of the Sun, 
 
 THE fhadow of figures is found by the fame methods as thofe of other bo- 
 dies, that is, by parallels both from underneath the figure, and from the 
 fun i with this difference only, that the fhadow of other bodies or objecls 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 fill perpendicularly, which line is to 
 ferve as a plan. 
 
 For example, In a figure naked, or mdreffed without a cloak or gown , as the firft 
 figure hereto adjoining, with its back towards us-, from under its feet, as A, 
 draw a line to the point of fight B, and to this line A B drawoccult lines from 
 all the points that may contribute to the true fhadow ; thus from the hand C, let 
 fall a perpendicular, cutting the line A B in the point D, and from the elbow E 
 Jet fall another to the point F, and a third from the head G to the point H, and 
 from all theie points DFH, as alfo from the end of the ftaff I, draw parallels to 
 the bafe line. 
 
 Then having determined the height of the fun, a line muft be drawn from the 
 fame, as K, pafiing 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 fhadow. And again, from 
 the hind edge of the hat M, draw a parallel to K G L, till -it likewife cut the line 
 H in the , point N, *thefe two points N and L will be the fhadow of the hat. A 
 third parallel muft be drawn through the point C, till it cut the line D in the point 
 O, this point O will be the fhadow of the hand that holds the ftaff * drawing 
 therefore a line from the point O, to the point I, the line O I will be the fhadow 
 of the ftaff. A fourth parallel is to be drawn through the point E, which cut- 
 ing F in P, will be the fhadow of the elbow. The fame do from all the other 
 parts, as the knees, the feet, &c. Thefe feveral points connected together, aive 
 the (hadow of the whole figure. The fhadow of the little figure QJs done by 
 the fame method. I have not exp.effed all the points and parallels therein, in 
 order to avoid confufion. 
 
 To find the jhadows of figures cloathed in long garments; draw a line from un- 
 der their feet to the point of fight, as here the line S R, and through 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 fun, to be con- 
 tinued till it cut the line X in the point Z ; which point Z will be the extreme 
 where the fhadow is to terminate. The reft of the fhadow 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 \ Z, till they cut 
 the line V. And thus f gives the fhadow of the elbow, and * that of the folds 
 of the gown. 
 
 9 
 
140 PRACTICAL Part V. 
 
 An eafy Method of finding the Shadow of a Body from the 
 
 Sun. 
 
 WERE I here to add the fhadows of all the obje&s that might be 
 given, it would be a work without end, obje&s being multipli- 
 able 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 many and various manners, each of 
 which has its feveral fhadows. But the labour would be ufelefs, inaf- 
 much as every body will be prepared to make any at pleafure, provided 
 he be matter of two or three rules already laid down for the fhadows of 
 obje&s taken from the fun, two kinds of lines have been fhewn to con- 
 tain the means for finding all fhadows imaginable j one of the lines com- 
 ing from under the fun, and pafiing over the plan, and the other pro- 
 ceeding from the fun itfelf, and pafiing over the object, and cutting the 
 former line in the place where the fhadow is to terminate. But as thefe 
 lines are to be all parallel, that is, thofe from under the fun parallel to 
 each other, and thofe from the fun likewife parallels among themfelves, it 
 may be necefifary 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 under the fun, 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 another piece of wood, well 
 fquared, and grooved quite through, fo as the rule F G may be move- 
 able therein with fome force, and that having taken an inclined line, as 
 If D, another parallel thereto I K may be taken by means of this bevel, 
 which is the name the workmen give this moveable fquare E F G. This 
 inftrument fhortens the work exceedingly, when fhadows are to be made 
 by the fun, on which occafion there is no line of any inclination what- 
 ever, but parallels will be required thereto. The application will evince* 
 its ufefulnefs. For fhadows by the candle or torch, it is of no import- 
 ance, by reafon all the lines are there drawn from a center. 
 
 a 
 
PRACTICAL 
 
 Part V. 
 
 Shadows from a Torch, Flambeau, Candle, and Lamp,, 
 
 T T has been already obferved, that there are two points required for 
 the finding of fhadows ; 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 firfr. poinJ:, 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 fhadow is required ; and the fecond point gives 
 other rays, which paffing through the angles of thofe objects, inter- 
 fect the former lines, and mew where the madow is to terminate. I 
 fhall illuftrate this by an example, wherein the fame letters {hall 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 fhadows B of the cubes A be required, lines- 
 muft be drawn from the point Q, which is the foot of the luminary, 
 through all the angles of the plans of thofe cubes, as O D, OE, OF, 
 O G, and then from the point C, which is the light or fire of the lumi- 
 naries, other lines muft be drawn through the angles of the objects,, and 
 continued till they interfect the former lines from O. 
 
 Thus having drawn a line from the point O through the angle of the 
 plan D, drawing another line from C, through the correfpondent angle 
 of the object P, this latter line being continued, will cut the firft from: 
 the angle D in the point H, which point will be the fhadow 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 lliadow of the cubes, as in the three figures. From this 
 inftance it readily appears, that the method is the fame in one as ; another 0 . 
 
 In the following page we fhall mew how to find the bottoms or feet, 
 of candles and lamps. 
 
142 
 
 PRACTICAL 
 
 Part V. 
 
 Of the foot of the Luminary. 
 
 SINCE the method of finding fliadows by the torch, candle and lamp is the fame in 
 all, as already obferved, there is no oceafion 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 (hall ufe the word light indifferently for all three. 
 
 As to the foot of thefe luminaries, which muft ftand 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 fide, or in the middle 
 thereof (inftances of each hereof we have in the erected figure) we muft consider all the 
 parts of the room, namely, the cieling, floor, fides, &c. as having points wherein the 
 foot of the luminary may be placed, and that from thefe points lines may be drawn through 
 all the angles of the plan of the object whofe fhadow is required, as fhall be exprefTed more 
 at large in the following page, my chief defrgn 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, though the 
 foot may be found on all fides. 
 
 To find the foot of the luminary on the fide of the wall C, draw a parallel to the bafe 
 line from the point A, till it cut the ray DE in the point F, from which point erect a 
 perpendicular F G. Then from the point B, which is the fire, draw another parallel to 
 the bafe line till it cut F G in the point H, which H will be the foot of the luminary j 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 dnw a parallel 
 to the bafe line, as G I, and from the point B erect a perpendicular to the fame G I ; this 
 gives the point K for the foot of the luminary, as if the torch were turned upfide down. 
 
 To find it on the other fide of the room, the fame method muft be obferved as for the 
 fide C, and you will have the point L. * 
 
 To find the foot of the luminary in the middle of the room, draw a Kne from the point 
 H to the point of fight, 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, taking 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, it is this arm or branch, that determines the line where the foot of 
 the luminary fhall be. For inftance, in the plate P, through the arm Q_draw a perpendi- 
 cular to the bafe line, as R S. Then from the fire T, draw a little parallel to the bafe 
 line, which cutting R S in the point V, gives the foot of the luminary for that fide. The 
 point X will be the foot for the floor, the point Y for the cieling, and Z for the front 
 wall of the room. 
 
 As to lamps, it is the place they are hung in that determines the foot, as here the charac- 
 ter * ; from which place a parallel to the bafe line is drawn as far as the firft ray, &c. 
 The relt the fame as in the torch or candle. 
 
*43 
 
 PRACTICAL 
 
 Part V. 
 
 To find the Shadows of a Torch on all the Sides of a Room, 
 
 THE fhadows taken from the fun always tend towards the earth, by reafon that ftar 
 never gives us any of its light, but when above our horizon, and of confequence raifed 
 above our ordinary objects, and fo occafioning their fhadows to defcend. But the cafe is 
 different in torches, candles, and lamps, which may be placed either above, below, or on 
 the fides of objects, and therefore may yield fhadows on all fides, as we are now to fhew. 
 
 The preceding figure will help to find the fhadows of objects difpofed on all fides 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 page 141. 
 to which recourfe may be had. However, to fave you the trouble of going fo far back, I 
 fhall here obferve, that to find the fhadow of the table the torch is placed in, you muff, 
 draw lines from the foot of the torch A, through all the feet of :he table C. Then from 
 the point of light B, draw lines overall the points of the table III, &c. till they inter- 
 fect the rays C C, C5c. in the point O O, csV. which will give the bounds of the fhadow 
 of the table. 
 
 The fhadow 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 per- 
 pendicularly. Then from the point of the light B, drawing lines over the object D, and 
 obferying the angles correfponding to the lines of the plan, you will have the fhadow F of 
 the object D. 
 
 The fhadows of all the other pieces are found after the fame manner : fo that all we 
 fhall here no'e, is the foot of the luminary, the fire itfelf being fuppofed to be fixed in the 
 point B. 
 
 For finding the fhadow of figure G, the point L is the foot of the luminary. 
 
 To find the fhadow of figure N, the point H is the foot of the luminary. 
 
 To find the fhadows of the figures I and M, the point K is the foot of the luminary. 
 
 Fcr the fecend figure ; having found the foot of the lumirwry on all the fides of a room, as 
 directed in the preceding page, the fhadows 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 it? 
 fire P, if you would have the fhadow of the object R, dnw rays from the point Q_over the 
 plan of the object, continuing them indefinitely. But inafmuch as they meet with the wall, 
 or fide of the room T, in the places S and S, where they meet the fame, they muff all be 
 raifed ; then drawing other lines from Pover the fame object R, they will cut thofe of the 
 plan, and mark the place of the fhadow 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 fhadow of a 
 -cube, will make no difficulty of finding the fhadow of any other object whatever. For this 
 reaf|>n, having defcribed that method for the cube in page 141. and added this above, which 
 an effect is the fame; I imagine I have given abundant inftruction for the managing of 
 all fhadows, and may be excufed from repeating the fame in the feveral figures following. 
 Wherein all I fhall note, is the point for the foot of the luminary. 
 
 To find the fhadow of the figure V, the point X is the foot of the luminary. 
 To find the fhadow of figure Y, the point Z is the foot of the luminary. 
 To find the fhadow of the figure +, the point & is the foot of the luminary. P is the 
 €re a or light itfelf, for all the objects in the fecond figure. 
 
Part V. PERSPECTIVE. 
 
 143 
 
PRACTICAL Part V, 
 
 The Shadow of an ereEi and inverted Pyramid by Torch- 
 light* 
 
 T H E fhadow of an erect pyramid by torch-light, falls as it would 
 by the light of the fun, and in both cafes there is but one line 
 wherein the vertical point of the pyramid will be found. Upon the 
 plane BCDE draw the diagonals EB and D C, through the central 
 point F raife the perpendicular F A, and from the four points BCDE 
 draw lines to the point A, and the pyramid will be erected. Then to 
 find its fliadow, draw an indefinite line from the bafis G of the illumi- 
 nating body, paffing through F, and from the central flame of the 
 torch H draw another line over the vertex of the pyramid in the line 
 O F, till it cut the point I, which point will limit the fliadow of the 
 pyramid. Laftly, draw a line from C to I, and another from E to I, 
 and the triangle C I E will be the fhadow of the pyramid. 
 
 To gain the fliadow 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 fun, page 138. And 
 from all the angles 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 fliadow will be defined as we before ob- 
 ferved, in other inftructions relating to the torch. 
 
 The Shadow of a Crofs* 
 
 WE before confidered the fliadow of a crofs by the fun, let us now 
 fuppofe the fame object placed in the light of a torch, that we 
 may find the difference between the two cafes. The conftruction of 
 the latter is obvious enough, particularly if compared with the method of 
 finding the plane, delivered in page 137, and the other directions laid 
 down for fliadows by torch-light. 
 
*45 
 
 PRACTICAL 
 
 Part V' 
 
 Jo find the Shadows of round ObjeEis by Torch -light. 
 
 THERE may feem to be more difficulty in reprefenting the fliadows of 
 globes, bottles, drinking-veffels, and o;her bellied objects, by torch- 
 light, than in thofe of fquare ones, but the directions already given will ferve 
 for thefe alfo ; for there is nothing more, required here, but to reduce fquares 
 to rounds, as we taught in pages 19, 20, 28, 29, and 86; which contain all 
 the neceflary instructions for giving the plans of round objects in perfpective, 
 whence all other cafes of that kind may be eafily understood. 
 
 We gave in pige 138, the method for finding the plan of a ball, and by 
 means of that plan, the precife .magnitude of the fhadow by the fun. But as 
 the cafe of the torch differs from that, we mall be a little more particular upon 
 the ball, becaufe it will facilitate all the other directions relating to rounds. 
 
 Having by means of a pair of compaflfes marked out the great circle of the 
 ball A, draw its diameter B C, and below this circle draw a line parallel to 
 B C touching the circle in the point H. Then from the extremes of the dia- 
 meter B C let fall perpendiculars upon the line below, as B D and C E, and 
 with thefe points D and E make a plan D EFG in the ufual manner, the 
 diameter whereof F G, will divide D E at the point H. And this plan will 
 ferve. to find the fhadow of the ball A. Now, hiving drawn from the bafis of 
 the illuminating body I, lines touching this plane on both fide?, 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, mall divide 
 the line I H at the point M : this point muft terminate the fhadow. To gain 
 the firft part of this fhadow, draw from the fame point N another line, touch- 
 ing the fore-part of the ball, an 1 dividing alfo the line I H a? the point Q, 
 then the diftances between and M will be the length of the fhadow. And 
 fox its breadth, draw from the fame point N two lines touching the extremes 
 of the diaine:er of the ball Z Z, and dividing the lines I K at the point R, 
 and I L at the point S. Now then, as R S is the breadth of the fhadow, and 
 M the length of it, if the four points R S QJVI be joined with curve lines, 
 there will be an oval formed for the fhadow of the ball A. 
 
 I have been the larger upon this fhadow, becaufe I judge the direction given 
 about'it alone fufficient for finding the other Shadows of rounds, as of the ob r 
 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 corref- 
 ponding thereto, one for the neck of the bottle, another for its beliy, 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 
 unnefceifary. 2 
 
146 
 
 PRACTICAL 
 
 Part V. 
 
 Shadows on fever al parallel Planes, 
 
 THE fii ft plane here is the floor whereon the chair A (lands; 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 fhadow of the 
 object. Suppofe the foot of the illuminating body to be C, and the flame B^. 
 from thefe points C and B draw lines through the upper and under part of ther 
 obj<r<5t D > which, will give the fhadow E upon the table. 
 
 To find the fhadow of the chair A, which is placed on the ground - r determine 
 the" foot of the luminary on the table in< C, on the ground : this is cleared bjr 
 the inflections following.. 
 
 From the point of diflance, which is here fuppofed without the limits of the 
 paper, draw a line through 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 ; and 
 from H draw a parallel to the bafe H I, which is equal to the upper part of the 
 table, and will direct us to the thing required. For r drawing a line from the 
 point of fight 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 fight 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 founds 
 there will be no difficulty in finding the fhadow 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 
 fhadow. For the reft the figure gives fufficient directions, 
 
 The fecond figure is not here added as if there were any particular circum- 
 flances different from thofe of the figure above, but only to put you upon re- 
 collecting what has been already taught j. namely, that objects call their fhadows 
 differently, according to their different difpofitions about the luminary.. Thus 
 the little objects on the table project their fhadows this or that way as the lumi- 
 nary is on this or that fide, as is found from the common rules relating to the 
 foot of the luminary, and the light itfelf. Mofl of the objects here reprefented 
 are broader at the tops than bottom fo that it will be necefiary tamake plans 
 thereof, after the manner already fhewn.. 
 
PRACTICAL Part V. 
 
 Shadows of Cjelings by 'torch-light, 
 
 T U J l E %™n ^ " ot P lac J d In ^ fun ' s 1; ght, becaufe that luminary is high above 
 all the objeds of the earth, and confequently can give no fhadow where the illu- 
 minating body is fuppofed to be under the objea. If k be faid, though the fun's rav* 
 .enter a room, yet the fhadows of bodies continue to appear ; I anfwer, that fuch fhadows 
 are not .mmediately caufed by the fun, but by the light reflected into the room from other 
 object 5 and that they cannot be reprefented by parallel lines, as thofe of the fun, but 
 by rays ifiumg f rom the fame center, as thofe of a torch, taking the refleding body for 
 the illuminating point, and proceeding in drawing fuch a fhadow as in the cafe of a torch/ 
 
 The directions hitherto given, which turn upon the forming of plans, and drawing of 
 hues from the angles of objects to find the bounds of the fhadow, would be too tediou 
 here, and the great number of lines neceffary to be drawn, would render the figure ex- 
 ceeding intricate, on account of the feveral beams, fupporters, and rafters that would oc- 
 cur. This inconvenience drove me to invent a fhort, eafy, praftical method for the fame 
 purpofe, without departing from the rules of art, - 
 
 The floor being put in perfpedive, as was taught in pages ce, and 57, and the illumU 
 nating body fixed, we muft find by means of the" bans ofthat body w^eVe the afuSl 
 ing point ought to be, To find this point, when the illuminating body is at B, draw from 
 the foot of it C, a parallel to the bafe D E, till it cut the ray E F in the point G, from 
 this point G raife a perpendicular G L, and from the flame of the torch B draw a paral'el 
 to D £, dividing the perpendicular G I at the point L, and this point L will give th« 
 place and length of the fhadow, . - b 
 
 For example ; to find the fhadow of the band A, from the point L draw a line touching 
 the vertex of the angle H, and obferve where this line L divides the firft rib, as at thS 
 point I, which is the place of the fhadow's ending. From this point draw a parallel I £ 
 and mark upon the ribs the place of the fhadow O. And to find the fhadow of the fpace 
 betwixt : them , draw another line from the point L, touching the vertex of the an^le of 
 the frtft rib M, which will divide the angle of the interval at the point N. Now then 
 
 bwmA P0 ' nt a P3ral,el N ? ' 7 ° U WiU thC0Ce h3Ve * U the ^ ad ° W ^ for ch ' c ' 
 
 To find the fhadow of thejoifts, draw a line from the illuminating point B, touching 
 tne angle S, and dividing the bottom of the entab'ature at the point T. Proceed thus with 
 pU the other ribs, and the fhadow will appear to be longer the farther it is removed from 
 the luminous body. Then mark upon one beam all the points T, and from the point of 
 
 ? 11 /f, W Ua £ ^ r ° Ugh each of thefe P° ims » and then ^ fhadows of all the other 
 nbs will fall exadly between 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 
 I t r u,d f ha : /e ? bfc L ured the I«ter. ™° 'he fine lines neceiTary in the oth £r : onlvTe re 
 the fhadow oHhe jambs of the gate muft be taken from the foot or the i««minatin/body 
 
To find the Shadow by the Foot of th Luminary, 
 
 F the objects be perpendicular to the bafe line, and higher than the 
 flame of- the candle Aj we need only draw lines from the foot of the 
 binary B through the moft advanced angles of the objects; for ex~ 
 ample, C and P of the fkreen, Jig, I. and others from the angle of the 
 wall E, Thefe lines B C, B D, and B E, give the place of the fhadow 
 |n the points where the angles made by the leaves of the fjcreen, meet 
 the floor ; as alfo the return of the wall in the point G, from whence 
 perpendiculars mud be raifed, as G which will terminate the fhadows 
 given by the candle A. 
 
 The reafon hereof is, that the line A B being parallel to the line C H, 
 P I, li and E L, occafions the flame, in what part foever of the line 
 A B it be found, whether on high in the middle or below, to give a 
 like fhadow, 
 
 It muft here be obferved, that this rule only holds good of objects 
 railed above the flame, as thefe are in the prefent figure. For fuch as 
 (hew their upper part, as here the object M, the preceding rules take 
 place | that is, lines muft be drawn from the foot and flame of the lumi~ 
 
 nary, 
 
 The Shadow doubled. 
 
 % TTHEN two luminaries mine on the fame object, two fhadows 
 W mu ^ b e produced, each by means of the luminaries occafioning 
 the refpective fhadow, 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 object than the other, the fhadows will be unequal. 
 Thus the object O being illumined by two candles, the one near at hand 
 in F, the other farther off in Q^jt is evident, the fhadow of the candle 
 P will be deeper than that of the candle as is expreffed in the figure. 
 
 The rules for fuch fhadows are the fame with thofe already given both 
 
 for the fun and the torch. 
 
149 
 
 PRACTICAL 
 
 Part V. 
 
 The Shadows of human Figures by Torch-light. 
 
 I HAVE reafon to hope that the advice already given, not 
 to turn over the page to a new figure, before the pre- 
 ceding one be well underfbod, has been carefully obferved. 
 Suppofing therefore my reader to have maftered what was 
 directed in page 139. for finding the fhadows of human 
 figures by the fun ; 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 fhadow projeded by a torch is not equal to the body, 
 as is the fhadow projeded by the fun, a farther confidera- 
 tion muft here be added ; namely, that inftead of drawing 
 the lines parallel to one another, they muft here be all 
 drawn 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 figure from the point of the flame, 
 in like manner as for the other fhadows of the torch ; which 
 it would be needlefs here to repeat, the figure itfelf giving 
 abundant fatisfadion. 3 
 
*5o PRACTICAL p ar t V. 
 
 the different Difpoftlons and Heights of Shadows by torch- 
 light. 
 
 QHADOWS from the fun are all caft the fame way, and 
 k3 have the fame difpofition ; it being impoffible the fun 
 fliould occafion one fliadow to tend towards the eaft, and 
 another towards the weft, at the fame time. True, in dif- 
 ferent times of the day it makes this difference : but never 
 in one and the fame hour. 
 
 But the torch, candle and lamp have always this effetf: ; 
 for in what place foever one of thefe luminaries be found, 
 provided there be a number of objecls about them, the 
 ihadows will be call: various ways ; fome to the eaft, fome 
 to the weft, fome to the north, and others to the fouth 
 according to the fituation of the objects around the luminary \ 
 the foot of which, here reprefented by A, ferves as a com- 
 mon center from which they all proceed ; and the flame 
 here reprefented by B mews where they are to terminate, 
 though at different diftances ; as the neareft produce the 
 fhortefi; ftiadows,. and the remoteft the longeft. ' 
 
 Though in the fecond figure the luminary be not placed 
 in the middle, yet the fame rule obtains, with refpecl to 
 the fhadows as in the former figure; being all drawn from 
 the foot of the luminary C, and terminated by lines from 
 the flame D. 
 
 4 
 
 F I N 1 & 
 
ri