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THE 
 
 ART 
 
 OP 
 
 DRAWING IN PERSPECTIVE 
 MADE EAST. 
 
 EDINBURGH : 
 PRINTED BY J. PILLANS & SONS, 
 LAWNMARKET. 
 
•the 
 
 A ]R T 
 
 OF 
 
 DRAWING IN FERSPEClIVlL 
 MADE EASY 
 
 TO THOSE WHO HAVE NO PREVIOUS KNOWLEDGE 
 OF THE MATHEMATICS. 
 
 A NEW EDITION. 
 By JAIMES FERGUSON, F. R. S. 
 
 ILLUSTRATED TV ITU JPLATES, 
 
 PRINTED Fcs. DEXHAIM & DICK, 19. college-street. 
 
 STEWART CHEYKE, GEORGE-STREET, EDINBURGH J A. K. 
 
 ^.'A1R^■, 23. chasdois-street, losdon ; 
 
 EDINBURGH: 
 
 4^ 
 
 SOLD BY 
 
 AP.CHER 5C WARD, AND T. STORIE, 
 BELFAST. 
 
PREFACE, 
 
 IN my infirm ftate of health, a fitua- 
 tion that is very apt to affect the 
 mental faculties, I thought my late 
 book of Mechanical Exercifes would 
 have been the laft I ihould ever pub- 
 lifh. But, ?s I have been conftantly 
 accuflomed to an active life, and to 
 coniider idlenefs as an infupportable 
 burden, I have of late amufed my- 
 felf at intervals, as my ufual bufinefs 
 w^ould permit, with ftudying Pe?'fpec- 
 tive ; which is an art that every one 
 who makes drawings,, were it but for 
 plates (efpecially of folid figures) in 
 books, fhould be acquainted with. 
 And indeed I drew the figures which 
 are now engraved for this Book, \vith 
 A no 
 
ii 
 
 PREFACE. 
 
 no other view than to inftrud: others 
 verbally by, who came to me to learn 
 fomething of that branch of fcience, 
 without having the leaft thought of 
 ever laying them before the Public. 
 
 But, upon fhewing thefe drawings 
 accidentally to fome friends, they ex- . 
 preffed their defire that I fhould write 
 a defcription of the rules by which 
 they were delineated. I complied with 
 their defire ; and it is entirely owing 
 to their partiality to me that I have 
 confented to this publication. 
 
 I NEED not obferve how requifite 
 it is for painters who put groupes of 
 figures together, but alfo for thofe 
 who draw landfcapes, or figures of 
 machines and engines for books, to 
 know the rules of Perfpeftive. The 
 want of this branch of knowledge is 
 the reafon why we not only fee very 
 
 bad 
 
PREFACE. iii 
 
 bad and diftorted figures of machines 
 and engines in printed books, but 
 alfo why we fee many hiftorical paint- 
 ings, in which the different pidlures of 
 men, women, hills, houfes, birds, and 
 beafts, are put together without any 
 regard to what painters call keeping ; 
 which is the fame thing as reprejenting 
 objects in the fame manner that they 
 appear to the eye, at different diflances 
 from it, 
 
 I SHALL only mention two inftances 
 in the Works of one of the greatefl 
 painters that ever exifted ; — I mean 
 the celebrated Raphael Urbin. 
 
 Every man is fenfible, that, if he 
 fhould ftand by the fea-fide, and look 
 at a boat with men in it at fome dif- 
 tance, he could not diftindly fee the 
 features of thofe men, m.uch lefs the 
 wrinkles and marks of the mufcles 
 A 2 in 
 
iv PREFACE. 
 
 in -their faces or bare arms. And if ' 
 he were in a boat^ at fome diftance 
 from the land, he could not perceive 
 the eyes and beaks of fowls on the 
 Ihore. 
 
 Yet fo It is, that, in one of the fa- 
 mous Cartons of Raphael, reprefent- 
 ing the miraculous draught of fifhes^ 
 the men in each of the two boats ap- 
 pear of full fize, the features of their 
 faces ftrongly marked ; and the boats 
 are reprefented fo fmall, and the men 
 io big, that any one of them appears 
 fufficient to fink either of the boats by 
 his own bare weight ; and the fowls 
 on the fliore are likewife drawn fo 
 big, as to feem very near the eye of 
 the obferver ; who could not pollibly, 
 in that cafe, diftinguifh the features of 
 the men in the diftant boats. Or, 
 fuppofmg the obferver to be in either 
 
 of 
 
PREFACE. V 
 
 of the boats, he could not fee the eyes 
 or beaks of the fowls on the fhore. 
 
 The other inftance is of a very ca- 
 pital millake in Raphael's hiftorical 
 picture of our Saviour's transfigura- 
 tion on the Mount ; where he is re- 
 prefented with thofe who were then 
 with him, almofl as large as the reft of 
 his difciples at the foot of the Mount, 
 with the father and mother of the boy 
 whom they brought to be cured : 
 and the mother, though on her 
 knees, is more than half as tall as 
 the Mount is high. So that the 
 Mount appears only of the fize of a 
 little hay-rick, with a few people on 
 its top, and a greater number at its 
 bottom on the ground : in which cafe, 
 a fpedator at a little diftance could as 
 well diftinguilh the features of thofe 
 on the top as thofe on the ground. 
 But upon any large eminence, defer\'- 
 - 3 ing 
 
vi 
 
 P R E F A C £. 
 
 ing the name of a Mount, that would 
 be quite impofGble, — My only reafon 
 for mentioning thefe extraordinary 
 particulars, is to fliew how neceflary 
 it is for painters to be well acquainted 
 with the rules of Perfpeftive. 
 
 I AM far from conlidering the fol- 
 lowing Work as a complete fyftem of 
 PerfpeBive^ for that would require a 
 very large volume. But I think I 
 may venture to fay, that, when the 
 learner is fully mafler of what is there 
 contained, he will not find any great 
 difficulty in proceeding to what length 
 he pleafes in the attainment of this 
 fcience, without any further aflift- 
 ance. — Or, if he ftiould grow tired, 
 and be weary of goitig on accordmg 
 to the rules, he may make ufe of the 
 Perfpedive Machine defcribed and de- 
 lineated at the end of this fmall trad, 
 by which he may draw every thing 
 , equally 
 
R E F A C E. 
 
 vii 
 
 equally eafy that he fees before him, 
 without knowing any rule at all. But 
 I hope there are very few who will 
 have recourfe to fuch an unfcientific 
 method. 
 
 It is very probable, that thofe who 
 already underftand Perfpective, if they 
 take the trouble of reading this fmall 
 Treatife, may think I have been ra- 
 ther too verbofe in moft of my defcrip- 
 tions. I only requeft of fuch to con- 
 fider, that I never wrote any thing 
 for thofe who are well (killed in the 
 few branches of fcience whereof I 
 have treated, but only for thofe who 
 wifh to attain a moderate knowledge 
 of them ; and to fuch, I think, every 
 thing ought to be made as plain and 
 eafy, and be as minutely defcribed, as 
 is poffible. 
 
 A 4 PERr 
 
PERSPECTIVE MADE EASY. 
 
 CHAP. I. 
 
 The Theory of Perspective. 
 
 1 . irjERsPECTivE is the art of draw- 
 A ing the refemblances or pic- 
 tures of objects on a plane furface, as 
 the objects themfelves appear to the eye. 
 — Thus, fuppofe a perfon at a window 
 looks through an upright pane of glafs 
 at any object beyond it, and, keep- 
 ing his head fteady, draws the figure of 
 the object upon the glafs wdth a black- 
 lead pencil, as if the point of the pen- 
 cil touched the object itfelf ; he would 
 then have a true reprefentation of the 
 object in perfpective, as it appears to 
 his eye. 
 
 In 
 
10 
 
 PERSPECTIVE 
 
 In order to this, two things are ne- 
 ceflary ; firft, that the glafs be laid over 
 with ftrong gum-w^ater, which, when 
 dry, will be fit for drawing upon, and 
 will retain the traces of the pencil ; 
 and, fecondly, that he looks through a 
 fmall hole in a thin plate of metal, fix- 
 ed about a foot from the glafs, be- 
 tween it and his eye, and that he keeps 
 iiis eye clofe to the hole ; otherwife he 
 might fhift the pofition of his head, 
 and confequently make a falfe delinea- 
 tion of the object. 
 
 Having traced out the figure of the 
 objed, he may go over it again with 
 pen and ink, and, w^hen that is dry, 
 put a fheet of paper upon it, and trace 
 it thereon v/ith a pencil ; then, taking 
 away the paper, and laying it on a 
 table, he may finiili the pidure, by 
 giving it the colours, lights, and 
 fhades, as he fees them in the objed 
 
 itfelf; 
 
MADE EASY. ii 
 
 itfelf ; and then he will have a true 
 refemblance of the objed. 
 
 2. The nearer that any objecl is to 
 the eye, the bigger it appears ; the far- 
 ther from the eye, fo much the lefs, 
 both in height and breadth. 
 
 3. All objects become vifible by the 
 rays of light which flow from them 
 into the eye. Thefe rays pafs through 
 the pupil, and fall upon the retina, 
 which is a fine expanfion of the optic 
 nerve, interwoven like net-work in 
 the back-part or bottom of the eye ; 
 and there the rays form a picSure of 
 the obje6l, whofe apparent bulk de- . 
 pends upon the fize of fuch picture, fo 
 formed upon the retina. 
 
 In Fig. I . of Plate lAtl P h d c a P 
 be the eye, P the pupil, or round black 
 opening in the middle or fore-part of 
 
 the 
 
12 PERSPECTIVE 
 
 * 
 
 the eye, through which the rays of 
 light enter, and proceed to the retina 
 or back-part b c d where they are 
 intercepted, and form the pictures of 
 the objeds from which they flow. 
 Every point of the objed throws off 
 rays of hght in all manner of ftraight- 
 lined directions ; and therefore, every 
 vifible point of an objeft will fend 
 fome rays through the pupil into the 
 eye ; and thefe rays, falling upon the 
 retina, will form all the correfponding 
 points of the pifture or image of the 
 obje£l thereon. The rays are colour- 
 ed according to the colours of the ob- 
 jects they flow from, and give the like 
 colours to its picture formed in the 
 eye. 
 
 4. To fliew that the pictures of ob- 
 jects are thus formed upon the retina, 
 take the eye of a flieep or bullock, 
 newly killed, and cut off all the opaque 
 
 part 
 
-MADE EASY. 
 
 13 
 
 part from the outfide of the back of 
 the eye, till the tranfparent retina ap- 
 pears ; then hold up the eye between 
 your own eye and any objecS, with 
 the fore-part of the eye toward the 
 objed, and you will fee a fine inverted 
 pidure of the objedl on the retina, 
 having all the colours of the objedt it- 
 felf 
 
 5. In Fig. I . let <? 5 be an objedt, 
 whofe diftance from the eye is P e. 
 A ray A P a from the top of the ob- 
 jed, paffing through the pupil P of 
 the eye, and going on to the retina, 
 forms the pidure or image of the 
 point A thereon, at a; and a ray B P 
 from the foot of the objed, paffing 
 through the pupil P, and going on to 
 the retina, forms the image of the 
 point 5 at ^ on the retina. — All the 
 intermediate points of the objed, from 
 A to By fend rays of light into the 
 
 eye, 
 
14 
 
 PERSPECTIVE 
 
 eye, which form all the intermediate 
 points of the image between a and b 
 in the eye. So that the image of the 
 obje£l is inverted in the eye ; and its 
 whole length is included between the 
 points a and b on the retina. Thofe 
 who want to know why we fee the 
 objeds themfelves in an inverfe pofi- 
 tion to that of their pictures in the 
 eye, muft read what optical writers 
 have faid on that fubjed. 
 
 Let the fame objefl: be placed twice 
 as far from the eye, as at CD; then 
 the diftance P f will be double the 
 diftance P e. The ray C P c forms the 
 image of the top C at c on the retina, 
 and the ray D P d forms the image of 
 the bottom-point D of the objed at d 
 on the retina. — Now, it is plain, that 
 as the fpace between c and d is only 
 equal to half the fpace between a and 
 b^ the image of the objed will be but 
 
 half 
 
MADE EASY. 
 
 ^5 
 
 half as long upon the retina, when 
 the diftance Pf of the object is twice 
 as great as its diftance Pe was before : 
 — And thus, by removing the object 
 further and farther from the eye, or 
 removing the eye further and further 
 from the object, it would feem at laft 
 to be no bigger than a mere point, 
 becaafe the angle under which it Vv'as 
 then feen would be next to nothing. 
 
 6. An angle is formed by two lines 
 approaching toward each other till 
 they meet ; and the point where they 
 meet is termed tbe angular point. Thus, 
 in Fig. I . the lines A P and B P tend- 
 ing toward one another, form an an- 
 gle ; and the point where they meet 
 at P is the angular point ; and whether 
 thefe lines be long or {hort, it makes 
 no alteration in vv^hat is termed ths 
 ineafure of the angle ; as we fhall fhew 
 in the next fection. 
 
 In 
 
x6 PERSPECTIVE 
 
 In defcrlbing an angle, three letters 
 are generally ufed, the middle letter 
 always meaning the angular point 
 where the two lines meet. Thus, A P 
 B denotes the angle formed by the two 
 Jines A P and B P, meeting at P; and 
 C P D denotes the angle formed by the 
 
 two lines CP and D P, meeting at P 
 
 In this cafe, as the objedl A e B fub- 
 tends (or is feen under) the angle 
 A P Bj and the object C/Dis feen 
 under the angle C P the former is 
 called the angle of vifion of the objed 
 A e B^ and the latter the angle of vi- 
 fion of the objedl CfD. But, as the 
 lines C P and D P fall within the lines 
 A B and B P, the angle of vifion of 
 Cf D is lefs than the angle of vifion 
 of A e B ; and juft as much lefs as the 
 diftance of the object C f D from the 
 eye, is greater than the diftance of 
 the objeft A e B from it. — So that the 
 apparent height (or breadth) of any 
 
 objedl 
 
MADEEASY. 17 
 
 objed is diredlly as the me^fure of the 
 angle under which it is feeti. 
 
 7. If a circle, of any diameter what- 
 ever, be divided into 360 equal parts 
 or degrees, and the angular point be 
 at the centre, the number of degrees 
 between the two lines which form 
 the angle is the meafure thereof. 
 Thus, in Fig. 2. of Plate I. the lines j4 C 
 and B C form the angle A C B j of 
 which, the point C p.t the centre of the 
 femicircle d/lB e is the angular point ; 
 and the number of degrees of the fe- 
 micircle contained between the points 
 A and i?, in the arc AB^ is the meafure 
 of the angle AC B. 
 
 Let the femicircle be divided into 
 three equal parts, as dyl^ A Bj and 
 Be; then each part will contain 60 de- 
 grees (the whole femicircle containing 
 1 80), and that will be the meafur^ of 
 
x8 PERSPECTIVE 
 
 either of the three angles d CA^ ACB^ 
 or BCe, 
 
 Join the points and B by the 
 ftraight Une A 5, and a triangle will be 
 formed by the three lines C A B^ and 
 B C, all of equal length ; and all the 
 three angles at A^ 5, and C, will be e- 
 qual, each containing 60 degrees. — So 
 likewife, in the lefler femicircle k ab ly 
 the lines ab^ bC^ and C are of equal 
 length ; and each angle at C, and b^ 
 contains 60 degrees. 
 
 8. Any triangle whofe fides are all 
 equal, is called an equilateral triangle ; 
 and the angle oppofite to either fide 
 thereof contains 60 degrees. 
 
 9. To make an equilateral triangle upon 
 a line of any given lengthy as fiippofe the 
 line ^5 (Plate I. Fig. 2.); take the 
 length A B between *the points of 
 
 your 
 
MADE EASY. 19 
 
 your compafles, and, with that ex- 
 tent, fet one foot on the end of the 
 line at ^, and with the other foot de- 
 fcribe the arc/C^ ; then, without al- 
 tering the compafles, fet one foot on 
 the end 5, and with the other foot 
 defcribe the arc h Ci : laftly, from the 
 ends A and B draw the two hnes A C 
 and B C to the interfedion of thefe 
 arcs at C ; and you will have an equi- 
 lateral triangle, formed by the three 
 lines or fides A i?, B and C A ; and 
 each fide will fubtend an angle of 60 
 degrees. — In the fame manner may an 
 equilateral triangle be made upon 
 the given line ab^hy the lines b C and 
 C a. 
 
 10. No obje6l can be wholly and 
 diftindly feen (if the eye be kept 
 fleady v\^hile looking at it) under a 
 larger angle than that of 60 degrees. 
 — Thus, an eye at C may fee the whole 
 B 2 linp 
 
to PERSPECTIVE 
 
 line or object A B [ov a b)^ without 
 moving or {training, when the dif- 
 tance of the eye from each end of the 
 line is juft equal to the length of the 
 line, or objed And as this is gene- 
 rally reckoned to be a good angle of 
 vifion, we fhall keep generally by it, 
 in the following pradical part of this 
 Work, where the reprefentations of 
 large obje6ts are delineated. But it 
 will not do fo well in reprefenting 
 fmall objeds, which are better feen 
 under a fmaller angle than that of 60 
 degrees : for, when a perfon looks at 
 a common drinking-glafs, or a dye, 
 he never brings it fo near to his eye 
 (unlefs he be very near-fighted) as to 
 view it under fo large an angle as 
 that of 60 degrees ; becaufe expe- 
 rience teaches him, that he can fee 
 it better under a fmaller angle ; that 
 is, when at a grt-ater diftance from 
 his eye. Thus, the fmall objed: a b 
 
 will 
 
Made easy. 
 
 21 
 
 will be better feen by an eye at 7?, 
 viewing- it under an angle of 30 de- 
 grees, (as a D b)^ than if his eye were 
 only at half that diftance at C, view- 
 ing the fame objedl a b under an an- 
 gle (aC b) of 60 ; and therefore, 
 in delineating the perfpedive figures of 
 fmall objeds, the artift fhould always 
 fuppofe the obferver to be fo far off 
 from the objedl, as to be viewing it 
 under a lefs angle than that of 60 
 degrees : and then the perfpeftive pic- 
 ture will appear more natural, and 
 confequently fo much the more plea- 
 fing to the eye. 
 
 II. When a perfon ftands right 
 againfl: the middle of one end of a 
 long avenue or walk, which is ftraight, 
 and equally broad throughout ; the 
 fides thereof feem to approach nearer 
 and nearer to each other as they are 
 further and further from his eye, as 
 B 3 the 
 
22 
 
 PERSPECTIVE 
 
 the angles under which their differ- 
 ent parts are feen become lefs and 
 lefs, according as the diftance from 
 his eye increafes, (§ 2. and 5.) ; and if 
 the avenue be very long, the fides of 
 it at the fartheft end will feem to 
 meet ; and thej-e^ an objed that would 
 cover the whole breadth of the ave- 
 nue, and be of a height equal to that 
 breadth, would appear only to be a 
 mere point. 
 
 Thus, in Fig. 3. of Plate 1. let AB 
 be part of one fide of a long avenue, 
 D C 2LS much of the other fide thereof, 
 and thefe fides be parallel to each 
 other ; and fiippofe the avenue to be 
 divided into equal fquares, as ^ <?/ i), 
 e g h g i h &c. ; a perfon ftanding 
 at 0 will fee thefe two fides as if they 
 were gradually approaching toward 
 one another, as in Fig. 4. ; and the 
 fquares will feem to diminifli in fizc 
 
 as 
 
MADE EASY. 
 
 as they are further and further from 
 his eye. So that the firft fquare AefD 
 in Fig. 3. will appear as AefD in 
 Fig. 4» the fecond fquare eghf in Fig. 3. 
 will appear as eghf in Fig. 4. and fo 
 on, till the laft fquare of the avenue, 
 produced to the utmoft bounds of 
 fight, would vanifli into a point, as S 
 in Fig. 4. where the fides A S and D S 
 meet, 
 
 12. The point 5*, where the parallel 
 fides of the avenue feem to meet, is 
 called The Point of Sight ; the point 0, 
 where the obferver's eye is placed, is 
 called The place of the Ohferver ; the line 
 tS* P, paffing through the point of 
 fight, is called The Horizon; and a 
 point taken therein, either to the right 
 or left hand from 5, and as far from 
 S as 0 is from is called The Point of 
 
 Diflance. N. B. In whatever point 
 
 the obferver's eye is fuppofed to be 
 B 4 placed, 
 
^4 PERSPECTIVE 
 
 placed, either for a dired or oblique 
 view of the fide of the objeft that is 
 neareft to him, a Jlraight Vine drawn 
 from the point of fight to his eye mufl be- 
 perpendicular to the horizon ; which will 
 be nearer to the eye, or further from 
 it, as the obferver is fuppofed to ftand 
 upon lower or higher ground* 
 
 Ghar 
 
MADE EASY. 
 
 CHAP. 11. 
 The Practice of Perspective. 
 
 OPERATION I. 
 
 To put a Square in PerfpeBive^ as viewed 
 by an Obferver Jlanding right againji the 
 Middle of one of its Side and having his 
 "Eye above the Plane of the Square. 
 
 \Z' TN Fig. 5. of Plate I. let ABCD 
 A be a fquare, viewed by an ob- 
 ferver at 0, who fees the fide A D (next 
 to him) under the angle ACD of 60 
 degrees (§ lo.j. 
 
 Make JD in Fig. 6. equal to AD in 
 Fig. 5. At any convenient diftance, 
 draw the horizon S P parallel to A D. 
 Take the place of the obferver, ac- 
 cording 
 
2(5 PERSPECTIVE 
 
 cording to the rule in § 9. ; and from 
 the point 0, make 0 S perpendicular 
 to SP^ meeting it in 6', which fliall be 
 the point of fight (§ 12.). 
 
 Take OS in your compafles, and, 
 fetting one foot in Sj defcribe the qua- 
 drant (0 pP) of a circle meeting the 
 horizon in P, which, in all cafes, fhall 
 be the true point of diftance (§ 12.). 
 
 From A and D (the ends of the fide 
 of the fquare next the obferver at OJ 
 draw the fl:raight lines A S and D ^ to 
 the point of fight S : then, from A 
 draw the ftraight line A P to the point 
 of diftance P in the horizon, cutting 
 the line DS in the point C : this done, 
 draw B C parallel to A D ; and A BCD 
 will be a true perfpedive reprefenta- 
 tion of the firft fquare A BCD m Fig. 5. 
 as feen by an obferver at 0. 
 
 Remark, 
 
fvlADE EASY. 
 
 27 
 
 Remark, — If the obferver (Fig. 6.) had 
 flood further than 0 from the fide AD 
 of the fquare, as fuppofe at 0, he 
 would have feen that fide under a lefs 
 angle than 60 degrees ; as the angle 
 AoD is lefs than the angle ^OD; 
 and then, the point of diftance muft 
 have been at d in the horizon ; be- 
 caufe the point of diftance in the ho- 
 rizon muft always be taken as far from 
 the point of fight therein, as the place 
 of the obferver (0 or 6) is from the 
 point of fight, as we fliall prove in 
 §14.; and that, if the point of dif- 
 tance in the horizon be taken either 
 nearer to or further from the point of 
 fight than the diftance of the obferver 
 is fuppofed to be from that point, 
 there will unavoidably be a falfe per- 
 fpedlive reprefentation of the objed:. 
 
 For, fuppofe the placing of the point 
 of diftance in the horizontal line be 
 
 left 
 
2§ PERSPECTIVi: 
 
 left to the difcretion of the artift, as k 
 generally done by writers on the 
 fcience of Perfpedive, and that he 
 had put it at e (Fig. 6.) in the line 
 SP ; then, a ftraight line drawn from 
 ^ to ^ would have cut the line D S in 
 the point b j and ^ h (parallel Xo AI>) 
 would have been the top of the fquare 
 AghD ; but it is plain to the eye and 
 judgement, that ^^^^ D would havebeen 
 a very bad and unnatural perfpedive 
 reprefentation of the fquare A BCD 
 in Fig. 5. Or, fuppofing the point of 
 dillance (Fig. 6.) to have been taken 
 at /, in the horizon S P, the ftraight 
 line A f would have cut DS in k ; and 
 I k would have been the top of the 
 fquare. But a child could tell, that 
 AikD would be a monftrous repre- 
 fentation of a fquare in perfpedive. 
 
 The angle of 60 degrees is only af- 
 fumed here, as being the largeft angle 
 
 under 
 
MADE EASY. 
 
 29 
 
 under which the eye can fee an objed: 
 diftindly ; and not as a conftant angle, 
 tinder which all reprefentations in perr 
 ipeftive mull be drawn. See § 10. 
 
 A Demonjiration of the above Rule (§ 12. 
 and 13.) for finding the true Point of 
 Dijiance, 
 
 14. In Fig. I. of Plate II. IttAI 
 and be part of the two parallel fides 
 of a ftraight avenue^ divided into equal 
 fquares, as ABCD, BEFC, EGHFy 
 &c. and let trees be planted at the' 
 corners of each fquare, as at A^ 6, 
 E,F,G,HyI, andK. 
 
 Let 0 be the place of the obfervei", 
 SP his horizon, and 5* the utmoft 
 point of his view% called the point of 
 fight ; from which the line 5 0 is 
 perpendicular to SP, (fee § 12.). To 
 
 him 
 
3^ 
 
 PERSPECTIVE 
 
 him the two lides of the avenue feern 
 to come nearer and nearer to one 
 another, as they are farther and far- 
 ther from his eye, tending toward the 
 point of fight Sj in the diredion of the 
 two ftraight lines and DS^ (§ 1 1 
 
 In the parallel-fided avenue, draw 
 a ftraight Hne BO from the tree B to 
 the obferver's eye at 0; this hne cuts 
 the perfpedlive fide AS of the avenue 
 in the point ^, w^hich is the apparent 
 place of the tree as feen by the obfer- 
 ver. From the tree C draw the ftraight 
 line CO to the obferver's eye at 0, 
 and that line will cut the perfpedivc 
 fide D S of the avenue in the point 
 
 Vv^hich is the apparent place of the 
 tree as feen from 0; then draw dc pa- 
 rallel to J and J be D will be the 
 true perfpedive reprefentation of the 
 fquare J BCD. 
 
 In 
 
MADE EASY. 
 
 3^ 
 
 In like manner, from the other trees 
 E,- G, /, and F, K, draw ftraight 
 lines to the obferver's eye at 0; and 
 tnefe lines will cut the perfpedive fides 
 and DS of the avenue in the points 
 i, and ]i; which are the ap- 
 parent places of the trees, as feen by 
 the obferver. Laflly, draw the lines e 
 gh^ ik^ parallel to ^i), and they will 
 divide the perfpedive view of the ave- 
 nue, fo as to make it a juft reprefenta- 
 tion thereof, with all its trees and 
 fquares, as feen from 0, 
 
 Thus we find the apparent places of 
 the trees 5, £, G, /, muft demonftra- 
 tively be at ^, g^ i ; and that the ap- 
 parent places of the trees G, ZT, if, 
 muft be at /, as feen from the 
 point 0 ; the trees J. and i), which are • 
 neareft to the eye, appear in their true 
 places. — Now, we fhall fee, by placing 
 the point of diftance in the horizon SP^ 
 
 according 
 
3^ 
 
 PERSPECTIVE 
 
 according to the above*mentioned rule, 
 whether we fhall or fliall not have the 
 apparent places of the trees in the 
 fame points as before, without drawing 
 lines from their true places in the fides 
 of the avenue to the pbferver's eye at 
 
 Take SP equal to S 0, and call P 
 the point of diftance. From ^ draw 
 the ftraight line ^ interfering the 
 perfpedive fide 13 5 of the avenue in 
 the point r, and to that point draw I? c 
 parallel AD ; and you have the firfi: 
 perfpedive fquare AbcDoi the avenue, 
 the very fame as was foun4 before, by 
 the lines BO and CO. 
 
 From the point h draw ^P, interfed- 
 ing BS \Yv the point /; and to that 
 point draw e f parallel to ^/D, and you 
 have the fecoiid perfpedlive fquare 
 b ef f , the fame as before. 
 
 From 
 
MADE EASY. 
 
 33 
 
 From the point e draw eT^ inter- 
 ieding DSvn the point and draw gh 
 parallel to A D j then egbf will be 
 the third perfpedive fquarfe of the ave- 
 nue, as before. 
 
 From the point ^ draw g inter- 
 feding D 5 in the point and drawiit 
 parallel to J which finifhes the 
 fourth and laft perfpedive fquare^ii^ 
 of the avenue. 
 
 In the fame manner you may go 
 on, drawing as many more perfpec- 
 tive fquares up towards S as you 
 pleafe. 
 
 Now, as the ftraight lines AP^ bP^ 
 e P, and g P, (all drawn to the point 
 of diftance P), give the fame points 3, 
 ?*, and /, ^, for the apparent 
 places of the trees, as viewed from 0, 
 that the lines BO, EO^ GO, 10, and 
 g CO, 
 
34 P£ R S PE C TIVE 
 
 CO, FO, HO, and KO, gave before, 
 when drawn from the places of the 
 trees themfelves ; it is plain, that we 
 have put the point of diftance' P in 
 the very point where it ought to be ; 
 that is, juft as far from the point of 
 light S as the obferver's eye at 0 is 
 from it. 
 
 And hence it is evident, that, fup* 
 pofing the eye to be at 0, if the point 
 of diftance had been taken any where 
 between P and S in the horizon S P, 
 all the lines drawn from it into the 
 perfpeftive avenue A i kD would have 
 gone above their true places, and 
 would have given the points for the 
 apparent places of the trees beyond 
 thofe in v/hich the eye at 0 could fee 
 them ; and would alfo have made all 
 the perfpective fquares in the avenue 
 
 too broad. On the contrary, if the 
 
 point of diftance had been taken any 
 
 where • 
 
M A D E E A S Y. 35 
 
 where beyond P from all the lines 
 drawn from that point of diftance 
 would have gone below their true 
 places in the perfpedive avenue ; and 
 confequently have brought the ap- 
 parent places of the trees too near 
 the obferver's eye, and have made all 
 the perfpeclive fquares of the avenue 
 narrower than they could really ap- 
 pear to the obferver at 0. 
 
 15. Hence it is manifeft, that, when 
 large objects are to be drawn in per- 
 fpedive, the point of diftance muft 
 be taken at leaft as far from the point 
 of fight, as the obferver could ftand 
 from the point of fight when he fees 
 the fide of the object next to him un- 
 der an angle of fixty degrees. But in 
 drawing agreeable perfpeclive views 
 of fmall objeds, the obferver fhould 
 be *confidered as viewing them under 
 an angle not exceeding 30 degrees at 
 moft : and fuppofing him to fee them 
 C 2 under 
 
S6 PERSPECTIVE 
 
 under that angle, take the diftance of 
 his place from the point of fight in 
 your compafles, and fet off that ex- 
 tent from the point of fight in the 
 horizon, to find the point of difl:ancQ 
 therein. 
 
 OPERATION XL 
 
 To put a Square in PerfpeBive^ as feen by 
 a Per/on not Jlanding right againji the 
 Middle of either of its Sides, hut rather 
 nearly even with one of its Corners. 
 
 i6. In Fig. 7. of Plate I. let JBCD 
 be a true fquare, viewed by an ob- 
 ferver, not fl:anding at o, directly 
 againft the middle of its fide A 
 but at 0 alm.ofl: even with its corner 
 jD, and viewing the fide AD under 
 the angle AO D ; the angle AoD (un- 
 der 
 
MADE EASY. 
 
 37 
 
 der which he would have feen AD 
 from 0 ) being 60 degrees. 
 
 Make JD in Fig. 8. equal to AD in 
 Fig. 7. and draw S P and 0 0 parallel 
 to A jD, Then, in Fig. 8. let 0 be the 
 ^lace of the obferver's eye, and •S 0 be 
 perpendicular to S'P (as before, § 12. 
 13.), then S fhall be the point of fight 
 in the horizon SP. 
 
 •Take 5 0 in your compafles, and fet 
 that extent from 5' to P; then P fhall 
 be the true point of diftance, taken 
 according to the foregoing rules, § 12. 
 and 13. 
 
 From A and D draw the ftraight 
 lines A S and D S : draw alfo the 
 ftraight line AP, interfering DS in C. 
 Laftly, to the point of interfedion 0 
 draw B C parallel to AD; and AB CD 
 in Fig. 8. will be a true perfpeftive 
 C 3 repre* 
 
PERSPECTIVE 
 
 reprefentation of the fquare A BC H 
 in Fig. 7. The point M is the centre 
 o each fquare, and A MC and 5 iW D 
 are the diagonals. 
 
 OPERATION III. 
 
 To put a reticulated Square in FerfpeElive^ 
 as feen by a P erf on Jlanding oppofiie tQ 
 the Middle of one of its Sides. 
 
 1 7. A RETICULATED fquare is one that 
 is divided into feveral Uttle fquares, 
 like net-work, as Fig. 4. of Plate II. 
 each fide of which is divided into four 
 equal parts, and the whole furface 
 into four times four (or 16) equal 
 fquares. 
 
 Having divided this fquare into the 
 given number of lefTer fquares, draw 
 the two diagonals Ax C and BxD. 
 
 Make 
 
MADE EASY. 
 
 39 
 
 Make AD in Fig. 5. equal to AD 
 Fig. 4. and divide it into four equal 
 parts, as A e g and iD, 
 
 Draw SP for the horizon, parallel 
 to AD^ and, through the nf^iddle 
 point ^ of AD^ draw 0 S perpendicu- 
 lar to ^ D and 5 P, — Make S the point 
 of fight, and 0 the plage of the obfer- 
 ver's eye. 
 
 Take S P equal tQ S 0, and P fhall 
 be the true point of diftance. — Draw 
 A S and D 5 to the point of fight, and 
 A P to the point of diftance, inter- 
 fering D S in C; then draw B C pa- 
 rallel to AD^ and the outlines of the 
 reticulated fquare A BCD wilj be finifh- 
 ed. 
 
 From the divifion-points <?, g^ draw 
 the ftraight lines ef^ g ik^ tending 
 towards the point of fight S ; and draw 
 BD for one of the diagonals of the 
 C 4 fquar^, 
 
40 
 
 PERSPECTIVE 
 
 fquare, the other diagonal AC being 
 already drawn. 
 
 Through the points r and j-, where 
 thefe diagonals cut ef and i draw 
 / m parallel to A D. Through the cen- 
 tre-point where the diagonals cut 
 ^ bj draw n o parallel to A D — Laftly, 
 through the points v and Wj where 
 the diagonals cut c f and i draw p q 
 parallel to AD; and the reticulated 
 perfpedive fquare will be finiflied. 
 
 This fquare is truly reprefented as 
 if feen by an obferver ftanding at 0, 
 and having his eye above the hori- 
 i:ontal plane A B C D on which it is 
 drawn ; as if OS was the height of 
 his eye above that plane : and the 
 lines which form the fmall fquares 
 within it have the fame letters of re^ 
 ference with thofe in Fig. 4. which is 
 drawn as it would appear to an eye* 
 
 placed 
 
MADE EASY. 41 
 placed perpendicularly above its centre 
 
 X, 
 
 OPERATION IV. 
 
 To put a Circle in TerfpeEtive, 
 
 18. If a circle be viewed by an eye 
 placed directly over its centre, it ap- 
 pears perfectly round, as Fig. 2.; but 
 if it be obliquely viewed, it appears 
 of an elliptical fhape, as Fig. 3. This 
 is plain by looking at a common wine- 
 glafs fet upright on a table. 
 
 19. Make a true reticulated fquare, 
 as Fig. 4. of Plate II. of the fame dia- 
 meter as you would have the circle ; 
 and fetting one foot of your compalTes 
 in the centre x, defcribe as large a 
 circle as the fides of the fquare will 
 contain. Then, having put this reti- 
 culated 
 
42 
 
 PERS PECTIVE 
 
 ticulated fquare into perfpeftive, as in 
 Fig. 5. obferve through what points 
 of the crofs lines and diagonals of 
 Fig. 4. the circle pafles ; and through 
 the like points in Fig. 5. draw the el- 
 lipfis, which will be as true a perfpec- 
 tive reprefentation of the circle, as the 
 fquare in Fig. 5. is of the fquare in 
 Fig. 4. 
 
 OPERATION V. 
 
 To put a 7' eticulated Square in PerfpeEiive^ 
 as feen by a Ferfon not Jlanding right 
 againjl the Middle of either of its Sides ^ 
 but rather nearly even with one of its 
 Corners. 
 
 20. In Fig. 6. of Plate II. let 0 be 
 the place of an obferver, viewing the 
 fquare A B G D almoft even with its 
 
 corner JD Draw at pleafure SP for 
 
 the 
 
MADE EASY. 
 
 43 
 
 the horizon, parallel to A D, and 
 make S 0 perpendicular to S P : then, 
 S fhall be the point of fight ; and P 
 tjie true point of diftance, if 5 P be 
 made equal to, SO. . . 
 
 Draw J S and D 5* to the point of 
 fight, and A P to the point of difl;ance, 
 interfering Z) S in the point C ; then 
 draw B C parallel to A Z), and the out- 
 lines of the perfpe£live fquare will be 
 finiftied. This done, draw the lines 
 which form the leflir fquares, as 
 taught in Oper. III. and the work will 
 
 be completed. You may put a per- 
 
 fpedive circle in this fquare by the 
 fame rule as it was done in Fig. 5. 
 
 OPERA. 
 
44 
 
 PERSPECTIVE 
 
 OPERATION VI. 
 
 To put a Cube in PerfpeBive^ as if viewed 
 by a Per/on Jlanding almojl even with 
 one of its Edges ^ and feeing three of its 
 Sides. 
 
 21. In Fig. 7. of Plate II. let ^5 be 
 the breadth of either of the fix equal 
 fquare-fides of the cube AG ; 0 the 
 place of the obferver, almoft even 
 with the edge CD of the cube, S the 
 point of fight, SP the horizon pa- 
 rallel to j4 D, and F the point of 
 diflance taken as before. 
 
 Make A B CD a true fquare ; draw 
 B S and C S to the point of fight, and 
 B P to the point of diftance, interfecl- 
 ing ^75 in G. — Then draw F G parallel 
 to B C, and the uppermoft perfpective 
 , fquare- 
 
MADE EASY. 
 
 45 
 
 fquare-fide ^ G C of the tube will be 
 finiflied. 
 
 Draw D S to the point of fight, and 
 A P to the point of diftance, interfer- 
 ing D 5" in the point / ; then draw G I 
 parallel to CD ; and, if the cube be 
 an opaque one, as of wood or metal, 
 all the outlines of it will be finiflied ; 
 and then it may be fhaded as in the 
 figure. 
 
 But if you want a perfpedive view 
 of a tranfparent glafs cube, all the 
 fides of which will be feen ; draw A H 
 toward the point of fight, F H parallel 
 to BA^ and ///parallel to AD : then 
 A HID will be the fquare-bafe of the 
 cube, perfpedively parallel to the top 
 BFGC ; ABFH will be the fquare- 
 fide of the cube, parallel to C G I D^ 
 ixnd FGIH will be the fquare-fide pa- 
 xallel to A BCD, 
 
 As 
 
46 PERS PECTIVE 
 
 As t6 the fhading part of the work^ 
 it is fuch mere children's play, iii 
 comparifon of drawing the lines which 
 form the fhape of any objedl, that no 
 rules need be given for it. Let a per- 
 fon fit with his left fide toward a win- 
 dow, and he knows full well, that if 
 any folid body be placed on a table 
 before him, the light will fall on the 
 left-hand fide of the body, and the 
 right-hand fide will be in the fhade. 
 
 OPERATION VII. 
 
 'To put a Square Taveinent in FcrfpeEtive^ 
 conjyiing of any given Square Numbe?'^ 
 of equal Hack and white Square Pieces of 
 Marble^ and viewed by a perfon Jlanding 
 
 at 
 
 * A fqvare numoer is the produ6l of any given number 
 multiplied by itfelf. Thus, 1^4 is the Square of i 2 j lor 
 times 12 is 144 ; and 256 is the fquare of 16, 
 
MADE EASY. 
 
 47 
 
 at a dijlance from it^ almojl even with 
 one of it^ Corners, 
 
 2 2. In Fig. I. of Plate III. let 5* P be 
 the horizon, 5* P perpendicular to S P, 
 0 the place of the obferver, viewing 
 the fquare black and white marble 
 pavement A BC nearly even with 
 the corner D ; S the point of fight, P 
 the point of diftance (§ I2.), and the 
 fide ^ jD be parallel to S P. 
 
 Suppose the fide AD (equal to the 
 breadth of the pavement) to be 1 6 feetf 
 and that each fquare piece of marble 
 in the pavement is a foot broad ; then 
 the whole pavement will contain 2^6 
 of thefe fquare pieces ; for i6 times i6 
 is 256; that is, 256 is the fquare of 16. 
 
 Divide A D into 1 6 equal parts, as 
 A bj b c 8cc. and from thefe points 
 
 of 
 
48 
 
 PERSPECTIVE 
 
 of divifion, &c. draw ftraight 
 
 lines to the point of fight iS*. 
 
 From P, the point of diftance, draw 
 the ftraight Une F Z), interfeding A S 
 in the point B; then, from B draw 
 B C parallel to A Z), which will com- 
 plete the outlines of the perfpeftive 
 fquare-pavement A B CD. 
 
 Through the points where the dia- 
 gonal B D interfedts the lines drawn 
 from <7, &c. toward the point of 
 ^ight draw ftraight lines parallel to 
 A D (as in Oper. III. and V.), and you 
 will have divided the fquare -pave- 
 ment A B CD into 256 lefler fquares ; 
 one half of which may be fliaded 
 black, and the other half left white, 
 to reprefent the 256 fquare pieces of 
 black and white marble which com- 
 ppfe the pavement. 
 
 OPERA- 
 
MAJ)E EASY. 
 
 49 
 
 OPERATION VIIL 
 
 To put an oblong Square Pavement in Per^^ 
 fpeSiivey who/e Length is equal to any 
 given Number of Times its Breadth. 
 
 23. In Fig. I. of Plate III. fuppofe 
 the given length D F ox A E to be 32 
 feet, and the given breadth ^ Z) to be 
 16. We have already got half the 
 given length DC in the perfpedive 
 fquare A B C D ; and fuch another 
 added to it will complete the perfpec- 
 tive figure of the pavement. 
 
 To the right-hand top-corner C of 
 the fquare A B C Z), draw the ftraight 
 line P C from the point of diftance P, 
 interfeding A S E : from the point 
 E draw E F parallel to A Z), and the 
 outlines of the fecond fquare B E F C 
 will be completed ; which, as in the 
 D figure, 
 
50 PERSPECTIVE 
 
 figure, may be divided into 256 lefler 
 fquares, by the fame method that 
 A B C D was fo divided : and then, in 
 perfpedive, the length of the oblong 
 fquare pavement AEFD will be twice 
 as great as its breadth ; and the whole 
 will contain 512 leffer fquares. 
 
 24. If the given length be equal to 
 three times the breadth, we muft have 
 a third perfpedive fquare L G H F 
 joined to the top of the fecond fquare 
 BEFC. 
 
 From the point of diflance P, draw 
 the ftraight line P F to the right-hand 
 top-corner F of the fecond fquare, and 
 interfeding A S 2ii G : then from the 
 point G draw G H parallel to A Z), 
 which will complete the third per- 
 fpedive fquare E G H F, — This fquare 
 (like the former two) may be fub- 
 divided into 256 lefler fquares ; and 
 
 then 
 
MADE EASY. 
 
 then we fliall have an oblong fquare 
 pavement AGHD^ whofe perfpedive 
 length is equal to three times each 
 breadth, and divided into 768 lefTer 
 fquares. 
 
 25. And thus (as is plain by the 
 figure) you may proceed, and make 
 as many more perfpedive fqUares 
 (GIKH, ILMK, LNOM, &c.) as you 
 pleafe. — There are ten fuch fquares 
 in this figure ; and if we fuppofe each 
 of them to be 16 feet broad, and paved 
 with black and white marble, as A BCD 
 is, the whole pavement, being ten 
 times as long as it is broad, will con- 
 tain 2560 fquare feet of marble fur- 
 face. 
 
 OPERA- 
 
PERSPECTIVE 
 
 OPERATION IX. 
 
 To put a Square Pyramid in PerfpeBive, 
 as if Jlanding upright on its Bafe^ and 
 viewed obliquely, 
 
 26. In Fig. 2. of Plate III. let JD be 
 the breadth of either of the four fides 
 of the pyramid ATC D at its bafe 
 jl B C D ; and M T its perpendicular 
 height. Let 0 be the place of the ob- 
 ferver, iS his point of fight, SE his 
 horizon, parallel to AD^ and perpen- 
 dicular to 0 ; and let the proper 
 point of diftance be taken in ^£ pro- 
 duced toward the left hand, as far 
 from as 0 is from S, 
 
 Draw A S and D S to the point of 
 fight, and D L to the point of difl:ance, 
 interfering A S in the point B. Then 
 
 from 
 
MADE EASY. 53 
 
 from draw jBC parallel to AD ; and 
 jlBCD fhall be the perfpedlive fquare 
 bafe of the pyramid. 
 
 Draw the diagonal A C, interfering 
 the other diagonal B D at M, and this 
 point of interfedion fhall be the centre 
 of the fquare bafe. 
 
 Draw MT perpendicular to u^Z), 
 and of a length equal to the intended 
 height of the pyramid : then draw 
 the ftraight lines JT, CT, and D Tj 
 and the outlines of the pyramid (as 
 viewed from 0 J will be finifhed ; 
 which being done, the whole may be 
 £0 lhaded as to give it the appearance 
 of a folid body. 
 
 If the obferver had flood at he 
 could have only feen the fide ATD of 
 the pyramid ; and two is the greatefl 
 number of fides that he could fee from 
 D 3 ^nV 
 
54 
 
 PERSPECTIVE 
 
 any other place of the ground. Bur 
 if he were at any height above the 
 pyramid, and had his eye diredly 
 over its top, it would then appear like 
 Fig. 3. and he would fee all its four 
 fides EFGHy with its top t juft over 
 the centre of its fquare bafe BCD ; 
 which would be a true geometrical, 
 and not a perfpedive, fquare. 
 
 OPERATION X. 
 
 To put two equal Squares in Ferfpeclive^ 
 one of which Jhall he direBly over the 
 other ^ at any given dijlance from itj and 
 both of them parallel to the Plane cf the 
 Horizon, 
 
 27. In Fig. 4. of Plate III. let A BCD 
 be a perfpedlive fquare on a horizon- 
 tal plane, drawn rxcording to the fore- 
 going rules (§ 1 6.% S being the point 
 
 of 
 
MADE EASY. 
 
 55 
 
 of fight, SP the horizon (parallel to 
 AD) J and P the point of diftance. 
 
 Suppose AD, the breadth of this 
 fquare, to be three feet ; and that it 
 is required to place juft fuch another 
 fquare £ jF G diredly above it, pa- 
 rallel to it, and two feet from it. 
 
 Make A E and D H perpendicular 
 to A Z), and two thirds of its length : 
 draw E which will be equal and 
 parallel to AD ; then draw E S and 
 H S to the point of fight and E P 
 to the point of difl:ance P, interfering 
 // S in the point G : this done, draw 
 F G parallel to E H ; and you will 
 have two perfpedive fquares A B CD 
 and EF G Hy equal and parallel to one 
 another, the latter diredly above the 
 former, and two feet difiant from it ; 
 as was required. 
 
 D4 JBv 
 
PERSPECTIVE 
 
 By this method, fhelves may be 
 drawn, parallel to one another, at any 
 diftance from each other, in propor- 
 tion to their length. 
 
 OPERATION XL 
 
 « 
 
 To put a Square Table in PerfpeBive^ 
 Jlanding on four upright Square Legs 
 of any given Length with refpeEt to 
 the Breadth of the T able. 
 
 ' 28. In Fig. 4. of Plate III. let A BCD 
 be the fquare part of the floor on 
 which the table is to fland, and 
 t) F G H the furface of the fquare 
 table, parallel to the floor. 
 
 Suppose the table to be three feet in 
 breadth, and its height from the floor 
 to be two feet ; then, two thirds of 
 
 AD 
 
MADE E A S Y. 
 
 57 
 
 A D or E H will be the length of the 
 legs / and k ; the other two ( 1 and m ) 
 being of the fame length in perfpec- 
 tive. 
 
 Having drawn the tw^o equal and 
 parallel fquares J B CD ^nd EFG H, 
 as fhe\ra in Oper. X. let the legs be 
 fquare in form, and fixed into the 
 table at a diftance from its edges 
 equal to their thicknefs. Take A a 
 and D d equal to the intended thick- 
 nefs of the legs, and a h and d c alfo 
 equal thereto. Draw the diagonals 
 A C and B D, and draw ftraight lines 
 from the points, ^, r, d^ towards the 
 point of fight 5, and terminating at 
 the fide B C. Then, through the points 
 where thefe lines cut the diagonals, 
 draw the ftraight lines and c?, p and 
 
 parallel to A D ; and you will have 
 formed four perfpeclive fquares (like 
 ABCD in Fig. 2.) for the bafes of the 
 
 four 
 
5S 
 
 PERSPECTIVE 
 
 four legs of the table : and then it is 
 eafy to draw the four upright legs by 
 parallel lines, all perpendicular to 
 A D, and to fliade them as in the fi- 
 gure. 
 
 To reprefent the intended thicknefs 
 of the table-board, draw e h parallel to 
 EH and HG toward the point of fight 
 S: then fiiade the fpaces between 
 thefe lines, and the perfpedive figure 
 of the table will be finiflied. 
 
 OPERATION XII. 
 
 To put an oblong Square Table in P erf pec- 
 tive^ of any given Length with refped 
 to its Breadth. 
 
 29. Suppose the given length to be 
 four feet, and the breadth to be three. 
 
 —In 
 
MADE EASY. 59 
 
 —In Fig. 6. of Plate II. let A D be the 
 length, and divide it into four equal 
 parts, u4 ej e g /, i D : draw A S and 
 to the point of fight S ; and A P 
 to the point of diftance P. 
 
 From the point which is three 
 fourths of A jD, draw i s toward the 
 point of fight, till it meets the dia- 
 gonal A C in J- ; then, through that 
 point of meeting, draw / m parallel to 
 AD; and you will have an oblong 
 fquare A Im D, whofe breadth A I ox 
 D m is perfpedively equal to three 
 quarters of its length A D, 
 
 30. Let the breadth of the table be 
 equal to half its length AD. — From 
 g^ the middle point between A and 
 JD, draw g x toward the point of fight 
 5, till it meets the diagonal AC in the 
 point X ; then, through the point 
 draw n 0 parallel to A Z), and you will , 
 
 have 
 
6o PERSPECTIVE 
 
 have an oblong fquare AnoD^ whofe 
 length AD is equal to twice its 
 breadth An ox D o. 
 
 31. Suppose the length to be equal 
 
 to four times the breadth From a 
 
 fourth part of the diftance between A 
 and jD, draw e v toward the point 
 of light Sj till it meets the diagonal AC 
 at V ; then, through that point of 
 meeting, draw p q parallel to A D, and 
 you will have an oblong fquare ApqDy 
 whofe length A D is four times as 
 great as its perfpeftive breadth Ap ox 
 Dp. 
 
 In this manner, you may make the 
 breadth bear any proportion to the 
 length that you pleafe ; and may put 
 legs to the table, as Ihewn in Oper, XI. 
 
 OPERA- 
 
MADE EASY. 
 
 6i 
 
 OPERATION XIII. 
 
 To put fiveSquarePyramidf in PerfpeBive^ 
 Jlanding upright on a Square Pavement 
 compofed of the Surfaces of Cubes, 
 
 32. In Fig. I. of Plate IV. let ^5 CD 
 be a perfpedlive fquare drawn ac- 
 cording to the foregoing rules ; S the 
 point of fight, P the point of diftance 
 in the horizon P 5, and A C and B D 
 the two diagonals of the fquare. 
 
 Divide the fide A D into 9 equal 
 parts, (becaufe 9 times 9 is 8 1 ) as ^ 
 ah^ hc^ &c. and from thefe points of 
 divifion, d^ &c. draw lines to- 
 
 ward the point of fight 5*, terminating 
 at the furthermofi: fide B C of the 
 fquare. Then, through the points 
 where thefe lines cut the diagonals, 
 
 draw 
 
62 PERSPECTIVE 
 
 draw ftraight lines parallel to A D 
 (as in Oper. III.)? and the perfpedive 
 fquare ABCD will be fubdivided into 
 8 1 lefTer fquares, reprefenting the up- 
 per furfaces of 8i cubes, laid clofe to 
 one another's fides, in a fquare form. 
 
 Draw A K and D L, each equal to 
 A and perpendicular to A D ; and 
 draw L N toward the point of fight S : 
 then draw KL parallel to A and 
 its difl:ance from A D will be equal to 
 A a, — This done, draw ^7/7, c d 0^ 
 c pjf q^g r, and h j*. all parallel to AK; 
 and the fpace A D L K will be fub- 
 divided into nine equal fquares, which 
 are the outer upright furfaces of the 
 nine cubes in the fide A D oi the 
 fquare ^5 CD. 
 
 Draw L N toward the point of fight 
 S; and from the points where the 
 lines which are parallel to A D in 
 
 this 
 
MADE EASY. 
 
 63 
 
 this fquare meet the fide CD thereof, 
 draw fliort lines to L all parallel to 
 D Lj and they will divide that fide 
 into the outer upright furfaces of the 
 nine cubes which compofe it : and 
 then the outfides of all the cubes that 
 can be vifible to an obferver, placed 
 at a proper diftance from the corner 
 D of the fquare, will be finifhed. 
 
 As taught in Oper. IX. place the 
 pyramid A E upright on its fquare 
 bafe A t V <7, making it as high as you 
 pleafe ; and the pyramid D H on its 
 fquare bafe b u w D, of equal height 
 with A E. 
 
 Draw E H from the top of one of 
 thefe pyramids to the top of the 
 other ; and E H will be parallel to 
 AD. 
 
 Draw ES and //5 to. the point of 
 
 fight 
 
64 
 
 PERSPECTIVE 
 
 fight and HP to the point of dif- 
 tance P, interfering ES in F. 
 
 From the point draw FG parallel 
 to E H ^ then draw E G, and you will 
 have a perfpeftive fquare E FGH (pa- 
 rallel to ABCD)^ with its two dia- 
 gonals £ G and F ZT, interfering one 
 another in the centre of the fquare at 
 /. The four corners of this fquare, 
 £5 Gy Hj give the perfpe£i:ive heights 
 of the four pyramids, BFj CG^ 
 and D H ; and the interferon / of the 
 diagonals gives the height of the py- 
 ramid M/, the centre of whofe bafe is 
 the centre of the perfpedtive fquare 
 A BCD. 
 
 Lastly, Place the three pyramids 
 B F^ C Gj Ml^ upright on their refpec- 
 tive bafes at C, and M ; and the 
 required perfpedive reprefentation will 
 be finiflied, as in the figure. 
 
 OPERA- 
 
MADE EASY. 65 
 
 OPERATION XIV, 
 
 To put upright Tyramids in PerfpsBive^ 
 on the Sides of an ohlong Square or Pa- 
 rallelogram ; Jo that their Dijlances 
 Jrom one another JJjall be equal to the 
 Breadth of the Parallelogram, 
 
 In moft of the foregoing operations^ 
 we have confidered the obferver to be 
 fo placed, as to have an obhque view 
 of the perfpective objeds : in this, we 
 ihall fuppofe him to have a dired: 
 view of Fig. 2. Plate IV. that is, ftand- 
 ing right againft the middle of the 
 end A D which is neareft to his eye, 
 and viewing AD under an angle of 
 60 degrees. § 10. 
 
 Having cut ^ D in the middle, by 
 the perpendicular line S Sj take S 
 E therein 
 
66 
 
 PERSPECTIV.E 
 
 therein at pleafure for the pomt of 
 fight, and draw £5* for the horizon, 
 parallel to AD, — Here Ss muft be 
 fuppofed to be produced downward, 
 below the limits of the plate, to the 
 place of the obferver ; and S E to be 
 produced towards the left hand be- 
 yond £, far enough to take a proper 
 point of diftance therein, according 
 to the foregoing rules. 
 
 Take ^ i at pleafure, and equal 
 to A for the breadths of the fquare 
 bafes of the two pyramids A E and 
 D F next the eye : then draw A S and 
 d and likewife D S and g Sj to the 
 point of fight S ; and Z) G on to the 
 point of diftance, interfering ^5 in 
 G : then, from G draw G I parallel to 
 A jD, and you will have the firft per- 
 fpedive fquare AG ID of the paral- 
 lelogram A BCD. 
 
 From 
 
MAl)E EASY. 
 
 67 
 
 From / draw IH to (or toward) the 
 point of diftance, interfeding ^ S in 
 H: then, from H draw H parallel 
 to ^ Z), and you will have the fecond 
 perfpedive fquare G HKI of the paral- 
 lelogram Go on in this manner 
 
 (which is the fame with the method 
 demonftrated in Ope?\ I.) till you have 
 drawn as many perfpedlive fquares up 
 towards S as you pleafe^ 
 
 Through the point e, where D G 
 interfeds g draw bf parallel to AD: 
 and you will have formed the two 
 perfpedive fquare bafes J h c and 
 efDg of the two pyramids at A 
 and JD. 
 
 F ROM the point / (the upper outward 
 corner of efDg) draw fh toward the 
 point of diftance, till it meet A S ui 
 b ; then, from this point of meeting, 
 E 2 draw 
 
68 PERSPECTIVE 
 
 draw h m parallel to G /, and you will 
 have formed the two perfpecSive fquares 
 Ghih and Imln^ for the fquare bafes 
 of the two pyramids at G and /. 
 
 Proceed in the fame manner to find 
 the bafes of all the other pyramids, at 
 the corners of the reft of the perfpec- 
 tive fquares in the parallelogram 
 A B C as fhewn by the figure — 
 Then, 
 
 Having placed the firft two pyra- 
 mids at A and D upright on their 
 fquare bafes, as fhewn in Oper. IX. and 
 made them of any equal heights at 
 pleafure, draw ES and FS from the 
 tops of thefe pyramids to the point of 
 fight S : place all the reft of the pyra- 
 mids upright on their refpedlive bafes, 
 making their tops touch the ftraight 
 lines E S and FS s and all the work, 
 
 except 
 
 V 
 
MADE EASY. 
 
 69 
 
 except the fhadiug part, will be finifh- 
 ed. 
 
 33. Remark It mufl be acknow- 
 ledged, that there is fomething in this 
 figure not quite agreeable to the eye ; 
 which is, that the two pyramids at 
 G and / feem to be too far from 
 thofe at A and D, when compared 
 
 with the diftances between the reft 
 
 But this arifes from their being viewed 
 (in the figure) at a greater diftance 
 than the obferver is fuppofed to be at 
 from the point of fight S; which is but 
 7 inches and three fourths of an inch, 
 in viewing A D under an angle of 60 
 degrees ; whereas, in viewing the fi- 
 gure, we feldom bring the paper with- 
 in lefs than a foot from the eye. — 
 But, if a perfon who looks at the fi- 
 gure will place his eye diredly over the 
 point of fight 5, fo that an imaginary 
 line 71 inches long, from the point of 
 fight, and perpendicular to the fur- 
 E 3 face 
 
70 
 
 PERSPECTIVK 
 
 face of the paper, fhall touch his 
 eye, the dilagreeable idea will vanifh, 
 and the reprefentation will appear na- 
 tural. 
 
 On which it may be proper to ob- 
 ferve, that, when people look at per- 
 fpective drawings, they generally keep 
 their eye at a greater diftance than 
 what would form an angle of 60 de- 
 grees with the boundaries of the ob- 
 ject ; and therefore they fee it under 
 an angle confiderably lefs than 60 de- 
 grees. And, for this reafoiL, it may be 
 proper to inform the learner, that, in 
 drawing perfpective reprefentations of 
 objects, he had better put his fuppofed 
 obferver's ftation fa far from the fide 
 A D next his eye, that it may not fub- 
 tend an angle of more than 45 degrees, 
 or 50 at moft ; and then the drawings 
 will have a much more agreeable ap- 
 pearance. 
 
 It 
 
MADE EASY. 
 
 It is true, that this caution, though 
 generally neceflary, is attended in 
 pradice with a fmall inconvenience ; 
 which is, that as the point of diftance 
 muft always be placed as far from the 
 point of fight as the obferver is fup- 
 pofed to be from it, the fchemes, 
 though but fmall, muft be drawn on 
 large paper ; otherwife the point of 
 diftance may fall without the limits of 
 the paper ; as it does even in this fi- 
 gure, (Fig. 2.), on account of the 
 breadth thereof from A to Z), although 
 it is drawn as if viewed under an angle 
 of 60 degrees — But this is of very little 
 moment, as it is eafy to fix a long flip 
 of paper by two wafers to the edge of 
 that on which any fcheme is drawn; fo 
 that the hori-^on-line may be extended 
 out on that flip, to find the point of dif- 
 tance therein, as far from the point of 
 fight as you pleafe. 
 
 E4 
 
 OPERA- 
 
7f PERSPECTIVE 
 
 OPERATION XV. 
 
 To put a Rummer or Drinking-Glafs in 
 PerfpeBive, 
 
 34. According to the foregoing me- 
 thod ( Oper. X.), draw the two equal 
 and parallel perfpedive fquares A BCD 
 and EFGH in Fig. 3. of Plate TV. the 
 latter diredly above the former. Then, 
 as in Oper. IV. put a perfpedive circle 
 in the lowermoft fquare for the bottom 
 of the cup, and one in the uppermoft 
 for the top or brim thereof, and draw 
 out the reft of the figure in whatever 
 fliape you pleafe. 
 
 OPERA 
 
MADE EASY. 
 
 OPERATION XVI. 
 
 To put a Square Pyramid of equal-fized 
 Cubes in Perfpeciive, 
 
 35. Fig, 2. of Plate V. reprefents a 
 pyramid of this kind ; confifting (as it 
 were) of fquare tables of cubes, one 
 table above another ; 81 in the loweft, 
 49 in the next, 25 in the third, 9 in 
 the fourth, and i in the fifth or upper- 
 moft. Thefe are the fquare numbers 
 
 9? 7> 5? 3> and I. 
 
 If the artift is already mafter of all 
 the preceding operations, he will find 
 lefs difficulty in this, than in attending 
 to the following defcription of it ; for 
 it cannot be defcribed in a few words, 
 but may be executed in a very fhort 
 timeo 
 
74 
 
 PERSPECTIVE 
 
 In Fig. I . having drawn P S for the 
 horizon, and taken S for the point of 
 fight therein, (the obferver being at 0), 
 draw ^ D parallel to P for the fide 
 (next the eye) of the firft and lower- 
 mofl: table of cubes. Draw y4 S and 
 D S to the point of fight S, and D P to 
 the point of diftance P, interfering 
 j1 S in the point B. Then, from jS 
 draw B C parallel to ^ D, and you will 
 have the furface ABCD of the firft; 
 table. 
 
 Divide A D into nine equal parts, 
 A ah^ b c &c. then make 
 A K and Z)Zi equal to Aa^ and perpen- 
 dicular to A D, Draw K L parallel to 
 AD^ and from the points of equal di- 
 vifion at <7, ^, &c. draw lines to KLj 
 all parallel to A K. Then draw h S 
 to the point of fight and from the 
 divifion-points <7, r, &c. draw 
 lines with a black lead pencil, all 
 
 tending 
 
MADE EASY. 
 
 tending towards the point of fight, till 
 Ithey meet the diagonal B D of the 
 fquare. 
 
 Fkom thefe points of meeting draw 
 black-lead lines to D C, all parallel to 
 AD; then draw the parts of thefc 
 lines with black ink which are mark- 
 ed I, 2, 3, 4, &c. between hE and 
 DC, 
 
 Having drawn the firft of thefe lines 
 A q with black ink, draw the parts a ?, 
 bk, c l^ &c. (of the former lines which 
 met the diagonal B D) with black 
 ink alfo ; and rub out the reft of the 
 black-lead lines, which would other- 
 wife confufe the following part of the 
 work. Then, draw L F toward the 
 point of fight S ; and, from the points 
 .where the lines i, 2, 3, 4, &c. meet 
 the line D C, draw lines down to L F, 
 gll parallel to D L ; and all the vifible 
 
 lines 
 
76 PERSPECTIVE 
 
 lines between the cubes in the firft 
 table will be finifhed. 
 
 Make / G equal and perpendicular to 
 fi /, and J M equal and parallel to i G: 
 then draw GM, which will be equal 
 and parallel to i q. From the points 
 i, /, &c. draw lo^ m p, &ic, 
 
 all parallel to i Gy and the outfides of 
 the feven cubes in the fide Gq of the 
 fecond table will be finifhed. 
 
 Draw G S and M S to the point of 
 fight 5, and M P to the point of dif- 
 tance interfeding G S in H; then, 
 from the point of interfeftion //, draw 
 /f/ parallel to AD ; and you will have 
 the furface GHIM of the fecond table 
 of cubes. 
 
 From the points /», q^ &c. draw 
 black-lead Imes tow^ard the point of 
 fight till they meet the diagonal 
 
 MH 
 
MADE EASY. 
 
 77 
 
 M H of the perfpedive fquare furface 
 G HI M ; and draw s M with black 
 ink toward the point of fight. 
 
 From thofe points where the lines 
 drawn from />, 5^, &c. meet the 
 diagonal M draw black-lead lines 
 to M/, all parallel to ; only draw 
 the whole firft line y i with black ink, 
 and the parts 2, 3, 4, &c. and fi tj 0 Uj 
 p &c. of the other lines between j N 
 and MIy and GM and 71, with the 
 fame ; and rub out all the reft of the 
 black-lead Unes, to avoid further con- 
 fufion. Then, from the points where 
 the fliort lines i, 2, 3, &c. meet the 
 line MIy draw lines down to g all 
 parallel to My, and the outer furfaces 
 of the feven cubes in the fide ME 
 will be finiflied; and all thefe laft lines 
 will meet the former parallels 2, 3, 4, 
 &c. in the line g E. 
 
 Make 
 
;3 PERSPECTIVE 
 
 Make tO equal and perpendicular to 
 7 and y equal and parallel lo tOj 
 then draw 0 P, which will be equal 
 and parallel to t y — This done, draw 
 0 S and P 5^ to the point of fight 
 and P P to the point of diftance P in 
 the horizon. Laftly, from the point 
 where P P interfeds 0 5, draw ^i? 
 parallel to 0 P ; and you will have the 
 outlines 0 P of the furface of the 
 third perfpe£live table of cubes. 
 
 From the points draw up* 
 
 right lines to 0 P, all parallel to t 0^ 
 and you wdll have the outer furfaces 
 of the five cubes in the fide Oy of this 
 third table. 
 
 From the points where thefe up- 
 right lines meet OP, draw lines toward 
 the point of fight till they meet the 
 diagonal P and from thefe points 
 of meeting draw lines to P P, all pa- 
 rallel to 0 P, marking the parts 2, 3, 
 
 4? 
 
MADE EASY. 
 
 79 
 
 4, 5, of thefe lines with black ink 
 which lie between Z r and F R, 
 Then, from the points where thefe 
 lines meet P draw lines down to 
 y N ; which will bound the outer fur- 
 faces of the five cubes in the fide FN 
 of the third table. 
 
 Draw the line 1 1 w^ith black ink ; 
 and, at a fourth part of its length, be- 
 tween S and Z, draw an upright line 
 to equal in length to that fourth 
 part, and another equal and parallel 
 thereto from Z to ; then draw Sy 
 parallel to S Z, and draw the two up- 
 right and equidiftant lines between 
 S Z and S and you will have the 
 outer furfaces of the three cubes in the 
 fide 5 Z of the fourth table. 
 
 Draw SS and VS to the point of fight 
 S in the horizon, and VF to the point 
 
 of 
 
3a PERS PECTIVE 
 
 of diftance therein, interfering 5^ 5 in 
 T ; then draw T U parallel to S V, and 
 you have STUV^ the furface of the 
 fourth table ; which being reticulated 
 or divided into nine perfpedive fmall 
 fquares, and the uppermoft cube W 
 placed on the middlemoft of the 
 fquares, all the outlines will be finifh- 
 ed ; and when the whole is properly 
 ftiaded, as in Fig 2. the work will be 
 done. 
 
 y 
 
 OPERATION XVIL 
 
 To reprefetit a double Crofs in Per- 
 fpeBive. 
 
 36. In Fig. 3. of Plate V. let ^ BCD 
 2Xi&EF G H be two perfpective fqures, 
 equal and parallel to one another, the 
 uppermoft direftly above the lower- 
 moft, drawn by the rules laid down in 
 
 Oper. 
 
MADE EASY. 8i 
 
 Oper. X. and as far afunder as is equal 
 to the given height of the upright 
 part of the crofs ; S being the point 
 of fight, and F the point of diftance 
 in the horizon F S taken parallel to 
 
 Draw E, D H, and CG; then 
 AEHD SLYid DHGG fhall be the two 
 vifible fides of the upright part of the 
 crofs ; of which, the length J E is 
 here made equal to three times the 
 breadth E H. 
 
 Divide D H into three equal parts, 
 HI, IK, and KD. Through thefe 
 points of divifion, at / and K, draw 
 MO and PR parallel to AD; and 
 make the parts MN, 10, P^, KR, 
 each equal to HI; then draw M P anci 
 0 R parallel to D H 
 
 From M and 0 draw M S and 0 S 
 F to 
 
82 PERSPECTIVE 
 
 to the point of fight 5^; and from the 
 point of diftance P draw P Nj cutting 
 M 5 in T: from T draw T U parallel to 
 MOj and meeting 0 in U; and you 
 will have the uppermofl furface MTUO 
 of one of the crofs pieces of the figure. 
 
 From i?, draw R S to the point of 
 
 fight .S ; and from [7, draw U V pa- 
 rallel to 07? ; and OIJVR ftiall be the 
 perfpe6live fquare end next the eye of 
 that crofs part. 
 
 Draw P Mx (as long as you pleafe) 
 from the point of diftance P, through 
 the corner M; lay a ruler to iVand 5, 
 and draw X N from the line P x ; — then 
 lay the ruler to / and 5, and draw 
 
 rZ S Draw X r parallel to MO, and 
 
 make XW and rS equal and perpen- 
 dicular to XT: then draw W B paral- 
 lel to Xr, and WXTB fliall be the 
 fquare vifible end of the other crofs- 
 part of the figure. 
 
 Draw 
 
MADE EASY. 
 
 83 
 
 Draw B K toward the point of light 
 S ; and from i/draw U P to the point 
 of diftance P, interfering rS in Z : 
 then, from the interfedlion Z, dra^^ 
 Z ^ parallel to M 0, and Z parallel 
 to HD^ and the whole delineation will 
 be finifhed. 
 
 This done, fhade the whole, as in 
 Fig. 4. and you will have a true per- 
 fpedive reprefentation of a double 
 crofs. 
 
 V 2 OPERA-^ 
 
84 PERSPECTIVE 
 
 OPERATION XVIII. 
 
 To put three Rows of upright Square Ob- 
 jects in PerfpeBive^ equal in Size^ and 
 at equal Dijlances from each other ^ on 
 an oblong Square Plane^ the Breadth 
 of which fhall be of any ajfigned Fro-- 
 portion to the Length thereof 
 
 37. Fig. 2. of Plate VI. is a perfpec- 
 tlve reprefentation of an oblong fquare 
 plane, three times as long as it is broad, 
 having a row of nine upright fquare 
 objects on each fide, and one of the 
 fame number in the middle ; all equal- 
 ly high, and at equal diflances from 
 one another, both long-wife and crofs- 
 wife on the fame plane. 
 
 In Fig. I . P 5 is the horizon, S the 
 point of fight, P the point of difl:ance, 
 
 and 
 
MADE EASY. 
 
 85 
 
 ^nd AD (parallel to P S) the breadth 
 of the plane. 
 
 Draw AS^ NS, and DS^ to the point 
 of light S} the point N being in the 
 middle of the line A D : and draw 
 D P to the point of diftance P, inter- 
 feding in the point B; then, 
 from B draw B C parallel to A D, 
 and you have the perfpedlive fquare 
 ABCD. 
 
 Through the point /, where D B 
 interfeds NS^ draw ae parallel to A Dj 
 and you will have fubdivided the per- 
 fpedive fquare A B C D into four lef- 
 fer fquares, ^sAaiNj NieDy aBkiy 
 and ikCe, 
 
 From the point C (at the top of the 
 perfpedive fquare A BCD) draw CP 
 to the point of diftance P, interfeding 
 ^ 5* in £ ; then, from the point E 
 F 3 draw 
 
8^ PERSPECTIVE 
 
 draw E F parallel to ^ D ; and you 
 will have the fecond perfpedtive fquare 
 BEFC. 
 
 Through the point /, where C E in- 
 terfeds NS^ draw b f parallel to J D; 
 and you will have fubdivided the 
 fquare BEFC into the four fquares 
 Bblk.k IfC, bEmk and Im Ff. 
 
 From the point F (at the top of the 
 perfpedive fquare B EF G) draw FP 
 to the point of diftance P, interfecling 
 ^ 5^ in /; then, from the point / draw 
 /iT parallel to J D ; and you will have 
 the third perfpeftive fquare EIKF. 
 
 Through the point where F I m- 
 terfeds NS^ draw eg parallel to ; 
 < and you will have fubdivided the fquare 
 
 EIKF into four lelTer fquares, Ecmn^ 
 mngFj clon^ and noKg, 
 
 From 
 
MADE EASY. B7 
 
 From the point K (at the top of the 
 third perfpedive fquare E I KF) draw 
 KP to the point of diftance P, inter- 
 fering AS in L ; then, from the point 
 L draw L M parallel to A D ; and you 
 will have the fourth perfpeftive fquare 
 ILMK, 
 
 Through the point where KL 
 interfeds NS^ draw dh parallel to AD; 
 and you will have fubdivided the 
 fquare ILMK into the four lefTer 
 fquares I dp 0, 0 ^ h d L q p^ and 
 p q Mh. 
 
 Thus, we have formed an oblong 
 fquare A L MDy whofe perfpedive 
 length is equal to four times its 
 breadth, and it contains 16 equal per- 
 
 fpedive fquares If greater length 
 
 was ftill wanted, we might proceed 
 further on toward S. 
 
 T.^E 
 
88 ' PERSPECTIVE 
 
 Take u4 3 equal to the intended 
 breadth of the fide of the upright 
 fquare objeft A ^ (all the other fides 
 being of the fame breadth), and A 0 
 for the intended height. Draw 0 1 8 
 parallel to JD^ and make D 8 and 4 7 
 equal to ^ 3 ; then draw 3 5", 4.Sj 7 5, 
 and 8 S, to the point of fight 5; and 
 among them we fliall have the perfpec- 
 tive fquare bafes of all the 27 upright 
 objeds on the plane. 
 
 Through the point 9, where DB 
 interfeds 8 draw i i o parallel to 
 A D, and you have the three perfpec- 
 tive fquare bafes A 123, 4567, 
 8 9 10 2), of the three upright fquare 
 objeds at Aj N, and /)» 
 
 Through the point 21, where eb 
 interfeds 8 5, draw 14 11 parallel to 
 AD; and you will have the three per- 
 fpedive fquares ^14 151 6, 171819 
 
MADE EASY. 89 
 
 20, and 21 1 1 ^ 22, for the bafes of the 
 fecond crofs-row of objects ; namely, 
 the next beyond the firft three at 
 N, and D. 
 
 Through the pomt zu^ where CE 
 interfeds 8.9, draw a line parallel to 
 B C\ and you will have three perfpec- 
 tive fquares, at and C, for the 
 
 bafes of the third row of objects ; one 
 of which is fet up at B. 
 
 Through the point r, where f c in- 
 terfeds 8 5, draw a line parallel to bf ; 
 and you will have three perfpective 
 fquares, at 3, /, and .v, for the bafes 
 of the fourth crofs-row of objects. 
 
 Go on in this manner, as you fee 
 in the figure, to find the reft of the 
 fquare bafes, up to L il/ ; and you will 
 have 27 upon the whole oblong fquare 
 
 plane, 
 
90 
 
 PERSPECTIVE: 
 
 plane, on which you are to place the 
 like number of objecSs, as in Fig. 2. 
 
 Having afTumed AO for the per- 
 fpedive height of the three objeds 
 (at and D ) next the obferver's 
 
 eye, and drawn 0 i8 parallel to AD, 
 in order to make the objeds at N and 
 D of the lame height as that at ) ; 
 and having drawn the upright lines 
 415, 7 H^, 8 and D 22, for the 
 heights N and D ; draw 0 S and R 
 i^ S and WSj X S and 22 all to the 
 point of fight S; and thefe lines will de- 
 termine the perfpedively equal heights 
 of all the reft of the upright objeds, 
 as fhewn by the two placed at a and 
 B. 
 
 To draw the fquare tops of thefe ob- 
 jeds, equal and parallel to their bafes, 
 we need only give one example, which 
 will ferve for all. 
 
 Draw 
 
MADE EASY. 91 
 
 Draw 3 R and 2 ^ parallel to ^ 0^ 
 and up to the line RS; then draw 
 P ^parallel to 0 R, and 0 P ^R ftiall 
 be the top of the objed at equal 
 and parallel to its fquare bafe -^123. 
 —In the fame eafy way, the tops of all 
 the other objeds are formed. 
 
 When all the reft of the objeds are 
 delineated, fhade them properly, and 
 the whole perfpedive fcheme will have 
 the appearance of Fig. 2. 
 
 OPERA- 
 
92 
 
 PERSPECTIVE 
 
 OPERATION XIX. 
 
 To put a Square Box in PerfpeBive^ con- 
 taining a given Number of lejjer Square 
 Boxes of a Depth equal to their Width, 
 
 38. Let the given number of little 
 fquare boxes or cells be fixteen, then 
 four of them make the length of each 
 fide of the four outer fides ab^ b c 
 da^ as in Fig. 3. and the depth ^/ is 
 equal to the width a e. — Whoever can 
 draw the reticulated Iqaare in Oper. V. 
 (Fig. 6. of Plate II.) will be at no lofs 
 about putting this perfpedive fcheme 
 in practice. 
 
 OPERA- 
 
MADE EASY. 
 
 93 
 
 OPERATION XX. 
 
 To put Stairs with equal and parallel 
 Steps iti Perfpeciive, 
 
 39. In Fig, I. of Plate VIT. let abh^ 
 the given breadth of each ftep, and a i 
 the height thereof. — Make b c de^ 
 &c. each equal to a b ; and draw all 
 the upright lines ai^ b I, cn^ dp^ &c. 
 perpendicular to ah^ (to which the ho- 
 rizon s S IS parallel), and from the 
 points /, 72, />, &c. draw the equi- 
 diftant lines i 5, /C, n D, &c. parallel 
 to ah thefe diftances being equal to 
 that of i B from a h. 
 
 Draw x/, touching all the corner- 
 points /, p^ t^ V ; and draw 216 
 parallel to x as far from it as you 
 want the lengths of the fteps to be. 
 
 • Toward 
 
94. PERSPECTIVE 
 
 Toward the point of fight Sj draw 
 the Hnes a i, ? 2, ^ 3, /4, &c. and draw 
 16 15, 14 13, 12 II, 109, 87, 65, 
 43, and 21, all parallel to and 
 meeting the lines W15, 2/13, j-ii, &c. 
 in the points 15, 13, 1 1, 9, 7, 5, 3, and 
 X; then, from thefe points draw 15 14, 
 13 12, II 10, 98, 76, 54, and 32, all 
 parallel to ha ; and the outlines of the 
 fteps will be finifhed. From the 
 point 16, draw 16 A parallel to h Qj 
 and A X lb will be part of the flat at 
 the top of the uppermoft ftep. — This 
 done, {hade the work as in Fig. 2. and 
 the whole wdll be finifhed. 
 
 OPERA- 
 
MADE EASY. 
 
 OPERATION XXI. . 
 
 To put Stairs zvith Flats and Openings in 
 PerfpeBive^ Jlanding on a Horizontal 
 Pavement of Squares. 
 
 40. In Fig. 3. of Plate VII. having 
 made V the point of fight, and drawn 
 a reticulated pavement j4 jB, as di- 
 rected in Oper, III. and done it only 
 with black-lead lines, becanfe many 
 of them muft be rubbed out again ; 
 at any diftance from the fide A B 
 the pavement which is nearefl: to the 
 eye, and at any point where you 
 chufe to begin the ftair at that dif- 
 tance, as <2, draw G a parallel to B 
 and take ah pleafure for the height 
 of each ftep. 
 
 > Take dh in your compaflcs, and fet 
 
 that 
 
96 
 
 PERSPECTIVE 
 
 that extent as many times upward 
 from to £ as is equal to the firft re- 
 quired number of fteps 0, N, M, K; 
 and, from thefe points of divifion in 
 jEF, draw i 2 3/, 4 and Ekj 
 all equidiftant from one another, and 
 parallel to Fa; then draw the equi- 
 diftant upright lines a by t uf^ v hj 
 w ky and / all perpendicular to Fa; 
 then draw m b, touching the outer 
 corners of thefe fteps at m, /&, fj 
 and b ; and draw n s parallel to m b^ as 
 far from it as you want the length of 
 the fteps L, M, iV, 0, to be. 
 
 Toward the point of fight 5", draw 
 mfiy I Si ^ Oy i6j bpyf2j dr^ and^/. 
 Then, parallel to the bottom-line B 
 through the points <9, />, r, draw 
 « 8, 5 14, 6 1 5, 7 16, T 17, and is; 
 which done, draw n 5 and 0 6 parallel 
 to 7w, and the outlines of the fteps 
 K, I, M, N, C, will be fimfced. 
 
 At 
 
MADE EASY. 
 
 At equal diftances with that between 
 the lines marked 8 and 1 4, draw the 
 parallel lines above, marked 9 i o 1 1 1 2 
 and 1 3 ; and draw perpendicular lines 
 upward from the point? 0^ s, 
 as in the figure. 
 
 MaiCe H m equal to the intended 
 breadth of the flat above the fquare 
 opening at the left hand, and draw 
 H tV toward the point of fight 5', equal 
 to the intended length of the flat ; then 
 draw W P parallel to H and the out- 
 lines of the flat will be finiftied. 
 
 Take the width of the opening at 
 pleafure, as from F to and draw 
 CD equal and parallel to F E. Draw 
 GH parallel to CD, and the fliiort lines 
 marked 33, 34, &c. jufl: even with 
 the parallel lines i, 2, &c. From the 
 points where thefe fliort lines meet 
 C Dj draw lines toward the point of 
 O fight 
 
gi PERSPECTIVE 
 
 fight S till they meet D E. Then, 
 from the points where the lines 38, 39, 
 40, &c. of the pavement meet Cy, 
 draw upright lines parallel to CD; 
 and the lines which form the opening 
 will be finifhed. 
 
 • The fteps F^ ^, R, T, and the 
 flat U above the arch are done in 
 the fame manner with thofe in Fig. i. 
 as taught in Oper. XX. and the equi- 
 diftant parallel lines marked 18, 19, 
 &c. are diredly even with thofe on 
 the left-hand fide of the arch and 
 the upright lines on the right-hand 
 fide are equidiftant with thofe on the 
 left. 
 
 From the points where the lines 18, 
 19, 20, &c. meet the right-hand fide 
 of the arch, draw lines toward the 
 point of fight S' : and from the points 
 where the pavement-lines 2y, 30, 31, 
 
 32, 
 
MADE EASY. 
 
 -99 
 
 32, meet the line drawn from A toward 
 the point of fight, draw upright lines 
 toward the top of the arch. 
 
 Having done the top of the arch, as. 
 in the figure, and the few fl:eps to the 
 right hand thereof, fliade the whole, 
 as in Fig. 4. and the work will be fi- 
 niflied. 
 
 And it is my opinion, that if the 
 young artifl: is mafl:er of all the pre- 
 ceding operations, he will underfl:and 
 thefe two figures better by a bare view, 
 than by any defcription that can be 
 given of them. 
 
 OPERATION XXIL 
 
 To put upright conical ObjeEis in Per/pec- 
 tivcj as if /landing on the Sides of an oh-- 
 long Square^ at dijlances from one an' 
 G 2 other 
 
xo4 PERSPECTIVE 
 
 other equal to the breadth of the oh^ 
 long, 
 
 41 . In Fig. I . of Plate VIII. the bafes 
 of the upright cones are perfpedive 
 circles infcribed in fquares of the fame 
 diameter, as fhewn in Oper, IV. and 
 the cones are fet upright on their bafes 
 by the fame rules as are given in Oper, 
 IX. and XIV. for pyramids, which we 
 need not repeat here. 
 
 In the foregoing operations, we 
 have confidered the obferver's eye to 
 be above the level of the tops of all 
 the ohjeds. as if he viewed thofe in 
 Plate IV. V. VI. and VII. when {land- 
 ing on high ground. In the three fi- 
 gures on Plate VIII. we fhall fuppofe 
 him to be ftanding on low ground, and 
 the tops of the objeds to be above the 
 level of his eye. 
 
 In 
 
^ M A D E E A S Y. loi 
 
 In Fig. I . let Z) be the perfpeftive 
 breadth of the oblong" fquare A BCD ; 
 and let A a and D d (equal to ^ be 
 taken for the diameters of the circular 
 bafes of the two cones next the eye, 
 whofe intended equal height fhall be 
 ^ £ and £) F. 
 
 Having made S the point of fight, 
 in the horizon, parallel to A D, and 
 found the proper point of diftance 
 therein, draw A S and a 5, to contain 
 the bafes of the cones on the left-hand 
 fide, and D S and d S for thofe on the 
 right. 
 
 Having made the two firfl: cones at 
 A and D of equal height at pleafure, 
 draw ES and FS from their tops to 
 the point of fight, for limiting the 
 perfpedive heights of all the refl: of 
 the cones. Then, according to the di- 
 redioiis in Oper. XIV. divide the paral-^ 
 G 3 lelogram 
 
Perspective 
 
 lelogram A BCD into as many equal 
 perfpedive fquares as you pleafe ; find 
 the bafes of the cones at the corners of 
 thefe fquares, and make the cones there- 
 dn, as in the figure- 
 
 If you would reprefent a cieling, e- 
 qual and parallel to ABCD^ fupported 
 on the tops of thefe cones, draw E F ; 
 then EE GH fhall be the cieling, and 
 by drawing e f parallel to E you 
 will have the thicknefs of the floor- 
 boards and beams, which may be what 
 you pleafe. 
 
 This (hews how any number of equi- 
 diftant pillars may be drawn of equal 
 heights, to fupport the cieling of a 
 long room ; and how the walls of fuch 
 a room may be reprefented in perfpec- 
 tive at the backs of thefe pillars. It 
 alfo fhews how a ftreet of houfes may 
 be drawn in perfpe£tive. 
 
 OPEP.A^ 
 
MADE EASY. 
 
 OPERATION XXIII. 
 
 To put a Square Hollow in Ferfpe6iive^, 
 the Depth of which Jhall bear any af* 
 Jigned proportion to its Width. 
 
 42. Fig. 2. of Plate VIII. is the re- 
 prefentation of a fquare hollow, of 
 which the depth A G \s equal to three 
 times its width AD ; and S is the point 
 of fight, over which the obferver's eye 
 is fuppofed to be placed, looking per- 
 pendicularly down into it, but not di- 
 redly over the middle. 
 
 Draw A S and D 5 to the point of 
 fight S : make S T the horizon, paral- 
 lel to A Z), and produce it to fuch a 
 length beyond T that you may find a 
 point of diftance therein not nearer S 
 than if A D was feen under an angle 
 of 60 degrees. 
 
 G 4 Draw 
 
I04 PERSPECTIVJJ 
 
 Draw DU to the point of diftance, 
 interfering S in B ^ then, from the 
 point B draw B C parallel to AD ; and 
 you will have the firft perfpedive fquare 
 J B C equal to a third part of the 
 intended depth. 
 
 Draw C F to the point of diftanc6, 
 interfering AS in E: then, from the 
 point E draw £F parallel to AD ; and 
 you will have the fecond perfpedlivc 
 fquare B EI C ; which, added to the 
 former one, makes two thirds of the 
 intended depth. 
 
 Draw FW to the point of diftance, 
 interfering A S in G: then, from the 
 point G draw G H parallel to AD; 
 and you will have the third perfpective 
 fquare E GH F ; which, with the for-r 
 mer two, , makes the whole depth 
 A G H D three times as great as the 
 width ADjin ^ perfpeftive view. 
 
 DrviDE 
 
MADE EASY. 
 
 Divide AD into any number of e- 
 qual parts, as fuppofe eight ; and from 
 the divifion-points 3, &c. draw 
 lines toward the point of fight and 
 ending at G H Then, through the 
 points where the diagonals B EC, 
 G i% cut thefe Hues, draw Unes parallel 
 to A D ; and you will have the paral- 
 lelogram A G HD reticulated or divi- 
 ded into 192 fmall and equal perfpec- 
 tive fquares, 
 
 Make A I and D M equal and per- 
 pendicular to AD: then, draw / M, 
 which will be equal and parallel to 
 AD ; and draw and MS to the point 
 of fight S. 
 
 Divide AI^ IM^ and MZ), into the 
 fame number of equal parts AD is 
 divided : and from thefe points of divi- 
 sion draw lines toward the point of fight 
 
ro6 PERSPECTIVE 
 
 ending refpedively at GK, KL^ and 
 LH, 
 
 From thofe points where the lines 
 parallel lo A D meet J G and D 
 drav/ upright lines parallel to A I and 
 DM; and from the points where thefe 
 lines meet IK and L M, draw lines pa- 
 rallel to IM ; then lhade the work, as 
 in the figure. 
 
 OPERATION XXIV. 
 
 To reprefent a Semicircular Arch in Per- 
 fpeSiive, as if it were Jlanding on two 
 upright Walls ^ equal in Height to the. 
 Height of the Obferver'^s Eye, 
 
 43. After having gone throns^h the 
 preceding operation, this will be more 
 eafy by a bare view of Fig. 3. in Plate 
 ^^III. than it could be made by any 
 
 defcription ; 
 
MADE EASY. 107 
 
 defcription ; the method being fo 
 much Hke that of drawing and fha- 
 ding the fquare hollow. — We need 
 only mention, that aT b E j1 and 
 D F c t d are the upright walls on 
 which the femicircular arch is built ; 
 that S is the point of fight in the ho- 
 rizon T/, taken in the centre of the 
 arch; that d (in Fig. 2.) is the point 
 of diftance ; and that the two perfpec- 
 tive fquares A BCD and DEFC 
 make the parallelogram i E F D of a 
 length equal to twice its breadth A D, 
 
 OPERATION XXV. 
 
 To reprejent a Square in PerfpeBive^ as 
 viewed by an Obferver Jlanding direStly 
 even with one of its Corners, 
 
 44. In Fig. I. of Plate IX. let J 
 BCh^z true fquare, viewed by an ob- 
 ferver 
 
io8 PERSPECTIVE 
 
 ferver {landing at fome diftance from 
 the corner C, and juft even with the 
 diagonal C 9. 
 
 luTLT pSP be the horizon, parallel to 
 the diagonal A B ; and S the point of 
 fight, even with the diagonal Cg. Here 
 it will be proper to have two points .of 
 diftance p and P, equidiftant from the 
 point of fight S. 
 
 Draw the ftraight line 117 parallel 
 to A By and draw Jl 8 and B 10 par 
 rallel to C S. Take the diftance be- 
 tween 8 and 9 in your compaftes, and 
 fet it off all the way in equal parts from 
 8 to r, and 10 to 17. — The line i 17 
 fliould be produced a good way fur- 
 ther both to right and left hand from 
 9, and divided all the way in the fame 
 manner. 
 
 From thefe points of equal divifion, 
 
 8, 
 
MADE EASY. 
 
 1 09 
 
 8, 9, TO, &c. draw lines to the point 
 of fight S, and alfo to the two points of 
 diftance p and P, as in the figure. 
 
 Now, it is plain, that a c b g is the 
 perfpedive reprefentation of A g B C, 
 viewed by an obferver even with the 
 corner C and diagonal C 9. — But if 
 there are other fuch fquares lying even 
 with this, and having the fame pofition 
 with refped to the line i 17, it is evi- 
 dent, that the obferver, who ftands di- 
 redly even with the corner C of the 
 firft fquare, will not be even with the 
 like corners G and K of the others ; but 
 will have an oblique view of them, over 
 the fides F G and IK which are nearefl: 
 his eye ; and their perfpedive repre- 
 lentations will be e^f6 and hki^^ 
 drawn among the lines in the figure : 
 of which, the fpaces taken up by each 
 fide lie between three of the lines drawn 
 toward the point of diftance and 
 
 three 
 
no PERSPECTIVE 
 
 three drawn to the other point of dif- 
 tance P. 
 
 OPERATION XXVI. 
 
 To reprefent a common Chair ^ in an ohliqm 
 View in PerfpeSfive, 
 
 45. The original lines to the point of 
 fight and points of diftance p and P, 
 being drawn as in the preceding opera- 
 tion, chufe any part of the plane, as 
 Imn 13, on which you would have the 
 chair L to ftand — There are juft as 
 many lines (namely two) between / 
 and ;77, or 13 and drawn toward the 
 point of diftance />, at the left hand, as 
 between / and 15, or ?n and «, drawn 
 < to the point of diftance P on the right ; 
 
 fo that Im^ mn^ ^13? and 13 /, form a 
 perfpective fquare. 
 
 From 
 
MADE EASY. 
 
 Ill 
 
 From the four corners /, 13, 
 of this fquare, raife the four legs of the 
 chair to the perfpedive perpendicular 
 height you would have them ; then 
 make the feat of the chair a fquare 
 equal and parallel to //t? 72 1 3, as taught 
 in Oper, X. which will make the two 
 fides of the feat in the diredion of the 
 lines drawn toward the point of diftance 
 and the fore and back part of the 
 feat in dire£lion of the lines drawn to 
 the other point of diftance P, This done, 
 draw the back .of the chair leaning a 
 little backward, and the crofs bars 
 therein tending toward the point of dif- 
 tance P. Then fliade the work as in 
 the figure ; and the perfpeclive chair 
 will be finifhed. 
 
 OPERA- 
 
til PERSPECTIVE 
 
 OPERATION XXVII. 
 
 To reprefent an oblong Square Table in an 
 oblique Perfpedlive View, 
 
 46. In Fig. t. of Plate IX. M is an 
 oblong fquafe table, as feen by an ob- 
 ferver ftanding diredly even with C 9 
 (fee Oper. XXV.), the fide next the eye 
 being perfpecSively parallel to the fide 
 ac oi the fquare ac b g. — The fore-^ 
 mentioned lines drawn from the line 
 I 1 7 to the two points of diftance p and 
 form equal perfpective fquares on 
 the ground-plane. 
 
 Chuse any part of this plane of 
 fquares for the feet of the table to ftand 
 upon ; as at />, ?\ and j-, in direction 
 of the lines 0 p and r s for the two long 
 fides, and t s and q r for the two ends ; 
 
 and 
 
MAD E EASY. 
 
 and you will have the oblong fquare or 
 parallelogram qr st iox the part of the 
 floor or ground-plane whereon the 
 table is to ftand ; and the breadth of 
 this plane is here taken in propor- 
 tion to the length as fix to ten; fo 
 that, if the length of the table be ten 
 feet, its breadth will be fix. 
 
 On the four little perfpedive fquares 
 at J, and r, place the four upright 
 legs of the table, of what height you 
 pleafe, fo that the height of the two 
 next the eye, at o and fhall be ter- 
 minated by a flraight line u v drawn 
 to the point of diftance P. This done, 
 make the leaf M of the table an ob- 
 long fquare, perfpedively equal and 
 parallel to the oblong fquare q s t on 
 which the feet of the table ftands. 
 Then fhade the whole, as in the figure, 
 and the work will be finiflied. 
 
114 
 
 PERSPECTIVE 
 
 If the line 117 was prolonged to the 
 right and left hand, and equally divi- 
 ded throughout, (as it is from i to 17), 
 and if the lines which are drawTi from 
 p and P to the right and left hand 
 fides of the plate were prolonged till 
 they came to the extended line 117, 
 they would meet it in the equal points 
 of divifion. In forming large plans of 
 this fort, the ends of flips of paper may 
 be pafted to the right and left edges of 
 the ftieet on which the plan is to be 
 formed. 
 
 CHAP. 
 
MADE EASY. 115 
 
 CHAP. III. 
 
 The Be/cription of a Machine^ by which 
 any Per/on may delineate the true Per^ 
 JpeElive Figures of ObjeBs^ without 
 having learned any of the preceding 
 Rules. 
 
 47. T?IG. 2. of Plate IX. is a plane 
 JL of this machine, and Fig. 3. 
 is a reprefentation of it when made ufe 
 of in drawing diftant objeds in perfpec- 
 tive. A fketch of it was given me 
 feveral years ago by the late ingenious 
 Dr Bevis, who then told me he had 
 never feen one of the like conftrudion ; 
 and as all thofe to whom I have had 
 the opportunity of fliewing it, have 
 told me that they never faw nor heard 
 of fuch a one before, I have great 
 reafon to believe that the Dodor was 
 H 2 the 
 
ii6 
 
 PERSPECTIVE 
 
 the inventor of it, although he never 
 made it pubHc. 
 
 In order that it may be the eafier 
 underftood, I have put the letters of 
 reference to the plane (Fig. 2.) in fmall 
 Italics, and the fame letters to the like 
 parts of it in the perfpedive view (Fig. 
 3.) in large Italics ; that the reader may 
 look at them both, as he goes on with 
 the following defcription. 
 
 In Fig. 2. abef is an oblong fquare 
 board, reprefented by ^J5£i^inFig. 3. 
 X and J (X and T) are two hinges on 
 which the part eld (C L D) is move- 
 able. This part confifts of two arches 
 or portions of circles cml ( CML J, and 
 dnl (DNL) joined together at the 
 top I (L)^ and at bottom to the crofs 
 bar dc (DC), to which one part of 
 each hinge is fixed, and the other part 
 to a flat board, half the length of the 
 
 board 
 
MADE EASY. 
 
 117 
 
 board abef (ABEF)^ and glued to 
 its uppermoft fide. The centre of the 
 arch c m I is at dj and the centre of the 
 arch dnlis at 
 
 On the outer fide of the arch dnlis 
 a Aiding piece n (much Hke the nut of 
 the quadrant of altitude belonging to a 
 common globe), which may be moved 
 to any part of the arch between d and 
 I; and there is fuch another Aider o on 
 the arch cmly which may be fet to 
 any part between c and /. — A thread 
 cpn (CPN) is fl:retched tight from 
 the centre c (C) to the Aider n (N)^ 
 and fuch another thread is ft retched 
 from the centre d (D) to the Aider 
 0 (0) ; the ends of the threads being 
 fattened to thefe centres and Aiders. 
 
 Now, it is plain, that by moving 
 thefe Aiders on their refpedive arches, 
 the interfedion p (P) of the threads 
 
 may 
 
PERSPECTIVE 
 
 may be brought to any point of the 
 open fpace within the arches. — In the 
 groove k (KJ is 3, ftraight Aiding bar 
 if/}, which may be drawn farther out 
 or pufhed farther in at pleafure. 
 
 To the outer end of this bar / (Fig. 
 5.) is fixed the upright piece H in 
 which is a groove for receiving the Ai- 
 ding piece In this Aider is a fmall 
 hole r for the eye to look through, in 
 iifing the machine : and there is a long 
 Ait in i?Z, to let the hole r be feen 
 through when the eye is placed behind 
 it, at any height of the hole above the 
 level of the bar /. 
 
 How to delineate the Pe?'fpeBive Figure 
 of any di/lant ObjeB or ObjeBs by 
 Means of this Machine. 
 
 48. Suppose you wanted to delineate 
 
 a 
 
MADE EASY. 119 
 
 a perfpeftive reprefentationof the houfe 
 qsrp (which we muft imagine to be a 
 great way off, without the limits of the 
 plate), place the machine on a fteady 
 table, with the end EF of the horizon- 
 tal board A B E F toward the houfe, 
 fo that, when the Gothic -like arch 
 D LC is fet upright, the middle part of 
 the open fpace (about F) within it may 
 be even with the houfe when you place 
 your eye at Z, and look at the houfe 
 through the fmall hole r. Then fix 
 the corners of a fquare piece of paper 
 with four wafers on the furface of that 
 half of the horizontal board which is 
 neareft the houfe ; and all is ready for 
 drawing. 
 
 Set the arch upright as in the fi- 
 gure, which it will be when it comes 
 to the perpendicular fide t of the up- 
 right piece s t fixed to the horizontal 
 board behind D. Then place your eye 
 
 at 
 
PERSPECTIVE 
 
 at Z, and look through hole r at any 
 point of the houfe, as and move the 
 Aiders N and 0, till you bring the in- 
 terfedlion of the threads at P, diredly 
 between your eye and the point q : 
 then put down the arch flat upon the 
 paper on the board as at S and the 
 interfedion of the threads will be at W. 
 Mark the point W on the paper with 
 the dot of a black-lead pencil, and fet 
 the arch upright again, as before : then 
 look through the hole r, and move the 
 Aiders N and 0 till the interfedion of 
 the threads comes between your eye 
 and any other point of the houfe, as p : 
 then put down the arch again to the 
 paper, and make a pencil-mark thereon 
 at the interfedion of the threads, and 
 draw a line from that mark to the for- 
 mer one at W ; which line will be a 
 true perfpedive reprefentatiou of the 
 corner pq of the houfe. 
 
 Proceed 
 
MADE EASY. 121 
 
 Proceed in the fame manner, by- 
 bringing the interfedion of the threads 
 fucceflively between your eye and other 
 points of the outUnes of the houfe, as 
 r. J-, &c. and put down the arch to mark 
 the Uke points on the paper, at the 
 interfeftion of the threads ; then con- 
 nect thefe points byftraight Hnes, which 
 will be the perfpe£live outlines of the 
 houfe. In like manner, find points for 
 the corners of the door and windows, 
 top of the houfe, chimnies, &c. and 
 draw the finifhing lines from point to 
 point : then fhade the whole, making 
 the lights and fhades as you fee them 
 on the houfe itfelf, and you will have a 
 true perfpecSive figure of it. — Great 
 care muft be taken, during the whole 
 time, that the pofition of the machine 
 be not fhifted on the table ; and to pre- 
 vent fuch an inconvenience, the table 
 fhould be very ftrong and fteady, and 
 the machine fixed to it, either by fcrews 
 or clamps. 
 
 I In 
 
122 
 
 PERSPECTIVE 
 
 In the fame way, a landfcape or any 
 number of objedls within the field of 
 view through the arch, may be deU- 
 neated, by finding a fufficient number 
 of perfpedive points on the paper, and 
 connecting them by ftraight or curved 
 fines as they appear to the eye. And 
 as this makes every thing in perfpedlive 
 equally eafy, without taking the trouble 
 to learn any of the rules for drawing, 
 the operations muft be very pleafing 
 and agreeable. Yet, as fcience is ftill 
 more fo, we would by all means recom- 
 mend it to our readers to learn the rules 
 for drawing particular objects ; and to 
 draw landfcapes by the ey^, for which, 
 I believe, no perfpedive rules can be gi- 
 ven. And although any thing may be 
 very truly drawn in perfpeclive by means 
 of this machine, it cannot be faid that 
 there is the leaft degree of fcience in 
 going t/jat way to work. 
 
 The 
 
MADE EASY. 123 
 
 The arch ought to be at leaft a foot 
 wide at bottom, that the eye at Z may 
 have a large field of view through it ; 
 and the eye fhould then be at leaft i 
 inches from the interfe£tion of the 
 threads at P when the arch is fet up- 
 right. For if it be nearer, the boun- 
 daries of view at the fides near the foot 
 of the arch will fubtend an angle at Z 
 of more than 60 degrees, which will 
 not only ftrain the eye, (§ 10.), but will 
 alfo caufe the outermoft parts of the 
 drawing to have a difagreeable appear- 
 ance. — Toavoidthis, itwill beproper to 
 drawback the Aiding bar/, till Z be 14^ 
 inches diftant fromP; and then the whole 
 field of view, through the foot-wide arch, 
 will not fubtend an angle to the eye at 
 Z of more than 45 degrees ; which will 
 give a more eafy and pleafant view, not 
 only of all the objeds themfelves, but 
 alfo of their reprefentations on the pa- 
 per whereon they are delineated. So 
 
 that, 
 
124 PERSPECTIVE, &c. 
 
 that, whatever the width of the arch be, 
 the diftance of the eye from it Ihould be 
 in this proportion : As 12 is to the width 
 of the arch, fo is 1 4^ to the diftance of 
 the eye (at Z ) from it. 
 
 If apane of glafs, laid overwith gum- 
 water, be fixed into the arch, and fet 
 upright when dry, a perfon who looks 
 through the hole r may delineate the 
 objedls upon the glafs which he fees at 
 a diftance through and beyond it, and 
 then transfer the delineation to a paper 
 put upon the glafs, as mentioned in § i . 
 
 J. PILLANS AND SONS, PRINTERS. 
 
Plate IL 
 
PL ATI; 
 
I'ialc- v. 
 
I 
 
 I 
 
 i 
 
 i 
 
/ 
 
 f1 
 
I.