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 in 2018 with funding from 
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 https://archive.org/details/practicalperspecOOnobl 
 

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Published/ Jan?. 1.180 &. lyJZJn’ ? 0 rme, 5 ^ Bimd Street u 
 
PRACTICAL 
 
 PERSPECTIVE, 
 
 EXEMPLIFIED ON 
 
 L*AJVDS (JdLPESm 
 
 By THOMAS NOBLE, 
 PROFESSOR OF PERSPECTIVE . 
 
 ENGRAVED by JOHN CLARK. 
 
 THE SECOND EDITION. 
 
 WITH AN ESSAY ON THE PRACTICE OF TAKING VIEWS, 
 
 AND MANY OTHER CONSIDERABLE ADDITIONS AND IMPROVEMENTS 
 
 BY THE AUTHOR. 
 
 Eontson* 
 
 PRINTED FOR, PUBLISHED AND SOLD BY, 
 
 EDWARD ORME, IIIS MAJESTY’S PRINTSELLER, BOND STREET; 
 
 SOLD ALSO 
 
 By Mr. TAYLOR, High Holborn; ROWE and WALLER, Fleet Street; 
 and to be bad of every Book and Printseller in the United Kingdom. 
 
 1809. 
 
 Printed by J. HAYES, Dartmouth Street, Westminster. 
 

 
 
 
 
 
 
 
 
 
 
 *>. 
 
 'I 
 
 
STANZAS on PERSPECTIVE: 
 
 ADDRESSED TO 
 
 THE RIGHT HONOURABLE THE COUNTESS OF OXFORD 
 
 WITH A COPY OF THE FIRST EDITION 
 
 OF THIS WORK. 
 
 ’(Se ^air PERSPECTIVE’S cjentle -Haw4 wexe known 
 ^/'f on Id doM Hdlledccjn fold daxinj jjormd cLdJilaj, 
 tdn colour*} Irijhter than the role4 ojj <_/l(aij; 
 
 ?A witfiotit order n>ae tun tattet e/rewn, 
 
 were the tender midtd ojj distance dhewn > 
 j\ ! OX) object*} Icddenincj thio’ the lencjthenmcj ivaj; 
 
 Met, a4 in dazzlnj noon'*} doldtitial uij, 
 l£$elujed with waved ojj licjht th’ uncertain LANDSCAPE dhu 
 
 lone. 
 
 Hi/ wad then GEOMETRY, dark, thonqhtlul daqe 
 
 T 
 
 Uht lorn hi*} cell reduce lu*} lovehedt child 
 
 
 PERSPECTIVE, 
 
 ? who had all hid toild lecjai id; 
 
 Hd'ot t rhe alone cou a to dojt cared enjacje 
 
 ctfoid cinxioud mind: dhe , when j'’air Mature dmil’cl\ 
 HI on Id utillj with mimic dcened, kid tcdioud lore addiiaje . 
 
(iv) 
 
 Xtraiafit, t/n juojcoitiond jaetj (fie ofjecte rteej 
 
 ioufj \lececLncj vi,ta dorodij ^acle4 
 
 X die jfar, jjamt ; dionzon; wdide die ,diadei 
 
 (d)jl internuny fed codumn,, rnitd ,urjuize ) 
 
 ddddivet upon one pdane d' admvcei', eve*), 
 
 ' ' J 
 
 tjd, do' a read distance did jiervade 
 d/die Jiortico, die dcentncj dime, die 'jdade, 
 Wood, and retvuna dudd,, dat me it into die Jut 
 
 Mu J,! too dike dier dfire, die nijmjtdi union'd 
 
 iiandei'd) ovdude dawde,, ,cene, umiji'd dier name: 
 dd)r kinem de wdiere de micjdit protection cdaim, 
 dJidd tdPenoe and dJa,te m OXFORD S jjicjwie moo'd, 
 ddiien ^edt dier do,om dope', endwemna ^dame ; 
 dJdat t e?frt ivoutd, heeji flee fated hi fXcautu'o tijid ajcji cov'd. 
 
 XM6JMX Js^MMi 
 
 c 
 
PREFACE 
 
 
 The necessity of easy Practical Instructions in Perspective is 
 universally acknowledged, and it is to be wondered that nothing of this 
 kind has been before attempted. Masters of Drawing, indeed, frequently 
 complain of the disadvantage of teaching an Art without its principles, and 
 :endeavour to let their Pupils supply the want of Science by a babit of copy¬ 
 ing from correct Drawings. But experience proves that such a system is 
 erroneous. Few of the most successful Scholars of such a practice, unless 
 endued with more than common perception, become capable of taking a 
 View from Nature, or of designing from Imagination: to copy a Print or 
 Drawing is their highest attainment, and even in doing that, the taste and 
 delicacy of the Pencil can hardly atone for errors which are continually appa¬ 
 rent in their Performances. 
 
 Perspective is the Grammar of Painting, and it is as impossible to be a Painter 
 without attention to it, as it is to be an Author without regarding the rules 
 of Syntax. The folly of resorting to an obsolete language, for the grammatical 
 rules of our vernacular tongue, has long since been exploded; and it is as¬ 
 suredly time to separate the Painters’ Grammar from a long and tedious 
 investigation of recondite truths. Indeed, were that close Geometrical inves¬ 
 tigation, which involves the study of Perspective at present, more necessary 
 than it is even generally thought to be, yet would it be proper to endeavour to 
 find a shorter and more pleasing path for the Man of taste, or for him who seeks 
 relaxation in the labours of the Pencil from more urgent occupations. 
 
 Science and Art are generally the provinces of different Men, because they 
 demand different faculties of the mind. Instead therefore of filling volumes, 
 with elaborate Science, it is certainly more useful to Mankind, that certain 
 parts should be selected, and applied to their appropriate Arts. Execution 
 would not then be impeded by useless study, nor would the Artist continue to 
 reject that knowledge, which is absolutely necessary for the perfection of his 
 talents. 
 
 b 
 
 Of 
 
Of such a nature is the present design. In it will be found enough of the 
 Theory of Perspective to enable the Artist to delineate his Landscape with 
 truth and accuracy; and as few instructions are given without such examples 
 as are continually the subjects of Drawing, the Pencil is kept in practice, 
 while the understanding is cultivated; taste and the powers of execution are 
 exercised, while the judgment is informed. 
 
 A very small number of Geometrical Problems, properly selected, will be 
 found sufficient for every purpose in Landscape Perspective. One Plate for 
 explanation will make the Learner acquainted with the lines and points by 
 which this Science performs its operation; and a single demonstration will 
 make clear to the dullest understanding the reason of those proportions on 
 which the practice of Perspective is founded. 
 
 I consider references as very preferable to repetition; they create a memory, 
 where that mental principle of Science is wanting, and they recal former 
 operations which explain each other, and thereby make an easy way to the 
 understanding. They will be found to be numerous. He whose perception 
 is strong, and memory tenacious, may think their number troublesome--^ 
 he has only to neglect them. To many, the Author believes, he had better 
 appear somewhat troublesome than in the least obscure. 
 
 The support of a candid Public, ever ready to patronize that which tends 
 to the improvement of the Arts, is respectfully solicited; and with some 
 confidence; since neither care nor exertion has been spared to render this 
 work adequate to the utility of its design, and thereby worthy their attention. 
 
 THOMAS NOBLE, 
 
 Blackheath, 180 p. 
 
ADVERTISEMENT 
 
 TO THE 
 
 ' SECOND EDITION. 
 
 >rp 
 
 X HE Author of this Work when he first presented it to the Public 
 ♦endeavoured to shew that a Science, which had so long been secluded from 
 the Artist and the Pupil of taste, was not incapable of being rendered simple 
 and accessible. His plan was to fix it upon its own principles, and while he 
 freed it from the irksomeness of Geometrical demonstration to set forth its 
 general truths in a manifest and incontrovertible light. His success in this 
 undertaking has been universally acknowledged : and rival publications have 
 started forth to participate in his merit. The course he had taken was, how¬ 
 ever, not so open as his followers seem to have imagined: he had not rejected, 
 but simplified Science: he had not exhibited a mere book of practice without 
 elements; and, therefore, when they pretended to imitate his labours, they 
 should not have omitted that foundation, which he had laid in the truths of 
 proportion, nor that arrangement which by its form alone elucidated the 
 principles of the Science, To a first attempt at reducing a branch of Mathe¬ 
 matical knowledge to so simple a structure, many improvements might 
 undoubtedly have been added; and he regrets that all those improvements 
 rare left to his own exertions. 
 
 In this second Edition it will appear that he has not swerved from his 
 •duty. The whole doctrine of vanishing lines and their central points 
 will now be found exhibited in one short, but perspicuous, survey of the 
 -subject; and their analogy with the Horizontal line and point of sight, will 
 be seen correctly exemplified by an additional plate. The principles, on 
 which the delineation of Shadows in perspective is determined, are explained 
 in a few general maxims, which are accompanied with distinct diagrams: from 
 these elementary precepts the whole of the practice of shadows is deduced 
 in a new and easy manner. Still something appeared to be wanting. The 
 young Artist in taking a view might still beat a loss how to direct his hand 
 
 by 
 
( viii ) 
 
 by the theory and instrumental practice he had acquired: An Essay on the 
 application of Perspective to the practice of taking views, therefore, concludes 
 the work; and, conducting the Student to the field, instructs him how his 
 acquirements are to influence his judgment and correct Ins eye. 
 
 In bringing his work a second time before a candid Public in so improved 
 a state the Author feels assured of its favourable reception; and ventures to hold 
 forth the promise of a work upon a more extended scale, that may exhibit the 
 contents of the fifth section of this, in a more enlarged and scientific manner. 
 
 &. jv : j 
 
 ii'CQ. ^ 
 
 INTRODUCTORY 
 
INTRODUCTORY PROBLEMS OF GEOMETRY. 
 
 (See the Title Plate.) 
 
 Tig. 1 . A Perpendicular is a right line directly standing upon, or falling beneath, 
 another right line, without inclining one way or the other: thus, A D is perpendicular 
 to B C, and (Fig. 2.) E D or E A is perpendicular to B C*. 
 
 I. To draw a right line perpendicular to a right line at a given point in it. 
 
 BC (Fig. 1.) is the given line, in which A is the given point. Take the points B 
 and C in the given line, equally distant from A. With any opening of your compasses 
 at B, as a center, strike the arc of a circle towards D; with the same opening of your 
 compasses, and at C as a center, cross the former arc at D: from D, the point in which 
 The arcs meet, draw D A, which will be perpendicular to C D. 
 
 II. To let fall a perpendicular to a given line from a given point. 
 
 B C (Fig. 2.) is the given line: A is the given point. From A, as a center, describe 
 an arc of a circle that may cut the given line in two points, as in B, C. At B and C, 
 as centers, describe the intersecting arcs at D, as in the last problem : join A and D-. 
 Then the line A D, that is, either the upper line A E, or the lower line E D, is perpen¬ 
 dicular to B C. 
 
 * It is manifest that B A or C A, in Fig. 1, is perpendicular to A D, because if the side of the paper be turned, 
 either B A or C A stands directly upon or falls directly beneath A. D. In like manner, E B or E C, in Fig. 2, is 
 perpendicular to ED or E A. Hence it follows, that any lines drawn to, or only toicards , each other, without 
 ■ any sloping or inclined direction, are reciprocally perpendicular. 
 
30 
 
 INTRODUCTORY PROBLEMS OF GEOMETRY. 
 
 III. To draw a Perpendicular to a right Line , at or near one extremity of iL 
 
 C A is the right line (Fig. 3.) and A is a point at or near one extremity of it. At 
 any point, not in the right line, as the point B, and with the distance B A, describe more 
 than half a circle, cutting A C in C. Through C and B draw a right line, cutting the 
 described arc in D, join D A: then is D A the perpendicular required. 
 
 1Y T . To bisect, or divide , a given Line in two equal Parts. 
 
 A B (Fig. 4.) is the given line. At A and B, its extremities as centers, describe 
 the intersecting arcs towards C and D. Join C D, and then will A E be equal to B F>. 
 
 An Angle is the inclination of one line to another. A line, perpendicular to 
 another line, is said to be at right angles with it; and the angle or angles, it makes with 
 it, are called right angles. An angle less than a right angle is called an acute angle . An 
 angle greater than a right angle is an obtuse angle. 
 
 Y. To make an Angle equal to a given Angle. 
 
 CAB (Fig. 5) is the given angle, and D E is a line on which a similar angle is to be 
 made. At A and at D for centers, describe arcs of circles with the same opening of the 
 compasses, and make E F equal to B C. Draw D F, and the angle F D E will be equal 
 to C A B. 
 
 VI. To bisect , or divide , a given Angle into two equal Parts . 
 
 BAG (Fig. 7) is the given angle. At A, as a center, describe any arc as B C. At 
 B and C, as centers, describe the intersecting arcs at D. Join D A. Then DAB and 
 D A C will be equal angles. 
 
INTRODUCTORY PROBLEMS OP GEOMETRY. 
 
 11 
 
 VIL To draw a Right Line making any given Angle with another Right Line. 
 
 A B is one right line, and A is the intended angular point. Open the Sector* and 
 take any distance from SO to SO on the lines of Chords, marked thereon C, and therewith 
 describe an Arcj- as BE D. On the Sector take the width of the given angle (suppose 38°) 
 from 38° to 38°, and lay it from B to E, draw E A. Then E A B is an angle of 38*. 
 
 If the given angle be obtuse, make two acute angles, which together may be equal 
 to the given obtuse angle. Thus the obtuse angle D A B (Fig. 8) is composed of the 
 two acute angles B A E and E A D, one containing 38° and the other 57 a , and there¬ 
 fore itself contains 93°. 
 
 Parallel Lines are such as would never meet, however far they might be con¬ 
 tinued either way. 
 
 VIII. At a given Point to describe a Line parallel to a given Line. 
 
 A B is the given line (Fig. 6.), and C is the given point. Draw B C, and make 
 the angle B C F equal to the angle A B C. The line C F will be parallel to A B. 
 
 Proportional Lines are such as have similar relations to each other, in the same 
 manner as proportional numbers in the rule of three ; thus 3: 5: : 6: 10, may represent 
 lines of different length, as well as pounds, cwts. &c. then it will be as a line of three 
 yards, or any other measure, is to a line of five yards, so is a line of six yards, to a line 
 of ten yards. 
 
 * The Sector is a ruler that doubles upon a hinge, and has various lines constructed upon it of various uses. 
 The lines of chords may be easily found upon it. 
 
 f An Arc of a circle is always the measure of an angle. Every circle is supposed to be divided into SGO parti, 
 ■called degrees, marked thus° A right angle contains 90°. 
 
12 
 
 INTRODUCTORY PROBLEMS OF GEOMETRY. 
 
 IX. To divide a Line into two Parts proportional to two other given Lines. 
 
 (Fig. 9.) A B and C D are the two given lines. A D is the line to be divided. 
 Draw A B, and at one extremity of it draw A D in any oblique direction. At D, place 
 C D parallel to A B, and draw the line C B, joining the other extremities of the given 
 lines, and cutting A D in the point E. Then, as A B is to C D f so is A E to E D. 
 

 
1 st . EXFLJHVJL TORT TL-ATJE 
 
 Published Jail *1.1800. byiidnS Ormc. Sg flond Street-. 
 
tactical |3er0j5tcttl3E. 
 
 (Explanatory Elate.) 
 
 Sect. Uf. I. Perspective is the art of delineating objects on a single plane (as paper, 
 canvas, &c.), in such a manner as that they may appear to retain their original distances 
 beyond that plane and beyond each other, and their original inclination towards that plane 
 and towards each other. 
 
 Thus: KTUR is the perspective representation of the original pyramids on the plane 
 PLNE, as they appear to the figure who is looking at them. 
 
 IT. In drawing the perspective representation KT U R, the figure who is supposed 
 to have drawn it must have used these following lines and points. 
 
 1st. The line II O, called the horizontal line, because parallel to the ground and 
 horizon. 
 
 2nd. The line C D, which is the distance of the eye from the plane of the picture. 
 
 3d. The point of sight, or perspective center C, which is a point in which a line, drawn 
 from the eye of the spectator perpendicular to the horizontal line, would cut the plane of 
 the picture. This point will always be on the horizontal line, and should be near the mid¬ 
 dle of the drawing or painting. 
 
 D 
 
 OBSERVATIONS. 
 
14 
 
 PRACTICAL PERSPECTIVE, 
 
 OBSERVATIONS. 
 
 Sec. 2. I. It is apparent to every one that distance lessens the appearance of every, 
 object, and that every object is lost in the boundary of our sight, which is the horizon, and! 
 is here represented by the horizontal line. 
 
 II. As we can only direct our sight to one point at a time, so there can be only 
 one point of sight in a picture. 
 
 III. All walls, sides of buildings, roads, See. and, in short, all lines, that are directed 
 straight forward from the spectator, must tend to the point of sight. 
 
 IV. All walls, sides of buildings, roads, &c. that are oblique to*the spectator, that is,, 
 are not directly straight forwards, tend to some point in the horizontal line, but not 
 to the point of sight. 
 
 V. All sloping walls, roofs of houses, hills, &c. must tend to some point either above . 
 fc>r below the horizontal line. 
 
 VI. In explaining the following plates, these points will be called vanishing points . 
 
 VII By looking at the first explanatory plate , the meaning of a cone or body of rays,, 
 cut by the plane of the picture (a thing particularly dwelt upon by all writers on 
 perspective) will be easily conceived. 
 
 The eye of the spectator is the point or apex of the cone, and the rays (represented 
 on the plate by fine dotted lines) proceed to every point of the original objects. 
 
 VIII. These rays may be supposed to pierce through the plane of the picture, or 
 to be cut by it : each ray must necessarily, in either case, touch the surface of the 
 picture in a point. These points together make up the perspective representation of the 
 objects; and it is the business of perspective to find the positions of these points on 
 the plane of the picture. 
 
PRACTICAL PERSPECTIVE. 
 
 15 
 
 IX. The point X of the nearest original pyramid has the ray X Z D, proceeding 
 from it to the eye of the spectator, and it touches the plane or surface of the picture in 
 the point Z. 
 
 Let X Y be a line perpendicular to the plane of the picture: it will then be the 
 distance of the point X from the plane of the picture : it will also be parallel to C D, which 
 represents the distance of the spectator from the plane of the picture. Its perspective re¬ 
 presentation will (by obser III. of this section) tend to the point of sight C : therefore, sup¬ 
 pose the line Y C to be drawn on the plane of the picture: then you may observe that 
 the ray X D performs on the line Y C the operation taught by the IXth Problem of the 
 preceding Geometry; it divides the line YC into two parts, proportional to the two 
 lines X Y and D C : thus the distance of the point X (that is X Y) is to Y Z, as the distance 
 of the eye at D (that is D C) is to C Z, the remainder of the line Y C. 
 
 Y Z is therefore the perspective representation of the line X Y, which is the distance 
 of the point X, and Z is the perspective point for the original point X : Z is also the 
 point which the ray X Z D (see obser. VIII.) must necessarily make upon the surface of 
 the picture. 
 
 The learner is desired to pay particular attention to this last observation, as it contains 
 all the demonstration necessary to enable him to understand the following plates, 
 and will therefore be frequently referred to, that he may not be fatigued by useless 
 repetition. 
 
 SECOND 
 
16 
 
 PRACTICAL PERSPECTIVE, 
 
 SECOND EXPLANATORY PLATE* 
 
 (Part the first.) 
 
 Sect. 3. In the ninth observation of the proceeding section it has been shewn, that-- 
 the principal object in the operations of perspective, is to divide a right line, drawn on the 
 plane of the picture, in such a manner, that one part of it may be to the distance of the 
 eye, as the other is to the distance of the object. This would be difficult, and indeed' 
 almost impossible, to perform, unless we suppose the three planes reduced into one plane: 
 that is, the horizontal plane, in which the eye is placed, and the base plane , in which the 1 
 point of the original object lies, must be conceived to be made straight, so as to coincide oiv 
 form a part of the plane of the picture. 
 
 I. The first part of the present plate exhibits these three planes in the form of one 
 plane : the upper part is the horizontal plane ; and the lower part is the base plane ; both 
 projected on the plane of the picture : their intersections with the plane of the picture 
 being preserved and represented by the horizontal line and the baseline. 
 
 II. The ground plan of a cottage or other building to be drawn in perspective is 
 represented by the figures A 13 C D, which hath two of its sides directed straight forwards 
 from the spectator : those two sides, being produced, will cut tiie base line (as in E & F) 
 and will be parallel to that right line drawn from the eye to the horizontal line, which by 
 Obser. 3. II. § 1. determines the perspective center or point of sight. 
 
 III. The representations of these sides must therefore (by § 2. III.) tend to the point 
 of sight. Let E S and F S be drawn : and the representations of the points A & B 
 C & I) will be in E 3 and in F S. 
 
 IV. Draw lines from the original points A 13 C D, to the eye, and those lines will 
 intersect E S and F3 in the points a, b, c, d; which will be the perspective representations 
 ol A s 13, C, D, by observ. IX. § 2. 
 
Part: the Second. 
 
 Pose Plan 
 

 ■ 
 
 
 
 
 
 
 
 
PRACTICAL PERSPECTIVE. 
 
 17 
 
 V. Again let Z Y X W be a ground plan of a cottage or other object; the sides of 
 which are oblique to the plane of the picture. At the eye draw lines parallel to Z X & X VV 
 intersecting the horizontal line in V1 and V2 : which will be the vanishing points for lines 
 parallel to Z X and X W. (see observe IV sect. 2.) 
 
 VI. C ontinue Z X and Y W to the base line in R and T; and W X, Y Z to the base 
 line in P and (); then with the representations of the two former lines tend to V 7 1, and of 
 the two latter to V2. 
 
 VII. From the eye draw lines to each point in the original ground plan Z Y X W: 
 then (by observ. IX sect. 2) the lines tending to V 1 and V2 will be divided proportionally 
 to the distances of V1 and Y2 from the eye , and to the distances of the original points from 
 the base line in the direction of lines parallel to the lines drawn from the eye to the vanish¬ 
 ing points. 
 
 VIII. The same sort of operation is more generally performed in the following 
 manner. Let the distance of the eye from the point of sight (S) be laid on the horizontal line 
 from S to D and D. Let also the distances of the points in the original ground plans be laid 
 on the base line; as in Fig. 1 . F D is laid from F to N and F B from F to M. Draw lines 
 from X and M to that distance point (D) which lays on the opposite side of the re¬ 
 ceding line F S. Those lines will pass through the points d and b; for F S wi 1 be divided 
 in the same proportions as before, since S D (equal to the distance of the eye) is parallel 
 to F N and F M (equal to the distances of the points D and B ). 
 
 IX. In like manner ( see Fig. 2 ) the distances of the eye from Vl and V2, are to 
 be laid to d 1 and d 2 on the horizontal line-, and the distances of the original points W 
 and Y may be laid on the base line either from T to L and H, or from O and P to G and K. 
 In the first case lines drawn from Land II to d 1 will pass through zv and y on the receding 
 line TV 1; and in the second case lines draw from G and K to d 2 will pass through the 
 same points y and w at their intersections on the receding lines OV 2, P V 2. In either 
 case the ninth problem of the introductory Geometry is performed according to observ. IX. 
 sect. 2. 
 
 E 
 
18 
 
 PRACTICAL PERSPECTIVE,. 
 
 SECOND EXPLANATORY PLATE. 
 
 (Part Second.) 
 
 Sect. 4 I. Hitherto the only vanishing line which has been mentioned is the hori¬ 
 zontal line; which is the intersection of the plane of the horizon with the plane of the picture.. 
 It is also apparent that the plane of the horizon passes through the eye, extending to the 
 boundary of oin sight called the horizon; and that it is parallel to all level surfaces . 
 
 II. Any other plane parallel to any other plane surfaces may also pass through the 
 eye, and intersect the plane of the picture: (except a plane parallel to the picture) and any 
 such intersection will also be a vanishing line, on which vanishing points may be found, and: 
 on which the distances of the eye from such vanishing points may be laid, in the manner 
 taught in the last section with respect to the horizontal line. 
 
 III. The first distance of any vanishing line is the length of a right line drawn fronn 
 the eye upon the vanishing plane, perpendicular to that vanishing line. 
 
 IV. The central point of a vanishing line is that point on which the perpendicular fromi 
 the eye cuts tiie vanishing line. 
 
 VANISHING LINES. 
 
 Sect. 5. Nothing facilitates the knowledge of a science so much as short general views; 
 of its fundamental principles: when all its diversities can be classed by some leading cha¬ 
 racteristic or agreement, common to them all, the mind of the student acquires at once 
 an extensive and systematic idea of the whole, which suggests of itself more real instruction 
 than could have been imparted in the most laboured and diffuse detail. Convinced of this 
 truth I have in the second part of the second Explanatory plate, exhibited at one view 
 
PRACTICAL PERSPECTIVE. 
 
 19 
 
 examples of almost every possible sort of plane surfaces and their vanishing lines. 
 This comprehends the foundation of the doctrine of Perspective as it was simplified by 
 Dr. Brook Taylor, and renders the easy operation, exhibited in Section 3, applicable, by 
 the exertion of a little common sense, to every variety in which an object consisting of 
 plane surfaces can be placed. 
 
 I. The plane surfaces marked 1 are parallel to the plane of the picture , and therefore 
 a plane parallel to them passing through the eye can never intersect the plane of the picture. 
 They have therefore no vanishing line, and are drawn in their natural forms, subject to no 
 other alteration but the diminution of distance (sect. 2. I). 
 
 II. The plane surfaces marked 2, are level , and therefore the plane of the horizon is 
 parallel to them; and their vanishing line is the horizontal line; the central point of which is 
 the point of sight. All lines or objects on such level surfaces are drawn by means of the 
 vanishing points and distance points on the horizontal line as in sect. 3* 
 
 III. The plane surfaces marked 3 are upright with a direction straight forwards or 
 perpendicular to the plane of the picture; they are therefore parallel to a plane passing 
 through the eye perpendicular to the picture and intersecting it in the point of sight by a 
 line perpendicular to the horizontal line . This line is called the vertical line, and will be 
 their vanishing line: and its central point will be the point of sight. Its first distance will 
 also be equal to the first distance of the horizontal line; and lines or objects may be drawn 
 on those upright direct surfaces by means of vanishing and distance points taken on that 
 vertical vanishing line as in the examples for the horizontal line in sect. 3. 
 
 IV. The plane surfaces marked 4 are upright but have an oblique direction to the 
 plane of the picture. Planes parallel to them and passing through the eye will therefore 
 intersect the plane of the picture on either side of the vertical line , in lines perpendicular 
 to the horizontal line: those lines will be the vanishing lines of such oblique upright planes. 
 Their central points will be their intersections with the horizontal line , and their first distance 
 will be the length of a right line drawn from the eye to each intersection. 
 
 V. The plane surfaces marked 5 are not upright , but are perpendicular to the plane 
 of the picture . A plane parallel to them passing through the eye will therefore intersect 
 
20 
 
 PRACTICAL PERSPECTIVE.. 
 
 the plane of the picture at the point of sight , and will make an angle with the horizontal line 
 equal to the slope of such inclined planes. 1 he central point of their vanishing line will be the 
 point of sight , and their first distance will be the same as the first distance oh the horizontal line. 
 
 VI. The plane surfaces marked 6‘ ascend, and that marked 7 descends in a straight 
 forwards direction. Planes passing through the eye parallel to such direct ascending or 
 direct descending planes will intersect the plane of the picture in lines parallel to the horizontal 
 line. The central point of such vanishing lines will be their intersection with the vertical line; 
 and are thus determined: let the first distance of the vertical tine be laid from the point of 
 sight on the horizontal line as a-t 33; and at the point D let an angle be made with the 
 horizontal line equal to the ascent or descent of such planes. The intersection of the elevated 
 or depressed line of such angle with the vertical line will be the central point, through which 
 the vanishing line may be drawn; and the first distance of those vanishing lines will be equal 
 to the distance of the central point from the point 13. 
 
 VII. The plane surfaces marked 8 and 9 ascend or descend in an oblique direction .■ 
 Planes passing through the eye parallel to such oblique ascending or descending planes will 
 pass through the vanishing point of right lines drawn on such planes in the direction of 
 their obliquity to the horizontal line, and through the vanishing points of right lines drawn 
 in the direction of the obliquity of such planes to the vertical line. The nature of such 
 planes will admit of much diversity in their vanishing lines, and practice will render their 
 delineation familiar. The central points of any oblique inclined vanishing, line is found by 
 drawing a perpendicular from the point of sight to such vanishing line: and the first distance 
 thereof will be found by lay ing th e, first distance of the horizontal line from the central point 
 of the oblique vanishing line and drawing thereto a line from the point of sight, which line 
 will be the first distance sought. Thus if V d V f be an oblique inclined vanishing line; draw 
 from S (the point of sight) a perpendicular intersecting V d V t inCpt; then C pt will 
 be the central point of Vd Vf; and laying the first distance of the horizontal line (that is 
 the distance from S to eye) from C pt to m, join S and m, and, the line S m will be the 
 
 first distance of that oblique inclined vanishing line. 
 
 These oblique lines will be seldom necessary to be actually determined by the land¬ 
 scape painter, but their general direction should be carefully considered tor ihe sake of those 
 vanishing points which, rising or descending in oblique directions will befound in them. All 
 lines that are parallel to each other in real objects, will, if they are not also parallel to the 
 
PRACTICAL PERSPECTIVE* 
 
 21 
 
 picture, tend to the same vanishing point. It is therefore the business of the landscape 
 painter to determine that common vanishing point as accurately as possible, even when 
 taking a view in the open fields without ruler or compasses; and this he cannot do without 
 a clear idea of the contents of this section. It is this clear idea, which, with the practice 
 contained in the following examples, will enable him to reap the knowledge of the genuine 
 principles of his^art; and to lay aside the tedious and intricate operations of perspective 
 delineation, with a certainty that his judgment hath imbibed from them such criterions 
 as cannot err*. 
 
PRACTICAL PERSPECTIVE* 
 
 22 
 
 PLATE L 
 
 Sect. 6. It has been said in sect. 2, observ. Ill,, that ail walls, sides of buildings, &c*. 
 that are directed straight forward from the spectator, must tend to the point of sight. Of 
 such a nature are the walls, &c. in this plate, that are not opposite or.facing to the spectator:- 
 except the sloping sides of the pyramid. 
 
 I. . All walls, sides of buildings, &c. which are exactly opposite or. facing to the; 
 spectator, are drawn in their natural forms, the dimensions only decreasing (sect. 2, observ*. 
 1.) according to the distance. 
 
 The fountain side of the pedestal of the pyramid is opposite to the spectator; also* 
 two sides of the building;. 
 
 II. In this plate the height of the eye is supposed to be the natural height of a humam 
 figure. This need not always be the case, but it is preferable in general, and particularly ire* 
 views where the ground is nearly level. 
 
 III. Having determined the height of the eye of the spectator, the horizontal line 
 II O, must be drawn that height above the lower line of the drawing (sometimes called the 
 
 ' ground line) , and parallel to that lower line. 
 
 IV. 'The center , C, is then determined, or as it is generally called the point of sight „ 
 at pleasure on the horizontal line. 
 
 V. Observ. IX. of the second section, has shewn the use of the distance of the 
 spectator in finding any point in the picture. Let the supposed distance be laid from; 
 the point of sight C on each side to D and D. 
 
 VI. Remember that the horizontal line, the point of sight , and the distance, are absolutely 
 necessary to be determined before any drawing is begun,, or some errors will unavoidably 
 happen. In taking views they will be found useful directors of the artist, and even in 
 copying prints they will be advantageously attended to.. 
 
b © 
 y 
 

 
 
 
 
 
 
 
 
 
 
PRACTICAL PERSPECTIVE. 
 
 23 
 
 VII. By observ. III. sect. 2. the tendency of the receding lines in this plate is known. 
 A thin ruler laid on the point of sight, C, and along any oblique line, will fully explain 
 any thing that may be required in that respect. 
 
 VIII. The proportions of the receding parts of the buildings remain to be explained: 
 for this let the reader call to mind theIXth observ. of sect. 2L 
 
 The line A BGH drawn from one corner of the building intended to be proportioned, 
 is parallel to the horizontal line. The part A B, represents the width of the first wing, if 
 it were opposite to the spectator;, the part B G represents the distance between the wings; 
 and the part G M is equal to A B, and is the width of the farther wing. A ruler laid 
 from the distance (D) near H, to B, to G, and to M, will give the perspective proportions 
 on the line drawn from A to the point of sight. (See observ. VII. this sect. ) 
 
 IX. The pedestal of the pyramid is square-; PR is therefore in the original object 
 equal to P W.. The line P Q is therefore drawn parallel to the horizontal line, and equal 
 
 % to P W. A ruler laid from Q, to the distance (D) near O, will give the point R on a 
 line drawn, from P to the point of sight, (See the lXth observ. sect. 2).. 
 
 X. If at R a line be drawn parallel to P W, and at W a line be drawn tending to the 
 point of sight, the figure PRTW will represent the square base of the pedestal. The 
 lines PT, W R, will cross each other at X, which will be the center of the square foun¬ 
 dation of the obelisk. Let XZ be drawn from X perpendicular to the horizontal line 
 (Geoin- Pr. II.), and the inclined sides of the obelisk will meet in a point on that perpen¬ 
 dicular line, as they do in the point Z. 
 
 XI. For the rest of the drawing, the eye and judgment may be trusted', the accuracy 
 of which po wers it is the business of perspective to increase. 
 
 XII. It must be carefully observed that figures supposed' to be about the same height, 
 and upon the same level ground, in a drawing in which the horizontal line is placed, as in 
 this plate, about the natural height of the eye, should have their heads touching the 
 horizontal line in whatever part of the drawing they may be. The neglect of this rule 
 produces great absurdities in many views, &c. which are otherwise beautiful. 
 
?A 
 
 PRACTICAL PERSPECTIVE. 
 
 PLATE II. 
 
 Sect. 7. AS the example of the last section was constructed upon the Illrd. observe 
 of sect. 2, so is this upon the fourth observation o( the same section. The walls, sides of 
 buildings, &c. of this example are all oblique to the eye, therefore do not tend to the 
 point of sight. 
 
 I. The horizontal line and the point of sight must be determined in the same manner 
 as in the last example. (Seeobserv. II. Iff. and IV. §6.) 
 
 II. Since the sides of the buildings are not directed straight forward, the angles they 
 make with the plane of the picture must be determined. In this example, the front of the* 
 abbey makes an angle of 48° with the plane of the picture, and as its walls are square with 
 each other, the other side must make an angle of 42°, which is the number of degrees 
 wanting to complete a right angle, (called the complement to the former angle). 
 
 III. At the point of sight, let C E be perpendicular to the horizontal line, and also- 
 let C E be equal to the distance of the eye of the spectator. Let the line P P be drawn 
 through E, parallel to the horizontal line. At E, let an angle be made of 48° with the 
 line P P, on that side of the picture to which the front of the abbey is directed, and let 
 the side EVa, of the angle be continued til! it touches the horizontal line in Va. The 
 point Va will be the vanishing point (IV. and YL of § 2.) of all the lines that recede 
 from the eve of the spectator, in the same direction as the front of the abbey. All which 
 lines will be easily discovered by laying a ruler on Va, and on any line of that tendency. 
 The point Vb is found by making an angle of 42° in the same manner as at E, and is the 
 vanishing point for the other side of the abbey, &c. as may be known by the application 
 of a ruler. 
 
 IV. The distance of the eye of the spectator from that point of the plane of the 
 picture in which the front of the abbey, &c. vanish, is the line Va E; the truth of which 
 may be easily apprehended. That distance being laid from Va to Da on the horizontal 
 line, the proportions of the towers and porch in the front of the abbey may be determined 
 in the same maimer as the proportions of the wings of the building were in the last example. 
 
ILJNES INCLINED, TCRTHE PICTURE. 
 
 'ub lulled- Jan. i.iSod . byJBdtvdOmu>, 5qBond/Streex 
 

 
 
 
 
 
 
 
 
 
 
 
PRACTICAL PERSPECTIVE. 
 
 25- 
 
 In the same manner E Vb is laid on the horizontal line, and determines the point 
 Db, by which any lines that tend to Vb may be proportioned 
 
 V. The cross is exactly opposite and parallel to the front of the abbey, and there¬ 
 fore tends to the same vanishing points. The rest of the drawing may be completed by 
 the observation of the pupil, attention being paid to what was before noticed concerning 
 the figures in the last examnlc. 
 
 O i- 
 
 Sect. 8. As the upright, stone on which the title is written in the title plate may also 
 illustrate the principles of this example, I shall here mention that it is drawn upon the 
 same oblique construction. The vanishing point of its front is out of the limits of the 
 paper, but the distance or proportion point of that vanishing point is marked Db. Va is 
 the vanishing point of the side of the stone, and Da is its distance or proportion point. 
 By help of these distances the length and thickness of the stone are determined. The line 
 N A M is drawn parallel to the horizontal line at the corner point A, taken at pleasure? 
 and because the stone is supposed to be three times as long as it is thick, three divisions 
 are laid from A to M, each division being | of what its length would be were it opposite 
 or parallel to the spectator. Then, because the bottom of the front tends to the vanishing 
 point Vb (which is out of the limits of the plate), a line drawn from Db to M will determine 
 the point L. For the thickness, one division is laid from A to N, and because the bottom 
 of the side tends to the vanishing point Va, a line drawn from Da to N will determine 
 the point B. Then A L is the perspective length, and A B the perspective thickness ot 
 the stone, in proportion to the distance of the eye of the spectator from those points in 
 the plane of the picture, which denote thse points in the actual horizon, to which the 
 sides of the stone are directed; and in proportion to the distances of the points A, L and B 
 in the real object, from the plane of the picture in the directions of the sides of the object. 
 See observ. IX. § 2. also Prob. IX. of Geom. 
 
 & 
 
 PLATE 
 
26 
 
 PRACTICAL PERSPECTIVE;, 
 
 PLATE XIL. 
 
 Sect. 9- AS in the two foregoing plates the Illrd and IVth observ. of sect. 2, were’ 
 exemplified, so in this will be found examples of the Vth, in which it is said that all sloping 
 walls, roofs of houses, hills, &c. must tend to some point either above or below the hori¬ 
 zontal line. 
 
 I. Having determined the horizontal line, the point of sight, and the distance, com. 
 sider what angles any leading object makes with the Picture; as, for instance, the pedestal ; 
 in front, parallel to the left side of which rises the first flight of steps. 
 
 II. At the point E, construct those angles* (as directed by observ. III. § 7-) andi 
 observe where their sides, cut the horizontal line as in Yb and Vc, and lay the distances * 
 of the vanishing points so found from Vc to Dc, and from Vb to Db, and construct the 
 pedestal as in the example given in the last section. 
 
 III. At Vb, which is the vanishing point for all lines parallel to the left side of the 
 pedestal, draw a line perpendicular to the horizontal line, 
 
 IV. If the angle which the first rise of the steps makes with level ground be known;, 
 make at Db (which is the distance of Vb), that angle with the horizontal line, and mark 
 where its side rising cuts the perpendicular raised at the vanishing point, as in Vd. 
 
 V. When the slope rises from the spectator, the angle is constructed above the 
 horizontal line: when the slope descends from the spectator, the angle must be beneath the 
 horizontal line. 
 
 * Those angles are not given here, and in taking views they,cannot be supposed to be as accurately determined 
 as when a piece of architecture is the subject to be drawn: but it must be remembered, that whatever angle is 
 assumed as the apparent angle, which the side of a building, &c. is supposed to make with the plane ot the picture, 
 the other angles of the building must be made to conform therewith: as if, for instance, the sides are at right?: 
 angles to each other, the correspondent angle at Emust.be the complement of the assumed angle. 
 
'‘ut'/tjhrJ .fast'', i itfo5 . Z>y Zuluu d Orme.jaJiond Store, 
 

 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
PRACTICAL PERSPECTIVE. 
 
 n 
 
 VI. As it will often happen that the angle of the slope cannot be exactly known ? 
 it will be sufficient for the accuracy of Landscapes to take a point in the perpendicular 
 drawn as directed in observ. Ill, according to the apparent slope of the hill or building. 
 
 VII. The perpendicular in which the point is either so taken, or found by the con¬ 
 struction of a known angle, must always be erected at the vanishing point of such level 
 lines, as might be supposed to pierce the hill or building directly from the rise or fall of 
 the slope, as the side lines of the tread of the steps, which are level, and tend directly from 
 the rise ot the slope, and have their vanishing point in Vb. 
 
 VIII. The supporting wall of the first steps is drawn by making the top'tend to its 
 vanishing point Vd. 
 
 IX. As any level line direct from the front of the rise of the second flight of steps 
 would tend to the point of sight, the vanishing point of the supporting walls will be in the 
 perpendicular to the horizontal line at the point of sight, that is the perpendicular C E. 
 
 X. If the angle were known, it might therefore be made at Da, or Da,, which are 
 both equal to C E, and its rising side would cut the perpendicular in Vf; but if it be not 
 known, the point Vf in C E may be assumed according to the supposed slope. Then 
 Vf is the vanishing point of the rise of the upper flight of steps. 
 
 XI. To proportion the heights of the steps, let a perpendicular line be drawn, as 
 A B, touching the bottom step, and set upon it the height of each step, proportionate to 
 the distance of the first step. From each point in the line A B, draw lines to the vanishing 
 point Vb, and observe where those lines cut the top of the wall in a, b, c, d, e; at the points 
 a, b, c, &c. draw lines parallel to A B, and you .will have the heights and treads of the 
 steps as in the example. Note, the bottom step in this example is much higher than the 
 others. The upper flight of steps may be proportioned in the same manner. 
 
 XII. The portico is constructed according to the instructions given to Plate I, as 
 tends to the center or point of sight; except the top or roof, which is constructed in the 
 following manner. 
 
.28 
 
 PRACTICAL PERSPECTIVE. 
 
 XIII. The nearest side of the sloping roof rises from the spectator, and since its level 
 lines tend to the point of sight, its vanishing point must be in the line perpendicular to* 
 the horizontal line at C. Let it be Yg, found either by knowing the angle and constructing , 
 it at Da accordingly, or by assuming it with regard to the apparent slope. 
 
 XIV. The further side descends from the spectator, or from the plane of the picture,,* 
 its vanishing point will therefore be beneath the horizontal line, and because the slopes of 
 each side are alike, it will be the same distance below the level vanishing point as the 
 former vanishing point is above it. Therefore make C Vh equal to C Vg. Then Vh is 
 the vanishing point for all lines descending from the plane of the picture in that direction, , 
 so that the lines composing the roof of the portico will tend either to Vg ascending or to* 
 Vh descending. 
 
 XV. The level lines of the right hand wall tend to the point of sight. The descend¬ 
 ing slope lines tend to Ve, found as before directed; as do all the lines of the declivity. 
 The house at the bottom of the hill is constructed according to the instructions given in 
 sect. 6, and in the present section. 
 
 XVI. The tops of the buttresses of the right hand wall meet in a point, and are 
 constructed according to sect. 6, X, as are also the feel of the buttresses, which if continued 
 would rise to the same point. 
 
 XVII. The circular parts of the openings in the portico may be drawn by hand> 
 their perspective construction depends upon the instructions in the. next section. 
 
 3?LAT£. 
 

 
 
 
 »* . 
 
 
 
 
'.iH.u.jj ,/ 'm. i. ox ’r:r/ r rr}jr,r sxoanro xr^Taovn 
 
 Published. Janfi.zSoS. iyMd». 4 Omu.SaJBmiStreet. 
 
PRACTICAL PERSPECTIVE. 
 
 29 
 
 PLATE IV. 
 
 Sect. 10. AS all plane objects, which are directly opposite to the eye or parallel to 
 the plane of the picture, are delineated in their original forms, so all the objects of this 
 plate depend upon the most simple principles of perspective. 
 
 The front and sides of the buildings are drawn by the instructions for the first Plate, 
 and the circular parts are opposite to the spectator, and therefore remain exactly circular. 
 
 I. The small square garden box, with circular apertures, on the mound on the right, 
 is thus constructed: 
 
 The sides, roof, and the square front posts, depend entirely upon the instructions 
 given for Plate the first. 
 
 II. Let the height of the upright part of the door-way be determined by the straight 
 line A B. Bisect A B in M, and at M, as a center, construct, the outer circle. 
 
 III. To find the center for the first inner circle: draw the lines BC and MC to 
 the point of sight, and at L draw L N parallel to A B. Then N will be the center of that 
 inner circle, and N L the radius. 
 
 IV. 7 he other aperture being determined by the process taught in sect. 6, observe 
 where the inner part of the upright part of the door-way cuts the line BC, as it does in the 
 point E. At the point E, draw a line parallel to A B, which will cut M C in O: then 
 O is the center, and O E the radius of the second inner circle. Then observe where the 
 outward part of the upright part of the door-way cuts the line B C as it does in the 
 point S, and draw a line at S parallel to E O or A B, which line will cut M C in P, then 
 is P the center, and PS the radius of the second outward circle. 
 
 A . 1 he Gothic arched way is likewise opposite to the spectator. The sides and the 
 
 upright parts ot the inside posts are constructed the instructions given in sect G. 
 
 II 
 
30 
 
 PRACTICAL PERSPECTIVE, 
 
 VI. The arch is composed of the parts of two circles, the centers of which are the 
 exterior points at the opposite sides. Thus, A is the center of the opposite circular parts 
 on the front post, and B is the center of the opposite circular parts at A. 
 
 VII. Let A C be drawn, and also B C. And let A B be divided according to the 
 widths of the posts, by the rule given in sect. 3, as it is in the points 1, 2, 3, 4, &c. and 
 draw lines across parallel to A B, cutting the line B C in G 2 C , 3 C , 4% &c. then the 
 points G, 2 C , 3 C , 4 C , &c. will be the centers of the opposite circles, which rise from the 
 line A G, as the points 1, 2, 3, 4, &c. will be centers of the opposite circles which rise 
 from the line B C. 
 
 PLATE: 
 

 
 
 
 
 
 \ 
 
 
 
 
 
Published. Jan/.'i, 1806.byEcLw*'Orme. 5 g Bond Street'. 
 
PRACTICAL perspective. 
 
 3t 
 
 PLATE V. 
 
 Sect. II. WHEN the plane object is not directly opposite to the spectator, or 
 parallel to the plane of the picture, then, as has been said before, the delineation becomes 
 different from the original form: the circle therefore cannot be described from a center 
 in its representation: it becomes an ellipse or oval, and certain points are to be found in 
 its periphery through which it may be described. Very great exactness is not irideed 
 necessary in landscape drawing, but since arched ways and other curvatures must frequently 
 occur,, and in many very beautiful drawings of ignorant artists, these objects, when intro¬ 
 duced, raise ridicule and disgust, it will be proper to pay a little attention to their 
 construction,, and for that purpose to consider these few diagrams which will be again 
 referred to in the following plates. 
 
 I. Fig. 1. is a circle on the ground, or some plane parallel thereto. Every circle 
 may be contained in a square. Let SQl T R be the representation of that square 
 (V 7 1 being supposed to be the point of sight or center of a picture, and Dl the distance), 
 and let A or B be a point perspectively bisecting S U or R Q. Draw A B parallel to S Q, 
 and bisect it in C, and draw C V through C, cutting U R in E, and S Q in H. Open your 
 sector and make C A or C B a transverse distance on the line* of sines between 90° and 90°. 
 Then take the distance between ‘ 30 ° and 30°, and lay it from C to 30 on each side: and 
 lay the distance between 60 ° and 6 0° from each side of C to 6‘0 and 60. By laying a thin 
 ruler from the distance Dl, transfer the points 30 and 60 each way to the line HE. 
 Through the points in the line A B draw lines to the point of sight. Through the points 
 in the line II E, draw lines parallel to the line A B. Observe the intersections of those 
 lines in a, b, c, d, e, f, g, h, which points, together with the four A, E, B, H, will make 
 twelve in the circumference of the circle through which its representation may be drawn 
 by the hand with ease. 
 
 * The line of Sines on the sector is generally on the same side with the double line of tangents marked T, 
 and is itself marked b, It may be distinguished from the line of secants, because the latter line does not rise to 
 so high a number as 90° 
 
PRACTICAL PERSPECTIVE. 
 
 IF. If the circle to he represented he too small for this operation with the sector*., 
 describe a circle with ihe radius of jour circle proportioned to the distance, on anv other 
 paper, as figure 5 Set the radius round it, which will measure it exactly six times, as 
 at r, r, r, r, r, r: divide any space, rr, in two at s, and continue that division round the 
 circle. Through anv opposite divisions, r, r, or s, s, draw the perpendicular diameters A B 
 and DT; and through the otner divisions draw lines parallel to A B and to D£, as in 
 the figure. Then on the lines C A, AG, &c. will be piojected the sines of 30° and 60°, 
 which may be then transferred to your figures. 
 
 III. Fig. 2. Represents a double arch, or the perspective delineation of two con¬ 
 centric semicircles. The vanishing point of the plane on which the arches are struck 
 is at V2, the point of sight or center is C, the distance D'2: A S represents the half- 
 side of a perspective square containing the largest semicircular arch, and is therefore a 
 radius of the semicircle. Draw any line, A L, parallel to the horizontal line. Lay AS 
 on it to II and to L. Make A S a transverse distance berween 90° and 90°, and take SO 1 
 and 60° as before; lay the 30 and 60 from A towards S, and from SI towards A and 
 towards L. From the divisions 30 and 6‘0, on the line A S, draw lines to the vanishing 
 point Y3, and by means of the distance, D2, project the divisions of the line A L on; 
 the line A B, as at a, h, b, a, and at those points draw lines parallel to A S, and the 
 intersections of those parallels with the other lines drawn to the point \ 2 from the points 
 of division, will give the points a 1 , r 1 , c 1 , h 1 , through which the greater arch may be de¬ 
 lineated. 
 
 IV. The smaller arch is projected in the same manner G R is radius, G I, I K, 
 is its diameter on the line parallel to the horizontal line, and a 2 , r, cr, Ir, are its four 
 points so found. The point A, X 1 , B, are easily conceived to be in the circumference 
 of the outward arch, and the points G, X', D, in the inward or smaller arch. 
 
 V. Fig. 3. Is anarch constructed in the same manner. Dl is its vanishing point, 
 and Vl is its dividing or distance point, instead of the sines of 30° and 60°, the sines 
 of 15°, 30°, 45°, 6.0°, 73°, are taken, by which means its circumference is exactly divided, 
 into twelve parts for the sake of drawing the surrounding stone work. 
 
PRACTICAL PERSPECTIVE. 
 
 33 
 
 VI. Fig. 4. Is an ellipse projected in perspective (vanishing point V2,distance D 2). 
 L X is its height with respect to distance, &c. L X is therefore made a transverse distance 
 between 90° and 90° on the sector, and the sines 15, 30, &c. are taken and laid on the 
 line LX. L P is its longest diameter, which is bisected in Y. L Y is then made a trans¬ 
 verse distance on the sector, and the points 15, 30, &c. taken as before: those points are 
 projected by means of the distance point on the perspective diameter LZ, and the points 
 b, c, d, f, g, &c. are found as similar points were in the last examples. 
 
 I 
 
 PLATE 
 
34 
 
 PRACTICAL PERSPECTIVE.. 
 
 PLATE VI. 
 
 Sect. 12. In this plate, the arch of the bridge is a double semicircle, and is delineated 
 according to figure 2, in the last section. It therefore scarcely needs a repetition of in¬ 
 structions. 
 
 I. The bridge is oblkpie to the picture and to the spectator, it therefore belongs to< 
 the instructions given in section 7- 
 
 II. Its vanishing points are Yl and V2, and its distance points are Dl and D2- 
 The center of the picture is Ck 
 
 III. The sloping parts of the bridge belong to the instructions given in sections 6 and 4: 
 the vanishing point of the rising part is V3; the vanishing point of the descending part 
 is V4. To these the rising and descending tops of the railing. &c. tend. The level part 
 of the bridge tends to the vanishing point Y2. 
 
 IV. The width of the bridge being determined, the farther railing may be drawn 
 tending to the same vanishing points. 
 
 Y. Ihe middle ol the level part of the bridge being determined by means of the 
 distance point D2, draw there a line perpendicular to the horizontal line, and let it cut 
 the line A M, V2 in M; on that perpendicular determine the height of the arch as M X 1 . 
 At M, draw the line M 11 parallel to the horizontal line, and set M X 1 to R. And laying 
 a ruler at D~ and R, mark where it cuts the line A M, as in A. And at A, draw the line 
 A S parallel to M X 1 , terminated at the point S by a line drawn through X 1 and the 
 vanishing point V2. Then the arches may be drawn as is shewn in fig. 2-(§ 11, observ. 
 III.) Note, the arch in the diagram of plate V is rather larger than that on the bridge, 
 for the sake of perspicuity. 
 
 VI. The horizontal line in this plate is about a foot below the height of a man. This 
 is done because the principal object is of itself low, as well as the surrounding country, 
 but by the lowness of the horizontal line it acquires some elevation, and looks better than 
 it would do were the horizontal line as high as usual. 
 
Published Jan ' l,i8o5, by Jldw d Orme. 5q Jiorul Street-. 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
PRACTICAL PERSPECTIVE. 
 
 55 
 
 VIT. The figures are all proportioned according to the height of the man who 
 appears to have caught a fish,, his height is projected to the bridge, and gives the height 
 of the figures on the bridge. The nearest figure who is fishing, is not so tall as the others.. 
 
 PLATE 
 
36 
 
 PRACTICAL PERSPECTIVE.. 
 
 PLATE VIL 
 
 Sect . 13. I. THE interior part of an ancient bath is here represented. The hori¬ 
 zontal line is about the height of a man. The center of the picture, or point of sight is at C. 
 The sides of the building vanish in Vl and Vg, which are the same as the distant points- 
 of the center of the picture, and their distance points are Dl and D2. That part of the 
 plate which consists of right lines and their divisions is therefore easily understood, from 
 what has been before observed in sections 3 and 4 particularly. 
 
 II. The elliptical or oval arch may also be delineated according to the instructions 
 given in section 8, VI; concerning fig 4. Thus LX in this plate is the same as L X in 
 Plate V, fig 4, and LP here is the same as L P in that example; the construction is 
 therefore exactly the same. So of the higher oval, T S is the height, and T W is the length* 
 and the construction is perfectly similar. 
 
 III. The rising sides of the roof are also elliptical. The small part which is seem 
 may be drawn by the hand, without recourse to points; but since exactness in buildings 
 is more requisite than in the general landscape, the manner of obtaining points shall be 
 explained. 
 
 IV. At the point where they meet, that is, at M, let a line parallel to the horizontal 
 line be drawn, at that point also let the lines be drawn that form the basis of the elliptical 
 arches of the sides (those lines are marked () and R)r On the lines O and II continued, find 
 the middle point of the sides, which may be more easily done, as the building is supposed 
 square, and project those middle points on the line at M, parallel to the horizontal line. 
 At M let a perpendicular be erected (this is supposed to be done on the plate, where most 
 of the lines belonging this operation are omitted, since it will be understood clearly 
 enough without them). On that perpendicular set the height of the ovals with respect to 
 that distance. The height of the ovals on the example is one-fifth of their length. You 
 will then have the height and half the length of each oval, and they may be projected in 
 the same manner as the former examples of elliptical arches. 
 
VARIOUS ARCHES INCLINED TO THE PICTURE. 
 

 
 
 
 
 
 \ 
 
 
PRACTICAL PERSPECTIVE. 
 
 37 
 
 V. The arches in the right hand wall are circular, but being oblique to the eye, are 
 constructed according lo the instructions given in section 8, fig. 2 and 3. A H is the 
 height of those arches according to the distance of the line A II from the eye. AZ is the 
 line parallel to the horizontal line on which the distances and widths of the arches are to 
 be set, according to the proportion of A II. Those widths, &c. are to be projected on a 
 line drawn from A, and tending to the vanishing point Vl, forming perspectiveiy the basis 
 of the arches. The arches may then be drawn through points found by the sines of the 
 sector as before taught. 
 
 VI. The bath is circular; two arches of circles must therefore be described repre¬ 
 senting the width of the rim of the bath. 
 
 VII. It was said before, that the building was exactly square, and that its sides 
 tended to points equally distant from the point of sight, and therefore to its points of 
 distance. The reason of the following operation will be manifest on a little reflection. 
 Having determined the point I, a point in the circumference of the outward circle exactly 
 opposite the middle of the great elliptical arch, let a line* be drawn from that point I to 
 the vanishing point V2. Then lay a ruler from the point of sight C to the corner point F; 
 observe where it cuts the last drawn line, as in the point N, and through the point N draw 
 a line from the vanishing point Vl. Then will those two lines be the two sides of a square 
 containing the proposed circle, of which I is a point in the circumference. Draw JK 
 parallel to the horizontal line, and on the side of the square tending to Vl you will have 
 the point K, another point in the circumference of the circle. T hen if the edge of a ruler 
 be laid on the point N, and the distance point D2, it will give the point Q on the line 
 parallel to the horizontal line, then I Q will be the radius of the circle with respect to that 
 distance. Let it be made a transverse distance on the sector, take the divisions of the sines 
 as before taught, and lay them both from I and from K. Let those from K be projected 
 on the side N K of the circumscribing square, and those from I on the side I N. Then lines 
 drawn to each point will give the points in the circumference of the circle required. The 
 inner circle may be drawn in the same manner. 
 
 * This line, and many of the others in this plate, are omitted, because they may he easily supposed, and expe¬ 
 rience shews that it is enough to describe the direction of lines perspicuously in such diagrams as these. 
 
 K 
 
38 
 
 PRACTICAL PERSPECTIVE. 
 
 VIII. For the pavement, let the length of a diagonal of one of the squares at the 
 bottom boundary of the picture, as L, be laid along the bottom line, and rule lines to each 
 vanishing point, and you will have the squares of the pavement. But since the bottom 
 boundary will not be sufficiently long to contain enough divisions for all the squares, another 
 line must be drawn where the squares begin to fail, and the diagonals laid upon that in pro¬ 
 portion to the distance, and lines again drawn to each vanishing point. Or, let the diagonals 
 proportioned to their distance be at first laid upon the line ION, continued to the inner 
 line of the front of the bath, and lines ruled to each vanishing point as before; by this 
 method more squares will be obtained at the same time. 
 
 PLATE 
 
OF INACCESSIBLE VAN LSI! I NO I V O IJV T S . 
 
PRACTICAL PERSPECTIVE. 
 
 39 
 
 PLATE VIII. 
 
 Of inaccessible vanishing Points , $c. 
 
 Sect. 14. IN perspective a great portion of the art depends upon the ingenuity of 
 the artist; the principles are of themselves simple, but the variety of the forms and posi¬ 
 tions of the objects to be delineated, renders the application of those principles sometimes 
 intricate. The instructor can do more than point out the principles upon which the artist 
 must proceed : That task is already performed in the foregoing observations; the present 
 plate exhibits a few difficulties with the expedients made use of to overcome them, and it 
 is hoped and believed, that with these and the foregoing lessons, the pupil will be fully 
 acquainted with as much of the practice of perspective as may enable him to take a view, 
 or draw a landscape with accuracy. 
 
 I. When the vanishing point of level lines receding from the eye is out of the limits 
 of the paper, canvas, &c. a difficulty arises, which must be thus supplied : 
 
 Let C be the center of the picture, or point of sight; let E be the eye, then C E is the 
 distance. Let V2 be one vanishing point found in the manner taught in section 7; the 
 complement of its angle is 18°, and its angle 72°. The other vanishing point to which the 
 lines in the left side of the building tend would be very distant, its visual line making an 
 angle with the line C E of 72°: it is therefore inaccessible. Therefore instead of the whole 
 line C E, take any part of it, as C A f, which is f of it, and then make an angle of 72°, by 
 drawing the line A| to Bf. At B^ raise a perpendicular, and take Bf E upon it, a 
 proportional line to C A J, in such proportion as 4 is toS*, and draw Ai F, which will tend 
 to the inaccessible vanishing point, and may be called the vanishing director. 
 
 * This may be done by dividing C A £ into four parts, and making Bf F equal to three of those parts, and if 
 C A is £,;, or l, Sec. of the whole height, it should be divided in 4, 5, 6, &c. parts, and B F be made equal to 
 3, 4, 5, &c. of those parts. Or on the line of lines marked L on the sector, make C A a transverse distance be¬ 
 tween 4 and 4, 5 and 5, &c. and take B F, the transverse distance, between 3 and 3, 4 and 4, Sec. 
 
40 
 
 PRACTICAL PERSPECTIVE. 
 
 II. Let O and H be two points in the corner of the building, from which it is required 
 to draw H N and O P, tending to the inaccessible vanishing point. O H* the perpendi¬ 
 cular junction of the sides of the building cuts the horizontal line in the point G, and the 
 vanishing director in the point I, and YKW the boundary of the picture (or any other 
 perpendicular line may be made use of) cuts the horizontal line in Y, and the vanishing 
 director in K. Make GLon the horizontal line equal to G I, and Y M equal to Y K. Join 
 L H, and at M draw M N parallel to L H, cutting the boundary line of the picture in N, 
 draw H N, and it will be the line required lending to the vanishing point. Also join LO 
 and draw M P parallel to L O, cutting the boundary line of the picture in P. Draw O P, 
 and it will be the other line required tending to the vanishing point. In the same manner 
 are drawn the other lines tending to the same vanishing point as the line Q X, and the lines 
 from the diameter of the semicircle. 
 
 III. When the vanishing point is inaccessible, the distance point cannot be obtained 
 
 by the method before taught. But since C Ai is \ of the distance of the eye from the 
 point of sight,B \ will be | of the distance of the inaccessible vanishing point, there¬ 
 
 fore take ZA| which is the excess of B^ A* above Bi C, and lay it four times from C 
 to Dl, then Dl is the distance point sought. 
 
 IV. When the vanishing point of lines descending or ascending is inaccessible, the 
 operation is nearly the same. 
 
 Let it be required to draw the ascending slope* on which are the steps in front of the 
 building. At the distance point Dl, make the known or supposed angle of the ascending 
 slope, which angle will be B Di A. Take D A equal to \ (or any other portion) of A^ BN 
 therefore equal to h of the whoie distance. At A erect a perpendicular, and at the point 
 B in which it cuts the ascending line Dl B, draw the line B F parallel to the horizontal 
 line, and make BF proportional to A Dl as 15 is to lG, and draw a line through the 
 points A and F , then both the lines Dl B, and A F are vanishing directors. Now, let it 
 be required to draw the ascending lines of the slope at H and 0, and first at H: draw 
 the line GUI through the point II parallel to A Dl, cutting one vanishing director in 
 G and the other in I. Make G L equal to G I and A M equal to A Dl. Join LII and 
 
 * "'his slope though descending from the ground on which the spectator is supposed to stand, yet ascends 
 from the picture. 
 
PRACTICAL PERSPECTIVE. 
 
 4>lt 
 
 and draw M N parallel to LH , cutting A D1 in N, then through N and II draw the 
 slope line required. In the same manner the point P is found, by means of which the 
 slope line at 0 is to be drawn. 
 
 V. The mitre point f or mitre vanishing pointy is a point in which one of the diagonals 
 of a square would vanish: its use is in projecting the jutting corners of buildings, &c. 
 which are always upon the diagonal of a square. Thus a line drawn through the mitre 
 point and the point II of the building will tend to the jutting corner, which may thereby 
 be easily determined. Also if the building be supposed square, and it be necessary to 
 find the center of it (suppose of the roof): let II H be the half of the perspective length 
 of the left side, and draw H Y2 and H to the mitre point, then their intersection at G 
 is the center of the building- If the corners of the roof tend to any point over the center 
 (as is frequently the case), erect at G a line perpendicular to the horizontal line, and on 
 it take the point I and make the corners of the roof tend to I as in the example. The 
 center will also be useful to find the tendency of the diagonal of the further corner L , by 
 drawing a line through G and L. 
 
 O O 
 
 \I. These modes will appear tedious to the painter of landscapes: use will enable 
 him to shorten them, and the more he becomes acquainted with the science by frequent 
 practice, the more likely will he be to discover simple expedients which may facilitate 
 his operations: bat he must indispensibly make himself acquainted with the regular 
 methods first, or he will fall into continual errors. On the right hand side of the print is 
 the representation of a shed, of which the open sides incline to an inaccessible vanishing 
 point in the horizontal line, and of which the sides of the roof incline to inaccessible 
 vanishing points above and below it, yet may be performed by simple expedients. 
 
 Let the bottom be drawn, and let the line at A tend to the inaccessible vanishing 
 point as before taught, and let it be perspectively bisected in J, and raising a perpendi¬ 
 cular at J, let the upper point 6 be determined, and also the depth of the roof at the lower 
 point 6, The line A 13 and the top line of that side, also the middle line of the roof, and 
 the line at the lower 6, will all tend to the accessible vanishing point V2; let them be 
 drawn and divided according to their distance point D2, as in the example: then lines 
 drawn from the points 1, 2, 3, 4, 5, 0, will complete the figure. 
 
 L 
 
 PLATE 
 
PRACTICAL PERSPECTIVE. 
 
 43 
 
 PLATE IX. 
 
 SHADOWS. 
 
 THE shadows of delineated objects form a part of perspective particularly necessary 
 to the landscape painter: for however inaccuracies may be covered by the artificial sha¬ 
 dows so,common in landscape drawing, yet it will be found not only useful, but in the 
 highest degree pleasing, if the true shadows are assigned to their several objects. 
 
 The sun must be either in the same plane as the picture, or before the spectator, or> 
 behind him : these make three principal distinctions in the shadows of objects. 
 
 The sun being supposed at an indefinite distance with respect to the picture, its , 
 rays are to be considered as parallel to each other, 
 
 When the sun is in the plane of the picture the representations of his rays are always-, 
 parallel to each other, and to the rising line of the angle of the sun’s elevation above the 
 horizon, made upon the horizontal line. 
 
 When the sun is not in the plane of the picture, let a line be drawn from the eye^ 
 making the angle of his supposed or known obliquity with the vertical plane, and where 
 such line intersects the horizontal line let a perpendicular be drawn each way. Again, let 
 a ray from the sun be supposed to pass through the eye piercing the plane of the picture, 
 as it necessarily must, in that perpendicular: then, the point in which it meets that per¬ 
 pendicular will be the place of the sun on the picture and will be the vanishing point of all 
 lines that represent the solar rays. To determine this let the distance of the point which 
 denotes the sun’s obliquity be laid on the horizontal line; and, at that distance make the 
 angle of the sun’s elevation above the horizon. It is manifest that the angle must be made 
 with a rising line, if the sun is before the spectator, and with a descending line if it is 
 behind him; because, the ray passing through the eye will, in the first case, pierce the 
 perspective plane above, the horizontal line, and in the other case, beneath that line. 
 
3 Sun 
 
 D.± 
 
 jsr? 3 . 
 
 £)iayram 2. 
 
 Sun 3. 
 
 <3)iacr 
 
 ram i 
 
 Sun | 
 
 2 . 
 
 Umbra 1 
 
 PitbTzjbeR Jan? i.j.8o5 .ly _Edw d Orme5gBanJ. Siradt. 
 
PRACTICAL PERSPECTIVE. 
 
 43 
 
 To comprehend this more clearly let the two small diagrams in this plate be considered. 
 In the first, PLNM is the plane of the picture: S is the point of sight thereon with respect 
 to the eye at E. II H is the horizontal line, and V T is the vertical line. The sun is tirst 
 supposed to be before the spectator as Sun E E O is a line making with E S (the distance 
 line on the vertical plane) an angle equal to the sun’s obliquity. K O R is the solar per¬ 
 pendicular drawn through the point O; this is intersected in the point Sol above the 
 horizontal line by a ray drawn from Sun 1 to the eye at E. The point Sol is the place of 
 the sun on the picture, from which all the representations of the solar rays must be drawn 
 The sun is,, secondly, supposed to be behind the spectator, as Sun 2. Then (the rest 
 remaining as before) E Q is the line which determines the angle of the sun’s obliquity and 
 D Q F is the solar perpendicular which the ray drawn from the sun through the eye at E 
 intersects in the point Sol below the horizontal line; which is the point from which all the 
 representations of the solar rays must be drawn on the plane of the picture. Thirdly, the 
 sun is in the plane of the picture as Sun 3, and its ray, passing through the eye of the 
 spectator cannot intersect the plane of the picture because it is parallel to that plane; the 
 representations of its rays will retain their original parallism, and will make angles with the 
 horizontal line equal to the angle of the sun’s elevation.. 
 
 The second diagram exhibits the practice of the theory which has been explained by 
 the first. E is again the eye and S the point of sight. The angle S E Q denotes-the sun’s 
 obliquity, and P Q R is the solar perpendicular. Q Z is made equal to the distance Q E; 
 and at Z the angle of the sun’s elevation is made either with a rising or descending line 
 according to the position of the sun before or behind the spectator; and intersecting the 
 solar perpendicnlar either at Sol l or at Sol 2. The shadow of the object A tends forwards 
 because the sun is supposed to be before the spectator: it tends also from the point Q 
 because, being the shadow of a perpendicular object on a level plane its vanishing point 
 will be the intersection of a perpendicular ray drawn from the sun, at Sol 1 , with the 
 horizontal line; as will be shewn hereafter. The shadow will be terminated by a ray 
 drawn through the top of the object A from Sol 1 . For the same reason the point Q is 
 also the vanishing point for the shadow of the object B but as the sun is, in this instance 
 supposed to be behind the spectator, the shadow tends towards instead of from its vanishing 
 point, and its length is determined by a ray drawn from Sol 2 to the top of the object. 
 
 MAXIMS 
 
44 
 
 PRACTICAL PERSPECTIVE 
 
 MAXIMS in the PERSPECTIVE of SHADOWS produced hj the SUN* 
 
 Maxim 1st. The shadow of any right line on any plane will tend to a point in the 
 vanishing line of'such plane: which point will be determined by a ray of the sun drawn 
 from the vanishing point of the right line until it intersects the vanishing line of the plane. 
 
 Maxim 2nd. The shadow of a right line upon a plane to which that right line is 
 parallel will tend to the vanishing point of that right line. 
 
 Maxim 3rd. The shadows of right lines that are in planes parallel to the plane oT 
 the picture, and which planes have therefore no vanishing line, may be resolved into* 
 two cases: viz, 
 
 Case 1. When the sun is in the plane of the picture, the shadow of any such 
 right line will be always parallel to the vanishing line of the plane that 
 receives it. 
 
 Case 2. When the sun is not in the plane of the picture a ray of the sun parallel 
 to any such right line will give the vanishing point of its shadow on the 
 vanishing line of the plane that receives it. Thus, the ray drawn from Sol l 
 (see diagram 2) parallel to the stick C gives the point F in the horizontal 
 line for the vanishing point of its shadow on any level plane 
 
 Maxim 4th. When the plane surface of any object that receives the shadow of a 
 right line is parallel to the plane of the picture (which can only happen when the sun is 
 behind the spectator) the shadow of such right line upon any such plane surface will be 
 parallel to the ray drawn from the vanishing point of the right line to the place of the sun 
 upon the picture. 
 
 Example (Diagram 2). 
 
 The shadow of the stick D (the right lines of which tend to the vanishing point X) 
 has three divisions. On the ground from k to m it tends to the point Y in the horizontal 
 
PRACTICAL PERSPECTIVE*. 
 
 45 
 
 line by maxim I. On the sloping suiface L, the vanishing line of which is V W it tends 
 from n to r to the point W by the same maxim. On the parallel plane surface G the part 
 m n is by maxim 4th parallel to the ray X W Y drawn from bol 2 to the-vanishing point X* 
 
 APPLICATION of the above MAXIMS. 
 
 (SHADOWS No. 1. Tlit Sun in the plane of the Picture.) 
 
 In this the sun’s rays will be parallel to each other and to the rising line of the sun’s 
 elevation; which is marked on the plate, as well as the vanishing lines of the different sur¬ 
 faces. The receedrng lines of the beam on the wall (marked 1) tend to the vanishing 
 point V2. To find its shadow on the wall draw the ray of the sun from V2 until it inter¬ 
 sects the vanishing line of planes A in Umbra 1, which will be the vanishing point for the 
 outlines of shadow required by maxim 1: these are terminated by rays, as a b in the example. 
 
 r Ihe upper bar of the lamp (maiked 2) has the same vanishing point, and therefore its 
 shadow on the Avail and on the side of the sentry box, tends also from the point Umbra 1 . 
 r i he part of the shadow on the roof of the sentry box tends to the vanishin point V2 by 
 maxim 2. The prop-bar of the lamp tends to A 3. T hen (bv maxim 1) the ray drawn from 
 V3 gives the point Umbra 2 on the vanishing line of planes A for the directing point of its 
 shadow on the wall and side of the sentry box; its shadow on the front over the door of 
 the box tends to V3 by maxim 2. 
 
 The upper bar of the sign (marked 3) and its prop-bar have the vanishing line of 
 their plane in the perpendicular at V4; which is the vanishing point of the upper bar 
 as Vo is of the prop. The points for the direction of their shadows on the front of the 
 house are found by maxim 1, at umbra 3 and 4 in the vanishing line of planes A, and the 
 shadows are drawn as in the example oi the lamp (2). 
 
 The post (marked) 4 has its upright lines in planes parallel to the picture and therefore 
 its shadows on the ground will (by Maxim 3, Case 1.) be parallel to the horizontal line; 
 and that part of its shadow on the front of the house will be parallel to the vanishing line 
 of planes A. 
 
 M 
 
46 
 
 PRACTICAL PERSPECTIVE. 
 
 The shadow of the bar (marked 5) on the roof of the house will by Maxim 3 Case l r 
 be parallel to the vanishing line of planes parallel to the roof. 
 
 The corner line of the house (marked 6) is projected in the same manner: and being 
 completed by the ray ry the shadow of the rising line of the roof (marked 7) is drawn on 
 the wall with a tendency to Umbra 5; a point in the vanishing line of planes A determined 
 by the ray drawn from the vanishing point of that rising line according to maxim 1. 
 
 The crane (marked 8) is parallel to the plane of the picture and therefore the whole of’ 
 its shadow will be parallel with the vanishing line of the planes A since it falls on the wall 
 marked A. 
 
 The shadow of the door (D) will be easily understood; the top and bottom of the 
 door have their vanishing point at Y7 and therefore by maxim 1st their shadows are 
 directed by Umbra 6 in the vanishing line of planes A. 
 
 The remaining shadows depend so entirely on the proceeding instructions,, that they 
 will require no further explanation. 
 
 (SHADOWS No. 2. The Sun behind the Spectator.) 
 
 In these examples the parallel rays of the sun will have a vanishing point; which being' 
 found according to the supposed obliquity and elevation of that luminary, as in the expla¬ 
 nations of the diagrams 1 and 2, let the point of the solar obliquity be in the horizontal line 
 at the point marked solar point , and let the place of the sun or vanishing point of his rays- 
 be (first) at{ Su ‘ ia j 
 
 By Maxim 3 Case 2 the shadow of the post (1) will on the ground tend to the solar 
 point, and that part of it against the cottage will be parallel to the object itself since the 
 right lines of the object being perpendicular and parallel to the plane of the picture have 
 no vanishing point. 
 
 The direction of the shadow of the pole and board will be determined by maxim 
 1, by drawing a ray from Dl (the vanishing point of the pole) until it intersect the vanishing 
 
PRACTICAL PERSPECTIVE. 
 
 47 
 
 line of the plane surface of the side of the cottage that receives the shadow; as it does in 
 S V. S V is therefore the vanishing point for the shadow of the pole and also for the 
 shadows of the top of the window and door as those shadows fall against the sides. 
 
 To find the vanishing point of the shadow lines of the chimney on the roof, suppose 
 the vanishing line of the plane of the roof drawn from Dl to Vr; which let the solar 
 perpendicular (by Maxim 3, Case 2,) intersect in the point Sr, which will be the vanishing 
 point for the shadows of all perpendicular lines on the roof of the cottage. It is, therefore, 
 to Sr that the shadow of the chimney tends. The shadow of the tree falls against the 
 open door, but is caught again on the side of the house, perpendicular to the point in which 
 it meets the threshold. It is again lost under the eaves of the roof but if from the point J 
 (a point in the wall level with the edge of the roof) a small line be drawn with a tendency 
 from the solar point , the shadow of the tree may be again drawn from that point in which 
 the edge of the roof is cut by such a line, (as in the point L. 
 
 The second compartment of this number contains various objects: let the shadow of 
 the arch be first determined. The sun’s place on the solar perpendicular is here marked 
 jsiin i ))_ '|’ a |. e an y points in the arch as X, Y, Z, and drop perpendiculars from them, as 
 X 13, Y A, Z C, and find the shadows of those lines, by the preceeding maxims. When 
 the shadows rise into the interior of the arch, their true terminations can only be found by 
 describingthe sections which each plane of shadow would make within the arch; these planes 
 of shadow would in that part be elliptical, and might be described by the directions given 
 concerning plate 5; but such extreme accuracy will seldom be necessary in landscape 
 drawing, although the trouble of it must be submitted to by the architectural draftsman. 
 
 The beam that overhangs the right hand building casts its shadow partly on the ridge 
 of the building, partly on the body of the building, partly on the wall by the side of the 
 arched entrance, and partly within the arched entrance. A little attention will shew 
 that it forms an example belonging to the second case of maxim 2nd. The right lines 
 that compose it are in planes parallel to the plane of the picture. A right line is therefore 
 drawn from 3 Su ^' b | parallel to those lines, which gives the point Ya on the vertical line 
 for the vanishing point of the shadow on the ridge and body of the building and on the 
 interior part of the arched entrance. The shadow on the wall by the side of the building 
 is parallel to its object, by maxim 2. The shadow of the ridge is determined on the same 
 principles: draw A B from the corner A parallel to the horizontal line, and let it termi- 
 
48 
 
 PRACTICAL PERSPECTIVE, 
 
 nate in the edge of the ridge: draw A C towards the point Va and let it be terminated by 
 BC drawn towards the point j Su 2 b |j then C is in the edge of the shadow of the ridge 
 which by maxim 2nd will tend towards C, the point of sight. 
 
 The shadows of the upright and horizontal paling will be easily understood by refering 
 to the preceeding maxims. 
 
 - —r~- — g—B) II. -— 
 
 (SHADOWS No 3. The Sun before the Spectator.) 
 
 In No. 3 the sun is supposed to be before the spectator, and the shadows will in every 
 respect be determined by operations similar to those in the last examples, except that the 
 sun is above the horizontal line instead of being below it, and that every line of shadow 
 will tend from its vanishing point instead of towards it. 
 
 Having determined the solar point in the horizontal line, raise on it a perpendicular, 
 and fix the point 3 Sun, which will denote the elevation of that luminary. 
 
 It would be impertinent and unnecessary to describe the operations for all the shadows 
 in this example. They are determined according to the preceeding maxims; and theref we, 
 those of the upright objects received on the ground or other level planes tend from the 
 solar point The left side of the church tends to the vanishing point Yl, and the shadows 
 which are perpendicular to it, or (which is the same thing) of those which tend to V2, 
 have their tendency from the point Si, where a ray drawn from V2 intersects the vanishing 
 line of surfaces parallel to that side of the church ; by maxim 1.. The level style of the 
 dial and the beam of the shed M will have the same tendency: the shadow of the oblique 
 part of the style tends also from a point in the same vanishing line. The shadow of the 
 s ;ed on the church and on the ground will have various vanishing points according to the 
 surfaces that receive it; all of which may be determined by the preceeding maxims. 
 
 The roof of the body of the church slopes with, an elevation towards V3. Therefore 
 its vanishing line being drawn will give S3 on the solar perpendicular for the point from 
 which the shadows of perpendicular objects will be directed on the roof. The roof of the 
 shed has the vanishing point of its sloping lines in Y4, therefore by a similar operation 
 the point S4 is found on the solar perpendicular for the shadows of upright lines or objects 
 upon it. 
 
PRACTICAL PERSPECTIVE. 
 
 49 
 
 The vanishing line of the hill passes through V5 and V2, therefore the edge of a ruler 
 laid on V2 and V5 will give Sh on the solar perpendicular, for the tendency of the shadows 
 of upright objects thereon. The shadow of the direction post is thus found; and that of 
 the wall is drawn with a tendency to V5, by maxim 2. 
 
 Nothing remains here but what a little attention will better decypher than the most 
 elaborate explanation would be able to teach. In the next plate, examples of shadows 
 are given in the three different cases, and it will be useful for the student to copy them, 
 as well as these, on a larger scale, attending to the angle of the sun in the first case, and 
 the inclination of the objects that receive the shadow: and in the other cases, to the 
 position of the solar point, and to the elevation of the sun, as well as to the planes or 
 surfaces on which the shadows of the objects fall. 
 
 PLATE 
 
50 
 
 PRACTICAL PERSPECTIVE, 
 
 PLATE X, 
 
 SHA DO TVS. 
 
 THIS plate contains three examples of shadows, according to the three different posi¬ 
 tions of the sun with respect to the picture. 
 
 In the first, the sun is in the plane of the picture, and his rays are therefore parallel 
 to it. The shadow of the various objects fall parallel to the horizontal line, and are ter¬ 
 minated by rays parallel to the angle of the sun’s elevation, which may be known by any 
 of the dotted rays in the example. From what has been said in the instructions given 
 with the last plate, all the shadows in this example may be readily comprehended. I shall 
 therefore only point out the shadow of the iron rail marked A, which falls upon the 
 slope. A line parallel to the horizontal line is continued from the bottom of the rail (the 
 middle of the three towards the garden gate) until it reaches the perpendicular back of 
 the slope, and there a perpendicular is raised that gives the point B at the top of the 
 slope, which will be the point to which the shadow of the rail tends on the slope. The 
 student will recollect that it is upon the same principle that the shadow of the rod is 
 obtained on the roof in No. 1 of the last plate. In the same manner is the shadow of the 
 rod on the roof of the summer house in this example obtained. 
 
 In the second example the sun is behind the spectator, and the shadows tend to the 
 solar point on the horizontal line, marked S P, and are terminated by rays drawn from 
 the sun, marked Sun l. Very few observations are here necessary after the instructions 
 given in the last section. 
 
 The right hand old building is square, and the shadow of its farther side must be 
 attended to, though it is not seen: an omission very frequently made in landscapes: by 
 its shadow that of the old gothic arch is almost lost. 
 
 The shadow of the roof of the circular welbhouse, which falls mostly upon the well- 
 house, will be best obtained by finding various points, by the terminations of the shadows 
 oflines drawn under its ridge. 
 
S HA DO WS 
 
 Published/ Jan *1 . l8o5 , byJBdn' ? Orme ., 6^ Bond Street 
 
 Sun 
 

 
 
 
 
 
 
 
 
 
 
 
PRACTICAL PERSPECTIVE., 
 
 51 
 
 Of the last example it need not only be observed that the sun is before the spectator, 
 and very much elevated. The solar point is S P on the horizontal line, and the point of 
 the sun is marked Sun 2, The shadow of the obelisk over the fallen pillar takes the cur¬ 
 vature ot the pillar. The shadow of the arch is obtained by finding the shadows of 
 perpendicular lines drawn from points in the arch, as in the preceeding instructions. 
 
 To obtain every shadow perspcctively would certainly be attended with considerable 
 trouble, and it is not supposed that the artist will submit continually to such a tedious 
 task. It is not required of him: the art, or rather the science of perspective, must be 
 cultivated with such attention at first, by the landscape painter, that his judgment with 
 respect to the form, dimensions, inclination and shadow of objects may be perfected, and 
 then he will have no need to recur to the actual practice of it, except upon particular 
 occasions. It is merely an introductory study: we cannot become acquainted with painting 
 without its assistance, but when once introduced, we find other subjects more tasteful and 
 more pleasing : yet, while engaged in the more agreeable labours of the pencil, we must 
 carefully retain in mind the principles of perspective, and its rules must always be 
 attended to, although they need not always be executed with the exactness of the ruler 
 and compasses. 
 
 ESSAY 
 
OK THE 
 
 APPLICATION OF THE PRINCIPLES OF 
 
 PERSPECTIVE, 
 
 TO THE PRACTICE OF 
 
 TA KIJVG VIE WS» 
 
 — M ■> i - 
 
 TPlIE cliief charge which those, who object to the study of Perspective, adduce 
 against this science, is the impossibility of performing its operations at the moment when 
 those operations appear to be the most necessary; that is, at the time when an artist is 
 taking a view. If Perspective had no fixed purpose but what depended on the com¬ 
 passes and ruler; nor any influence where actual measurement and determinate angles 
 could not be obtained, it would indeed be a science worthy the architect alone ; and 
 its claims on the Landscape Painter, or on the pupil of refined taste, however just those 
 claims might be, would be rendered nugatory by their impossibility. Nature has thrown 
 a pleasing irregularity over all her works, and the pencil or pen, that presumes to describe 
 her beauties, must not be trammelled by the formal precepts of pedants, however correct 
 may be the proportions, to which they would reduce the exertions of practice. Never¬ 
 theless there exist certain laws which Nature ever observes: these may be subject to slight 
 aberrations, but they still exist: it is the business of science to explain and render them 
 
ESSAY ON TAKING VIEWS. 
 
 53 
 
 accessible to the artist; and the poet or painter, who rejects them, will be as liable to error 
 although his errors may not be so glaring, as those of the mechanic or engineer. Those 
 laws of Nature with which it behoves the Landscape painter to be particularly intimate 
 are those of Vision. 
 
 To reduce the laws of Vision to the powers of the human understanding, it has been 
 necessary to investigate them with mathematical accuracy: the construction of the eye; 
 the motion, direction, reverberation, and composition of light; the proportion by which 
 distance decreases the appearances of objects, and, in short, every thing which relates to 
 the organs and faculties of sight has become the subject of separate research. Hence, from 
 the certainty of a few general truths, the whole system of Nature’s legislation, in the 
 government of that most delightful of our senses, has been clearly explained. Perspec¬ 
 tive is but one part of that system, and its proportions, although they are the most exten¬ 
 sive, may be esteemed as the most simple of the whole code. > 
 
 Those, who made the rules of Perspective the objects of their study, set out with 
 considering that any transparent plane (as the glass of a window) intercepting the rays 
 of vision, becomes a viezv or picture of the objects behind it. As the eye remained un-> 
 moved they perceived that the landscape remained also unmoved on the surface of the, 
 transparent plane, which they termed the plane of the picture. To preserve this stillness of 
 the objects, on the transparent plane, they perceived that the eye must be directed to one 
 point, at a constant distance therefrom: this point they called the point of sight , and ob¬ 
 serving that it was in the intersection of that level plane with the plane of the picture, 
 which extended to the boundaries of the horizon , they denominated that intersection the 
 horizontal line. As all level planes appeared to incline, and at length to vanish, in the ho¬ 
 rizontal line, and as all right lines in a straight-forward direction appeared to converge, 
 and, at length, to vanish into the point of sight, the first ideas of a vanishing line and 
 point became obvious, as the guides to that position, in which the eye was to be pre¬ 
 served so as to retain one view, ox picture, upon the transparent plane. The proportion in 
 which the ray from the object to the eye was intercepted by the transparent plane was 
 manifestly, that of the distance of the eye, to the distance of the object from the picture. 
 Thus the first principles of the science were strictly deduced from the desire to take a view; 
 or in other words to hx the appearance of objects upon a transparent plane. 
 
 O 
 
54 
 
 ESSAY ON TAKING VIEWS. 
 
 The intersection of the horizontal plane with the surface of the glass, having thus de¬ 
 termined the first vanishing line, with its central point and distance, other planes passing 
 through the eye parallel to other plane surfaces might easily have been conceived ; 
 and thereby other vanishing lines, with their central points, might have been obtained r 
 but the first writers on the subject were long contented with the horizontal line and 
 the point of sight, by means of which any direct distance was easily determined. By 
 supposing lines, parallel to the first distance of the horizontal line, to be drawn from 
 any point in an original object, they obtained its representation by the simple process of 
 dividing a line in two parts, proportional to two other lines: with this they were satisfied, 
 or, at furthest, they found the vanishing points of oblique level lines in the horizontal line. 
 The analogy between the horizontal plane and all other planes, whether vertical or in¬ 
 clined, was, however, no sooner explained by Dr. Brook Taylor, than the whole science 
 became reduced to the utmost simplicity; and it seems astonishing to hear any one now 
 discoursing on the difficulties of the theory of Perspective, when that theory is capable 
 of being reduced to a single proposition. 
 
 When an artist has once imbibed a correct idea of this theory; when he comprehends 
 that among the Perspective planes as they are exhibited in section the fourth, one has no 
 vanishing line, but contains its objects in their original forms, while all the rest have va¬ 
 nishing lines, central points and distances, by which the appearance of any known di¬ 
 mensions or tendency may be determined by one easy operation, what is to hinder him 
 from suffering his judgment to be directed by this knowledge, when he takes a view, where 
 he cannot use his ruler and compasses? Will it not enable him to determine more readily 
 the tendency of every line he has to draw? When the side or roof of a building, the 
 rise or descent of a hill or bridge, the obliquity of a wall are the objects of his delinea¬ 
 tion, can he not, by imagining the direction of their vanishing lines, determine with 
 greater facility the vanishing points of such lines as it may be necessary to draw upon 
 such plane surfaces ? The general landscape painter does not require the highest degree 
 of accuracy in his sketches, but it is surely desirable that he should understand how to 
 avoid any gross errors. Not only when his views consist of buildings, but even when the 
 common objects of landcape scenery form the features of his design he ought to con¬ 
 sult the theory, if he does not submit to the actual operations, of this science; and when 
 he transfers his rough sketch to paper, or canvas, he must not be ashamed of borrowing 
 assistance from the ruler, nor of considering attentively the direction of every vanishing 
 line, and the seat of every vanishing point. 
 
ESSAY ON - TAKING VIEWS. 
 
 55 
 
 In taking a view it will be useful to draw a line across the paper for the horizontal line, 
 before the artist begins his design. In the middle of the horizontal line the point of sight 
 may also be determined, and the vertical line may be likewise drawn. Then if any 
 buildings like those in Plate I, the sides of which are perpendicular and parallel to the 
 picture, are to be delineated, the vanishing point of level lines on the receding sides will 
 be already determined since their vanishing point will he the point of sight. When the 
 buildings are oblique to the picture as in Plate II. one vanishing point may generally he 
 determined with tolerable accuracy on the horizontal line, and the other may be easily 
 found with the compasses and ruler, (the angle which the sides of the buildings make, with 
 each other, being known) when a more correct sketch is to bemade within doors: through 
 those vanishing points, vanishing lines may he drawn ; and the direction of parallel lines 
 on such oblique planes may be corrected, if not determined, by the instruments. If 
 the objects, or the ground on which they stand, should be inclined and sloping, as in 
 Plate III. and VI, it will be useful to determine the vanishing points, and even to 
 trace the direction of ihe vanishing lines, if they are wholly oblique, particularly if the 
 objects on such slopes should be numerous or prominent. All this may easily be done, 
 and a little practice will render the eye accurate in determining a few vanishing points, 
 while a hundred times that practice would not be able to render the artist oidy tolerably 
 correct in sketching without those points, which will enable him to rectify any errors when 
 he improves his sketch within doors. 
 
 It is not my business to interfere with the regulations of taste, or to offer any obser¬ 
 vations on what the subjects of views ought to be, or how the artist should choose his po¬ 
 sition in taking them. As far as fancy is concerned truth willingly yields the scene to her 
 engaging pencil: she permits many irregularities of hills, of woods, of shadow and of ar¬ 
 tificial light to blend themselves under the hand of Genius, and to aid that general ef¬ 
 fect, which his creative energy alone knows how to produce. But Genius is not to de¬ 
 stroy Nature : true Genius reveres her; and is the greatest when acting most comformably 
 to her laws. The most beautiful pictures are those in which Nature has been most strictly 
 followed ; where the most regular delineations of Perspective, and the most coirect out¬ 
 line of Shadow have been unerringly pursued; and where the artist has shown his Genius 
 and created his effect, by choosing such a position of his perspective center, and of his 
 light, as necessarily gave prominence and richness to his design, rather than by grouping 
 the irregularities of uncertain delineation, and indefinable shadow, in the most glittering 
 and brilliant disorder. 
 
56 
 
 ESSAY ON TAKING VIEWS. 
 
 In determining his position the artist should be careful that his sight has sufficient 
 scope to survey, atone glance, the whole of the intended subject of his pencil. The most 
 interesting object should also have such a position with respect to the point of sight as 
 may give it a clear and perspicuous appearance. No series of similar objects should re- 
 ceed too abruptly; and therefore, in views of regular buildings, the inclined representation 
 should be chosen, where the oblique vanishing points may be at a considerable distance 
 on each side of the point of sight. The picturesque nature of the surrounding country 
 will indeed be the best guide for the tasteful judgment of the artist, and will induce him, 
 to give such a position to his principal object, as may allow him, if possible, to introduce 
 varieties of landscape to interrupt the uniformity of the architecture, with groups of 
 trees or other natural scenery. 
 
 The height of the eye or of the horizontal line will naturally be the height of the 
 eye of the person who takes the view. If in his delineations afterwards he shall, for the 
 sake of giving more elevation to the low or depressed character of a level country, make 
 his horizontal line still lower; or, that he may render the surrounding scenery of a moun¬ 
 tainous country more expanded, elevate his horizontal line higher than its natural place, 
 he must be careful to keep the true perspective position of his objects while he changes 
 the delineation of each from its real appearance to the appearance he designs it to 
 take. To diversify the position of the eye, in views, is always dangerous; and seldom 
 produces the intended effect. It is only where the measurement of angles, and the geo¬ 
 metrical accuracy of a plan, can be correctly obtained that the perspective of a view 
 may be varied at pleasure: a labour after all, more adapted to the objects of the archi¬ 
 tectural draughtsman than to the landscape painter, who should generally adhere with 
 precision to the appearance presented to his eye ; and should study his effect rather from 
 Nature than from art. 
 
 A scale accurate enough for the purposes of landscape painting may be obtained by 
 measuring some certain object; as the height of a door, a post, or any thing else that 
 presents itself in the picture, to which the artist can obtain access. By comparing the 
 relative proportions which other objects bear to this and to each other, he will be able to 
 determine their dimensions with tolerable precision. A few principal points may also be 
 found by such instruments as the Camera Obscara , or by the frame of squares, which is 
 formed with threads put across a frame, and fixed on a stand : in taking views of towns or 
 considerable buddings the Theodolite also might be used with advantage. On the utility 
 
ESSAY ON TAKING VIEWS. 
 
 57 
 
 of these helps I shall not pretend to insist: the eye by practice and by the assistance of 
 the theory of Perspective, becomes capable of ascertaining these proportions with suffi¬ 
 cient correctness; while the artist v at the same time, possesses in the actual practice of the 
 science the means to prove, and rectify the whole of his delineations* When perfectly 
 acquainted with the laws by which the dimensions of objects appear to be diminished in 
 distance, he has only to suffer his judgment to be directed by them, and he will soon, 
 acknowledge that the guidance of scientific truth never checks nor contracts the exer¬ 
 tions of true Genius, but informs it with those unerring principles which retain its. 
 course to the path of excellence. 
 
 John Hayes, Printer, 
 Dartmouth Street, Westminster, 
 
 P 
 

 
 
 v 
 
 
 
 
 
 
 7 
 
 i 
 
 
 
T. NOBLE, 
 
 Teacher of PERSPECTIVE 
 
 in general; 
 
 Particularly as it relates to 
 
 LANDSCAPE, ARCHITECTURE. 
 
 AND THE 
 
 PROJECTION of the SPHERE, 
 
 COTTAGE, Maize Hill, Blackheath. 
 
 {&' Purus in London attended three times a Week. 
 
Note.—I n Plate VIII, the letters which 
 have a small mark under them, are referred 
 to by Italics in the instructions; thus A is 
 called A; B, B, See . 
 

 
 
 
 
 
 
 


 
 

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