INTRODUCTION.

ficities X. In the fame diagram, the square Z is four times the distance from
the eye that is the square X; on which account its apparent dimenfions are,
when compared to the square X, but a fixteenth part of the square X, as is clearly
evident by the viſual rays K E, L E, and M E, which, interſeeting the square
X, determines thereon, a ſquare equal a fourth part of the square Aghi, and con-
ſequently but a fixteenth part of the square X; an apparent diminution agree-
ably to the proportion intimated, being inſuerely as the squares of the diſtances.

DEFINITION

1. A VISUAL RAY. Is an imaginary right line extended from the eye, to any particular point, the object of the eye's regard, or contemplation.

It is curious to obſerve the play of the eye, while it is employed in minutely
furveying any particular object, or objects; to remark its gradual shifting as it
changes the immediate ſpot of contemplation to the regarding of another, or
others. It will naturally refult from this consideration, and the knowledge of
viſual rays being right lines, that no two ſpots can be ſo near, but that the di-
reſection of the eye will be changed, and a new viſual ray be formed, in the ſepa-
rately examining the one and the other. Obſerve but the dial of a watch; and
the motion of the shifting of the eye will not only be felt as it paſſes from re-
garding one hour to another, but it will be ſenſibly felt as it glides by the minutes;
evincing in its progreſs a subtlety of motion, ſuperior to the mechaniſm of the
delicate machine it contemplates.

From the shifting of the eye, while employed in examination of any object, or
number of objects, it may be figured that while contemplating the borders of a
circle (as the minutes of the dial of a watch), there would be generated a cone of
viſual rays, of which the eye is the apex, or point, and the dial the bafe; as Fig. 1,
Plate 3. And it muſt of courſe be reflected, that, as the objects of contempla-
tion differ in figure, ſo muſt vary the body of the collection of rays proceeding
from the eye in their examination. As, ſuppofe the object a ſquare ſuperficie,
ſee Fig. 2. then will there be generated a pyramid of rays; if it be a triangle,
then is there another pyramid formed, having a triangular bafe, as Fig. 3; or,
the object being a ſolid, as Fig. 4; or the figure may be a man, or beaſt, as
Fig. 5. and 6. it matters not what, on the eye's regarding them all around,
there will be formed a body of viſual rays, of which the contour of the
object regarded, be it what it will, is the bafe, and the eye the apex.

PLATE 3.

Figs. 1, 2, 3, 4, 5, 6.

PLATE 4

Fig. 1.

Fig. 2.

Londres, Raphaël van der Merwe, Jan 1768.

# INTRODUCTION.
## DEFINITION

2. **VISUAL RAYS.** Are any number of imaginary right lines proceeding from the eye, to any object the subject of its contemplation.

If the pyramid of visual rays proceeding from the eye while contemplating an object, be cut by a plane making a section of those rays, the figure that would be generated on the plane by such section, would be what is termed a perspective representation of that object; which section would be varied in figure and in dimensions, accordingly as the plane making it, was inclined one way or another, and accordingly as it was taken nearer the eye, or nearer the object. Parallel sections would be similar figures, and all otherwise than parallel, dissimilar.

Thus of the cone of visual rays, proceeding from the circle ABCD, Fig. 1. Plate 4; the section e f, made by the plane FGHI, being nearer the eye than a b, made by the parallel plane KLMN, the former figure, though similar, is smaller; and the section c d, made by the inclined plane OPQR, is different in figure from those made by either of the two vertical planes. So of the pyramid of rays proceeding from the cube ABCD, Fig. 2; the sections made by the parallel planes FGHI and KLMN are similar, but differ in size from each other, and in figure from that made by the plane OPQR on account of its inclined position.

## DEFINITION

3. **A PERSPECTIVE DELINEATION.** Is a linear representation of any object or object's, as they appear to the eye that regards them: and is such a figure as may be supplied to be made by a plane making a section of the body or pyramid of visual rays directed from the eye to the object's, while contemplating of them. Which delineation, being so tinted as to resemble the local colours of the real object's, and having the effect of light and shade, will convey a lively idea of the real object's, and at the same time indicate their position and distance from the eye of the obferver.

A Perspective representation of any object, or multitude of objects, is such a representation as would appear to be made on a plate of glaſs, placed between the eye, and the object or objects of examination. A view seen through the window of a room, is, as it appears on that window, a perspective representation of that view; and if the light could be kept confined, and the hand at the fame time were to trace the figures of the objects on the glaſs, where they appear to touch it, the picture so drawn upon the glaſs, would be a perfect perspective view of the prospect behind it.

c

## INTRODUCTION.

12

Draw S G parallel to A B, and S L parallel to A D; also draw the vifual
rays S A, S B, S C and S D; produce the line B A till it touches the line G L
in the point I, and draw S O perpendicular to G L. Then, on a plane of paper
or canvafs as GHKL, Fig. 2, draw a line VZ, parallel to GL, and make it
one inch and a half above GL; VZ will be the horizontal line. Mark a point at
V, and another at Z, as far diffant from each other, as are the points G and L in
the plan, Fig. 1. Take the diffances G a, G b, G c and G d, where the vifual
rays interfect the line G L (Fig. 1.) severally in your compafes, and mark them
off on the line VZ (Fig. 2.) at 1, 2, 3, and 4, and draw fine perpendicular lines
through the points. Take the diffance G I (Fig. 1.), and mark it off at V I
(Fig. 2.) and draw a vertical line through the point I; upon which line mark the
height of the cube, equal to the length of one of its fides, in the plan, as O P.
Then are all the neceffary steps taken for obtaining the repreſentation required;
which is done by drawing the lines O V and P V (Fig. 3.) a Z and e Z; f V
and c Z, cutting each other in the point d, and completing the figure a b c d f g.
Which figure will be the repreſentative figure of a cube, as it would appear to
an obferver regarding it fituated on the ſquare A B C D, (Fig. 1.) whoſe eye
was one inch and a half above the point S.

If the drawing upon the plane G H K L (Fig. 3.) was placed perpendicu-
larly over the line G L, as is done (Fig. 4.) by turning the moveable plane
G H K L upright on the line G L, the relation it then has to the ground plan
will be more clearly difcernable, and the united operations and coincidence of
both, more readily ſeen; and where it may be noticed that were the figure
a b c d f g cut out, a folid cube ſtanding on the ſquare A B C D, would
appear exaſtly to fit the aperture, to the eye of a perfon elevated, one inch
and a half over the point S, with his eye oppofite the point O in the horizon.

## DEFINITIONS.

11. GROUND PLANE. Is the plane upon which the *Objects* to be drawn are placed; as also whereon it stands the *Obferver* and *Plane of Delineation*.

N. B. The *Ground Plane*, in perſpective enquiries, is considered an infinitely extended level, or horizontal, plane.

12. GROUND LINE. Is the line in which the *Plane of Delineation* reſts on the *Ground Plane*.

13. STATION POINT. Is a point on the *Ground Plane* perpendicularly under the *Point of Sight*, or *Point of View*.

In the proceeds of perſpective delineations, the horizon, or horizontal
line, is a consideration of the greatest importance, inasmuch, as it regulates

PLATE VI.

London Published by James Millar, A.B. 1620.

## INTRODUCTION.

12.

Draw S G parallel to A B, and S L parallel to A D; also draw the vifual rays S A, S B, S C and S D; produce the line B A till it touches the line G L in the point I, and draw S O perpendicular to G L. Then, on a plane of paper or canvass as GHKL, Fig. 2, draw a line VZ, parallel to GL, and make it one inch and a half above GL; VZ will be the horizontal line. Mark a point at V, and another at Z, as far diffrent from each other, as are the points G and L in the plan, Fig. 1. Take the distiances G a, G b, G c and G d, where the vifual rays interfect the line G L (Fig. 1.) severally in your compaffes, and mark them off on the line VZ (Fig. 2.) at 1, 2, 3, and 4, and draw fine perpendicular lines through the points. Take the diffance G I (Fig. 1.), and mark it off at V I (Fig. 2.) and draw a vertical line through the point I; upon which line mark the height of the cube, equal to the length of one of its fides, in the plan, as O P. Then are all the neceffary steps taken for obtaining the repreſentation required; which is done by drawing the lines O V and P V (Fig. 3.) a Z and e Z; f V and e Z, cutting each other in the point d, and completing the figure a b c d f g. Which figure will be the repreſentative figure of a cube, as it would appear to an obferver regarding it ſituated on the ſquare A B C D, (Fig. 1.) whoſe eye was one inch and a half above the point S.

If the drawing upon the plane G H K L (Fig. 3.) was placed perpendicu-
larly over the line G L, as is done (Fig. 4.) by turning the moveable plane
G H K L upright on the line G L, the relation it then has to the ground plan
will be more clearly discernable, and the united operations and coincidence of
both, more readily feen; and where it may be noticed that were the figure
a b c d f g cut out, a solid cube ſtanding on the ſquare A B C D, would
appear exacly to fit the aperture, to the eye of a perfon elevated, one inch
and a half over the point S, with his eye oppofite the point O in the horizon.

## DEFINITIONS.

11. GROUND PLANE. Is the plane upon which the Objeets to be drawn are placed; as also whereon ſtands the Obferver and Plane of Delineation.

N. B. The Ground Plane, in perſpective enquiries, is confidered an infinitely extended level, or horizontal, plane.

13. STATION POINT. Is a point on the Ground Plane perpendicularly under the Point of Sight, or Point of View.

In the proceeds of perſpective delineations, the horizon, or horizontal
line, is a consideration of the greatest importance, inſomuch, as it regulates

PLATE VI.

Fig. 4.

Fig. 5.

Fig. 6.

London: Published by J. Stockwell, Mather, Lons. 1615.

PRACTICAL GEOMETRY.

PLATE 9

Fig. 7.

Fig. 6.

Londes published by James Millen Fane stee.

Angles, formed by right lines, are of three kinds only; viz. Right Angles, [Plate 9.] Obtuse Angles, and Acute Angles. When one of the lines forming of an angle is perpendicular to the other, then is such an angle said to be a right angle; such is the angle ABC, Fig. 1, Plate 9, the line AB being perpendicular to the line BC. When the lines have a greater degree of expansion than a right angle, such an angle is said to be an obtuse angle, as the angle D E F, Fig. 2; and when they have a less degree of expansion than a right angle, such an angle is said to be acute, as the angle G H I, Fig. 3.

The magnitude of an angle is computed by the portion it comprehends of a circle, using the angular point as the centre to revolve the circle upon. For the general admeasurement of angles, the circumference of a circle is divided into 360 equal parts, called degrees; a divifion univerſally affented to; and an angle is said to contain, or to be an angle of as many degrees as fall within the expanſion of the two lines.

If two lines, one perpendicular to the other, croſs each other, there are formed four angles, all right angles. By the croſſing of the perpendicular lines AC and BD, (Fig. 4.) there are formed four right angles, and using the point of their common interſection, E, as the point to revolve a circle around upon, each angle will of course contain a quarter of that circumference; and the whole circumference being divided into 360 equal parts, each right angle, (all right angles being equal,) muſt contain a quarter of 360, that is 90 degrees. A right angle is a determinate one, and there can be no variety of them; but of obtuse and acute angles there may be many, of various magnitudes.

The circle ABCD, Fig. 4, is divided into 360 equal parts. The angle AEF, is an acute angle of 20 degrees; the angle AEG an acute angle of 50 degrees; and 90° on to any number ſhort of 90. The angle AEO is an obtuse angle of 130 degrees, and the angle AEL an obtuse angle of 170 degrees, and 90° on to any number ſhort of 180, at which period the expanſion of the two lines would fall into one right line, as AEC. For the greater accuracy, in the eſtimating of angles, each degree is ſubdivided into 60 equal parts, called minutes; and each minute into 60 equal parts, called ſeCONDS; 90° the meaſurement of an angle may be a certain number of degrees, minutes, ſeCONDS, thirds, &c.

An angle is not enlarged by lengthening of the lines forming of it; for the angle ABC (Fig. 5.) is ſtill the fame and not at all increased by extending of the lines to D and E. An angle is eſtimated only by the degrees of incli-

PRACTICAL GEOMETRY.

comprehend what he is about to erect. A plan, as most generally drawn, is properly an horizontal section of a building at a flated height; or it is the figure, which the top of the walls would exhibit, when raised all to the fame level a few feet above the ground, if looked at from above directly down upon them; whereby many incidents in the structure are expreſſed, that cannot be marked out in the trenches, or even take place, ſome four, five, or fix, feet above ground.

[Plate 11.] This will be better underſtood by reference to ſenſible figures. To thofe who are converſant in Architecture, the Elevation (Fig. 1, Plate 11,) would be nearly pictured in the imagination from the mere inſpeſion of the plan; Fig. 2; but the plan, Fig. 2, is not the figure that would be cut out in the ground, as shaping the foundation to the building; ſuch would be ſimply as Fig. 3, expreſſing little more than the length and breadth of the apartments, and thicknesss of the walls, more information could not be gathered from it. Whereas, from the plan, Fig. 2, is underſtood that in front there are two pillars ſtanding in a reeſs, with a door between them, and a niche in the middle of the pier on each ſide; alſo, that in each end of the apartment, within, there is a window, that there is a chimney in the middle of the croſs-wall, with a door on the right leading into another apartment, and a reeſs for a falſe door on the other ſide the chimney, to be uniform with the real door; that the lines 1, 2, 3, 4, 5, &c. expreſſs an ascending flight of flairs; that A is the half-landing, on which there is a window to light the flaircaſe, and that the dotted lines imply the returning flight to the next flory: all which is clearly gathered and immediately underſtood from inſpeſion of the plan ſimply, with other minute particulars; ſuch as the number of ſteps that conduct into the dwelling, implied by the lines marked a, b, c, that they fall within the pillars, that there is intended a plinth around the building expreſſed by the double line around, that there is meant a bafe to the pillars, and ſuch like minutia; and to the whole there is affixed a ſcale of ſeet, proportionally to the plan laid down, by means of which the dimenſions, that is, the lengths and breadths of apartments, may be known, and the breadths of doors, windows, fire-places, flairs, and treads of flairs, &c. may be accurately meaſured.

Such delineation is undoubtedly an horizontal ſection of the walls, taken ſome fix or ſeven feet from the ground; ſomewhere about the height of the line B C, Fig. 1. Indeed there are particulars expreſſed that cannot be noticed till the building is raſed considerably higher, as the window D, on the

PRACTICAL PERSPECTIVE.

[Plate 19.]

EXAMPLE XVI.

Suppose the arches of the laft example were required to be drawn above the horizon, at any height at pleasure, suppose at the height IN, Fig. 3; the horizon and flation remaining as before.

The flation and poſition of the arches being as before, the fame viſual lines with the laſt, both in plan and elevation, will ſerve; it will only be neceſſary to heighten the viſual lines, Fig. 2, to Fig. 3.

Make Nx and Nz, Fig. 3, equal the heights of the ordinates ct, and dv, of the plan Fig. 1, and draw the lines NV, zV, and xV, cutting the viſual lines of the ordinates and fpringings in the points o, o, o, o, o, &c. through which the curves may with care be traced.

Fig. 4, ſhows an arcade, flanding on piers, agreeably to the dimenſions and height of the arches of the laſt example.

Should the arches be unequal, as the arches of a bridge generally are, fill the fame mode of drawing ordinates, and finding their heights according to their diſtance, muſt be purſued. The arches differing in dimenſions or in figure, that is, being either ſemicircular, ſegments of circles, or ſemi-ellipſes, will cauſe only a little more trouble in the operation of finding them.

EXAMPLE XVII.

Let Fig. 5, be the geometrical elevation of a bridge. Let it be ſuppoſed to fland perpendicularly on the line AC; and let B be the ſlation whence it is viewed. Let IK be the ground line of the plane of delineation.

It is required to find the perſpective representation of the above bridge, under the flated premifes, fuppofing the horizon equal the height IN, Fig. 6.

Let the ordinates of the different arches be regularly affumed; and from their points of interſection, 1, 2, 3; 4, 5, 6; 7, 8, 9, on the chord line AC, let viſual rays be drawn to the ſlation B, as alſo from the piers or fpringing of the arches, cutting the plane of delineation in the points a, b, c, d, e, &c.; and let the chord line AC be produced to D for an interſection. Draw the line BE, from the ſlation B, parallel to the chord of the arches, AC, for the vanifhing point of horizontal lines in that direction.

Draw the horizontal line ON, Fig. 6, and parallel to it the ground line through the point I. Make NO equal the diſtance DE, Fig. 5, and let off the diſtances of all the viſual rays, Da, Db, Dc, &c. Fig. 5; at Ia, Ib, Ic, &c. Fig. 6, and draw the viſual lines through them.

PLATE XIX.

Published by J. Millon, Oct. 1787

PRACTICAL PERSPECTIVE,

[Plate 20.] The visual lines through the points b, c, e, and f, Fig. 6, are the visual lines from the near angles of the two squares of the great circle of the bafe of the object. The height MO, on the interfection, is the height of the bafe of the object, equal the height DC, Fig. 2. The bafe of the prefent example being exactly the fame with that of the former, it is needleſs to go through the proceſs of obtaining it; the practice of the preceding, and inſpection alone of this, will be ample information as to its attainment. MP, on the interfection, is the height of the circle HL, Fig. 2. The line Pg being drawn, interfects the viſual line of the angle of the ſquare, determining the point I of one of the near angles of that circumſcribing ſquare; from which point the whole may be readily completed; but which proceſs being the fame with the finding the circle of the gallery above, we will proceed to the deſcription of it, as, being more diſcernible, it will better anſwer the purpofes of both.

Draw up the viſual lines cc, and ee, the viſual lines of the two near angles of the ſquare circumſcribing the required circle. Make MQ, on the interfection, equal the height of the gallery TR, Fig. 2, and draw the diagonal line Og interfecting the viſual line ee, in the point e, anſwering to the point I of the ſquare below. Draw the horizontal line of the ſquare ce, and from the points c and e draw lines to O, the vanifhing point of lines perpendicular to the picture. The line from the point e interfects the diagonal in the point m, from which draw the line mn, parallel to ce, completing the ſquare ecm; in which, draw the other diagonal cn determining the centre of the circle a. Through the centre, a, let two lines be drawn through the ſquare, one parallel to ce, and the other in direction to the vanifhing point O, which will obtain four points, 1, 2, 3, 4, in the circumference of the circle. The ſhort lines r and t, anſwer to the viſual lines of the near angles of the inſcribed ſquare, agreeable to the viſual interfections r and t, Fig. 3. Thoſe lines interfect the diagonals in the points $\zeta$ and 6, from which, lines being drawn in direction to O determine the two other angles of the ſquare, and points in the circle, 7 and 8; through which eight points let the circle of the gallery be drawn. The ſquare 5678, is the exterior ſquare of the circle of the body of the object at top, in which, four points are already determined, x,x,x,x; and the four other points, z,z,z,z, are readily obtained from the viſual interfections oo of that ſquare in the plan Fig. 3, and the circle drawn through them; draw the lines of the conical body of the object xk and xl. There only remains to find the top circle at MN, Fig. 2.

PLATE XX.

PRACTICAL PERSPECTIVE.

60

[Plate 21.] nifhing point of the lines perpendicular to the picture; and the diffance of the picture S O, laid down on the horizon, on each fide the centre O, will give the vanifhing points of the diagonals of the fquare. Draw the vifual rays in direction to the flation cutting the plane of delineation in the points k, c, b, i, a, h, m, and produce the diagonal KM to N for an interfection.

Prepare the picture, Fig. 4, by drawing the ground line GL, and parallel to it, the horizon, YZ. O is the centre of the picture, and OY and OZ are each equal the diffance of the picture S O in the plan, wherefore Y and Z are the vanifhing points of the diagonals of the fquare, and of all lines parallel to them. The vifual lines through the points k, c, b, i, a, h, and m, anfwer to the cor- responding vifual interfections in the plan. L, in the interfeeting point, and LN, the interfeeting line. We will firſt obtain the representation of the octagon as lying in the ground plane.

Draw the diagonal line LY, from the interſting to the vanifhing point. The point f, where it cuts the vifual line through the point m, is the place of the near horizontal ſide of the ſquare, fg. Draw the lines gO, fO, and d1, which will complete the ſquare fgd1, of which, the line df is a diagonal. From the points c and e, where the vifual lines through the points a and h touch the near ſide of the ſquare, draw the lines cO, and eO, croſſing the oppoſite ſide of the ſquare in the points c and e; and where they croſs the diagonal df in the points v and x, let horizontal lines be drawn through thoſe points to the oppoſite ſides of the ſquare, cutting them in the points c, c, c, c; and drawing the corner lines ee, ee, &c. the octagon e, c, c, e, c, e, is completed.

Let it be required to find the appearance of the fame octagon, as ſeen elevated above the horizon, directly over the one found on the ground plane; ſuppoſe equal the height LP on the interſection.

Draw the vifual lines of the ground figure up to Fig. 5. Where the diagonal line PY croſſes the near vifual line in the point a is the place of the near ſide of the ſquare around the octagon, and the horizontal line ab is that ſide. Draw the lines bO, aO, and cd, completing the ſquare abcd. Where the vifual lines, through the points a and h below, croſſe the ſide of the ſquare ab, at o, o, let lines be drawn to the centre, O, croſſing the oppoſite ſide of the ſquare cd, in the points oo; and where they croſſe the diagonal line in the points m and n, let horizontal lines be drawn through thoſe points to the other ſides of the ſquare, cutting them in the points o, o, and o, o; the remaining ſides of the octagon at the corners being joined together, the whole octagon o, o, o, o, o, o, o, o, is completed, as required.

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 7.

Fig. 8.

PLATE 21

Eskimo Work by James Maitland, Esqr.

PRACTICAL PERSPECTIVE.

enter into an inquiry of a very important consideration. Methodically proceeding, it should have been antecedent to any practice; it is, however, sometimes expedient to do that first, which in just progression should follow; as it is not until fome insight is had into a subject that the necessity of certain inquiries becomes evident.

It has been matter of much difference of opinion, the adjusting what may generally be considered the best angle of vision, within which objects should be regarded to obtain the most agreeable representation of them. For, accordingly as the angle of vision is enlarged or lefzen, by viewing the objects near or remote, will their appearance vary, and their delineation in consequence be affected thereby.

[Plate 23.]

By the angle of vision, or angle of view, is to be understood, the expansion of the lines, proceeding from the eye, by the two extreme visual rays embracing the whole extent of the view; and this, whether it conſift of one object or of many. This can clearly be explained only by reference to fome figure. (Fig. 1, Plate 23.) Let A repreſent the plan of a manſion; let B be the situation of an outhouſe contiguous to the manſion; and let the places of trees be intimated by the ſpots C, C, C, and D, D, D. Let S be the ſlation or point of view whence the whole is regarded. Conſidering the manſion A, as a lone object, the extreme visual rays Sa, Sb, form at the eye, the angle aSb; then is the angle aSb the angle of view under which that object is ſeen, Sa and Sb being the two ex- treme visual rays embracing the whole extent of the object. Again, if the outhouſe B be considered as a lone object, then will the extreme visual rays, cS and dS, form, at the eye, the angle cSd, being the magnitude of the angle under which that object is ſeen. And fo of any object, the visual rays that embrace its whole extent, form the angle of view under which it is ſaid to be ſeen. It muſt be manifeſt then, that this angle of view will be large or ſmall, as the eye is near to, or remote from the object.

Let it be intended to take both objects A, and B, into one view, with the addition of trees to the right, and to the left of them. Let visual rays be drawn from the extreme tree on either side, to the ſlation S: the angle CSD is the angle of view under which the whole extent is ſeen; and the rays CS and DS are denominated the extreme visual rays of the view.

Objects may be placed too near the eye for faſtisfaſtory obſervance of them; they may be placed fo near as to pain the eye. The eye can contemplate only a point at one time; it is by its celerity and continual motion, that it becomes perſectly ſenſible of a whole, or many forms. But when an object, or many

PLATE XXII.

Published by J. Stockholme & Co., London.

PRACTICAL PERSPECTIVE.

[Plate 25.] Let the boundary line around Fig. 5, be the dimensions of a picture. Let the line AB be the horizon, parallel to the bottom edge, or ground line of the picture; then will the point C, in the middle, be the point that should be опofite the point of fight, or point of view; which point C, late writers on perſpective have termed the centre of the picture, and which has been ſo defined in this work. If the horizon, which is quite arbitrary, be placed higher on the plane of the picture, as at the line DE, then would the point F, agreeably to the principle laid down, be the moſt eligible place for the centre of the picture. If the horizon were taken ſill higher, as in ſuch repreſentations as are termed bird's-eye views, at G H for inſtance, then would the point I be the beſt situation for the centre; always placing it in the middle between the two extreme ends; as then the ſpectator being directly before the picture to obſerve it, places himſelf neareſt its true and juſt point of view, which would not be the cafe, had the effects of the linear repreſentation been calculated from the point K, K, or H; leſs ſo if it had been calculated from the point L, L, or E; and ſill leſs ſo, if delineated agreeably to the point M, M, or M, as the centre; but which, from want of knowing better, are often as erroneouſly, though unſwittingly, delineated.

From what has now been advanced in this work, if thoroughly underſtood, it is poſſible to perform any thing that linear perſpective can effect, but it is apprehended, few will feel themselves competent to ſuch a trial. There are perſons of ſuch profound thinking, ſo acutely penetrating, that from a cloſely compaſſed theory can extraſt a general practice. To ſuch, BROOK TAYLOR's condensed Elements on this ſubject, would be ample inſight. But works like his are not addreſſed to the many: one compaſſed general obſervation needs much elucidation to make it maniſect to the multitude: wherefore the neceſſity of works of a more open inquiry, of more familiar and minute inſtruction, and according to the different powers and intention by which authors work, different roads are made to the fame ſummit, and each who follows will prefer that path which, moſt agreeably to his humour, will conduct him to the object he wiſes to attain.

The endeavour to avoid trouble is continually inſtanced in every occupation in life: Lazy perſons give themselves moſt trouble, ſays the proverb. Complaint may be made of the extraordinary tediouſneſs of true perſpective delineation, and impatience may ſpurn at the apparent tediouſneſs of the proceeds. From my own experience I have ever found, when by laziines or impatience I have been induced to flight or reject the application of rule, that at laſt I have been forced to have recourse to it, even for the advantage of that diſpatch

PLATE 13.

A. M. B. K. C.