# PERSPECTIVE

, the art of delineating visible objects on a plane surface, such as they appear at a given distance, or height, upon a transparent plane, placed commonly perpendicular to the horizon, between the eye and the object. This is particularly called

*Linear* Perspective, as regarding the position, magnitude,
form, &c, of the several lines, or contours of
objects, and expressing their diminution.

Some make this a branch of Optics; others an art | and science derived from it: its operations however are all geometrical.

*History of* Perspective. This art derives its origin
from painting, and particularly from that branch of
it which was employed in the decorations of the theatre,
where landscapes were chiefly introduced. Vitruvius,
in the proem to his 7th book, says that Agatharchus,
at Athens, was the first author who wrote upon this subject,
on occasion of a play exhibited by Æschylus, for
which he prepared a tragic scene; and that afterwards
the principles of the art were more distinctly taught in the
writings of Democritus and Anaxagoras, the disciples
of A gatharchus, which are not now extant.

The Perspective of Euclid and of Heliodorus Larisseus contains only some general elements of optics, that are by no means adapted to any particular practice; though they furnish some materials that might be of service even in the linear Perspective of painters.

Geminus, of Rhodes, a celebrated mathematician, in Cicero's time, also wrote upon this science.

It is also evident that the Roman artists were acquainted with the rules of Perspective, from the account which Pliny (Nat. Hist. lib. 35, cap. 4) gives of the representation on the scene of those plays given by Claudius Pulcher; by the appearance of which the crows were so deceived, that they endeavoured to settle on the fictitious roofs. However, of the theory of this Art among the Ancients we know nothing; as none of their writings have escaped the general wreck of ancient literature in the dark ages of Europe. Doubtless this art must have been lost, when painting and sculpture no longer existed. However, there is reason to believe that it was practised much later in the Eastern empire.

John Tzetzes, in the 12th century, speaks of it as well acquainted with its importance in painting and statuary. And the Greek painters, who were employed by the Venetians and Florentines, in the 13th century, it seems brought some optical knowledge along with them into Italy: for the disciples of Giotto are commended for observing Perspective more regularly than any of their predecessors in the art had done; and he lived in the beginning of the 14th century.

The Arabians were not ignorant of this art; as may be presumed from the optical writings of Alhazen, about the year 1100. And Vitellus, a Pole, about the year 1270, wrote largely and learnedly on optics. And, of our own nation, friar Bacon, as well as John Peckham, archbishop of Canterbury, treated this subject with surprising accuracy, considering the times in which they lived.

The first authors who professedly laid down rules of Perspective, were Bartolomeo Bramantino, of Milan, whose book, Regole di Perspectiva, e Misure delle Antichita di Lombardia, is dated 1440; and Pietro del Borgo, likewise an Italian, who was the most ancient author met with by Ignatius Danti, and who it is supposed died in 1443. This last writer supposed objects placed beyond a transparent tablet, and so to trace the images, which rays of light, emitted from them, would make upon it. And Albert Durer constructed a machine upon the principles of Borgo, by which he could trace the Perspective appearance of ob- jects.

Leon Battista Alberti, in 1450, wrote his treatise De Pictura, in which he treats chiefly of Perspective.

Balthazar Per<*>zzi, of Siena, who died in 1536, had diligently studied the writings of Borgo; and his method of Perspective was published by Serlio in 1540. To him it is said we owe the discovery of points of distance, to which are drawn all lines that make an angle of 45° with the ground line.

Guido Ubaldi, another Italian, soon after discovered, that all lines that are parallel to one another, if they be inclined to the ground line, converge to some point in the horizontal line; and that through this point also will pass a line drawn from the eye parallel to them. His Perspective was printed at Pisaro in 1600, and contained the first principles of the method afterwards discovered by Dr. Brook Taylor.

In 1583 was published the work of Giacomo Barozzi, of Vignola, commonly called Vignola, intitled The two Rules of Perspective, with a learned commentary by Ignatius Danti. In 1615 Marolois' work was printed at the Hague, and engraved and published by Hondius. And in 1625, Sirigatti published his treatise of Perspective, which is little more than an abstract of Vignola's.

Since that time the art of Perspective has been gradually improved by subsequent geometricians, particularly by professor Gravesande, and still more by Dr. Brook Taylor, whose principles are in a great measure new, and far more general than those of any of his predecessors. He did not confine his rules, as they had done, to the horizontal plane only, but made them general, so as to affect every species of lines and planes, whether they were parallel to the horizon or not; and thus his principles were made universal. Besides, from the simplicity of his rules, the tedious progress of drawing out plans and elevations for any object, is rendered useless, and therefore avoided; for by this method, not only the fewest lines imaginable are required to produce any Perspective representation, but every sigure thus drawn will bear the nicest mathematical examination. Farther, his system is the only one calculated for answering every purpose of those who are practitioners in the art of design; for by it they may produce either the whole, or only so much of an object as is wanted; and by sixing it in its proper place, its apparent magnitude may be determined in an instant. It explains also the Perspective of shadows, the reflection of objects from polished planes, and the inverse practice of Perspective.

His Linear Perspective was first published in 1715; and his New Principles of Linear Perspective in 1719, which he intended as an explanation of his first treatise. And his method has been chiefly followed by all others since.

In 1738 Mr. Hamilton published his Stereography, in 2 vols folio, after the manner of Dr. Taylor. But the neatest system of Perspective, both as to theory and practice, on the samo principles, is that of Mr. Kirby. There are also good treatises on the subject, by Desargues, de Bosse, Albertus, Lamy, Niceron, Pozzo the Jesuit, Ware, Cowley, Priestley, Ferguson, Emerson, Malton, Henry Clarke, &c, &c.

*Of the Principles of* Perspective. To give an idea|
of the first principles and nature of this art; suppose a
transparent plane, as of glass &c, HI raised perpendicularly
on a horizontal plane; and the spectator S directing
his eye O to the triangle ABC: if now we conceive
the rays AO, BO, CO, &c, in their passage
through the plane, to leave their traces or vestiges in
*a, b, c,* &c, on the plane; there will appear the triangle
*abc;* which, as it strikes the eye by the same rays
*a*O, *b*O, *c*O, by which the reflected particles of light
from the triangle are transmitted to the same, it will
exhibit the true appearance of the triangle ABC,
though the object should be removed, the same distance
and height of the eye being preserved.

The business of Perspective then, is to shew by
what certain rules the points *a, b, c,* &c, may be
found geometrically: and hence also we have a mechanical
method of delineating any object very accurately.

Hence it appears that *abc* is the section of the plane
of the picture with the rays, which proceed from the
original object to the eye: and therefore, when this is
parallel to the picture, its representation will be both
parallel to the original, and similar to it, though smaller
in proportion as the original object is farther from the
picture. When the original object is brought to coincide
with the picture, the representation is equal to the
original; but as the object is removed farther and farther
from the picture, its image will become smaller and
smaller, and also rise higher and higher in the picture,
till at last, when the object is supposed to be at an infinite
distance, its image will vanish in an imaginary
point, exactly as high above the bottom of the picture
as the eye is above the ground plane, upon which the
spectator, the picture, and the original object are supposed
to stand.

This may be familiarly illustrated in the following manner: Suppose a person at a window looks through an upright pane of glass at any object beyond; and, keeping his head steady, draws the figure of the object upon the glass, with a black-lead pencil, as if the point of the pencil touched the object itself; he would then have a true representation of the object in Perspective, as it appears to his eye. For properly drawing upon the glass, it is necessary to lay it over with strong gum water, which will be fit for drawing upon when dry, and will then retain the traces of the pencil. The person should also look through a small hole in a thin plate of metal, fixed about a foot from the glass, between it and his eye; keeping his eye close to the hole, other- wise he might shift the position of his head, and so make a false delineation of the object.

Having traced out the figure of the object, he may go over it again, with pen and ink; and when that is dry, cover it with a sheet of paper, tracing the image upon this with a pencil; then taking away the paper, and laying it upon a table, he may finish the picture, by giving it the colours, lights, and shades, as he sees them in the object itself; and thus he will have a true resemblance of the object on the paper.

*Of certain Definitions in*Perspective.

*The point of sight,* in Perspective, is the point E,
where the spectator's eye should be placed to view the
picture. And the *point of sight,* in the picture, called
also the *centre of the picture,* is the point C directly opposite
to the eye, where a perpendicular from the eye
at E meets the picture. Also this perpendicular EC
is the *distance of the picture:* and if this distance be transferred
to the horizontal line on each side of the point
C, as is sometimes done, the extremes are called the
points of distance.

The *original plane,* or *geometrical plane,* is the plane
KL upon which the real or original object ABGD is
situated. The line OI, where the ground plane cuts
the bottom of the picture, is called the *section* of the
original plane, the *ground-line,* the *line of the base,* or
the *fundamental line.*

If an original line AB be continued, so as to intersect
the picture, the point of intersection R is called the intersection
of that original line, or its *intersecting point.*
The *horizontal plane* is the plane *abgd,* which passes
through the eye, parallel to the horizon, and cuts the
Perspective plane or picture at right angles; and the
*horizontal line bg* is the common intersection of the horizontal
plane with the picture.

The *vertical plane* is that which passes through the
eye at right angles both to the ground plane and to the
picture, as ECSN. And the *vertical line* is the common
section of the vertical plane and the picture,
as CN.

The *line of station* SN is the common section of the
vertical plane with the ground plane, and perpendicular
to the ground line OI.|

The *line of the height of the eye* is a perpendicular, as
ES, let fall from the eye upon the ground plane.

The *vanishing line* of the original plane, is that line
where a plane passing through the eye, parallel to the
original plane, cuts the picture: thus *bg* is the vanishing
line of ABGD, being the greatest height to which
the image can rise, when the original object is insinitely
distant.

The *vanishing point* of the original line, is that point
where a line drawn from the eye, parallel to that original
line, intersects the picture: thus C and *g* are the
vanishing points of the lines AB and *ki.* All lines parallel
to each other have the same vanishing point.

If from the point of sight a line be drawn perpendicular
to any vanishing line, the point where that line
intersects the vanishing line, is called the centre of that
vanishing line: and the *distance of a vanishing line* is the
length of the line which is drawn from the eye, perpendicular
to the said line.

*Measuring points* are points from which any lines in
the Perspective plane are measured, by laying a ruler
from them to the divisions laid down upon the ground
line. The measuring point of all lines parallel to the
ground line, is either of the points of distance on the
horizontal line, or point of sight. The measuring
point of any line perpendicular to the ground line, is in
the point of distance on the horizontal line; and the
measuring point of a line oblique to the ground line is
found by extending the compasses from the vanishing
point of that line to the point of distance on the perpendicular,
and setting off on the horizontal line.

*Some general Maxims or Theorems in*Perspective.

1. The representation *ab,* of a line AB, is part of a
line SC, which passes through the intersecting point S,
and the vanishing point C, of the original line AB.

2. If the original plane be parallel to the picture, it can have no vanishing line upon it; consequently the representation will be parallel. When the original is perpendicular to the ground line, as AB, then its vanishing point is in C, the centre of the picture, or point of sight; because EC is perpendicular to the picture, and therefore parallel to AB.

3. The image of a line bears a certain proportion to its original. And the image may be determined by transferring the length or distance of the given line to the intersecting line; and the distance of the vanishing point to the horizontal line; i. e. by bringing both into the plane of the picture.

Prob. *To find the representation of an Objective point* A.
—Draw A1 and A2 at pleasure, intersecting the bot-
tom of the picture in 1 and 2; and from the eye E
draw EH parallel to A1, and EL parallel to A2;
then draw H1 and L2, which will intersect each other
in *a,* the representation of the point A.

Otherwise. Let H be the given objective point.
From which draw HI perpendicular to the fundamental
line DE. From the fundamental line DE cut off
IK = IH : through the point of sight F draw a horizontal
line FP, and make FP equal to the distance of
the eye SK: lastly, join FI and PK, and their intersection
*h* will be the appearance of the given objective
point H, as required.

And thus, by finding the representations of the two points, which are the extremes of a line, and connecting them together, there will be formed the representation of the line itself. In like manner, the representations of all the lines or sides of any figure or solid, determine those of the solid itself; which therefore are thus put into Perspective.

*Aerial* Perspective, is the art of giving a due diminution
or gradation to the strength of light, shade,
and colours of objects, according to their different distances,
the quantity of light which falls upon them,
and the medium through which they are seen.

Perspective *Machine,* is a machine for readily and
easily making the Perspective drawing and appearance
of any object, with little or no skill in the art. There
have been invented various machines of this kind. One
of which may even be seen in the works of Albert|
Durer. A very convenient one was invented by Dr.
Bevis, and is described by Mr. Ferguson, in his Perspective,
pa. 113. And another is described in Kirby's
Perspective, pa. 65.

Perspective *Plan,* or *Plane,* is a glass or other
transparent surface supposed to be placed between the
eye and the object, and usually perpendicular to the horizon.

*Scenographic* Perspective. See Scenography.

Perspective *of Shadows.* See Shadow.

*Specular* Perspective, is that which <*>epresents the
objects in cylindrical, conical, spherical, or other mirrors.