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 aO, bO, cO, 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.

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Entry taken from A Mathematical and Philosophical Dictionary, by Charles Hutton, 1796.

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PERITROCHIUM
PERPENDICULAR
PERPETUITY
PERRY (Captain John)
PERSEUS
* PERSPECTIVE
PERTICA
PETARD
PETIT (Peter)
PETTY (Sir William)
PHARON