Dr. Kim H. Veltman

Appendix 2-Mediaeval Literature Concerning (Pseudo) Perspective

Damianos (or Heliodorus) of Larissa (fl. 4th c.)

ed. R. Schöne, Berlin, 1897, pp. 28 ff.

Proclus (c. 410-485)

A commentary on the first book of Elements., ed. Glenn R. Morrow

Prologue: Part one.

in Euclidem

ed. G. Friedlein, Leipzig, 1873, p. 40.

pp. 33:

Again optics and canonics are offshoots of geometry and arithmetic. the former science uses visual lines and the angles made by them; it is divided into a part specifically called optics, which explains illusory appearances presented by objects aseen at a distance, such as converging of parallel lines or the rounded appearance of square towers, and general catoptrics, which is concerned with the various ways in which light is reflected. the latter is closely bound up with the art of representation and studies what is called "scene painting", showing how objects can be represented by images that will not seem disprportionate or shapeless when seen at a distance or on an elevation. the science of canonics deals with the perceptible ratios between notes of musical scales and discovers the divions of the monochord, everywhere relying on sense perception and, as Plato says, ‘putting the ear ahead of the mind’.

Boethius (c. 480-524/525)

Philoponus (Ioannes Grammaticus) (late 5th-2nd half of 6th c.)

Commentary on Meteorology

From: Commentaria in Aristotelem Graece, Berlin, 1900 , XIV, I., p.73.

If you put white and black upon the same surface and then look at it from a distance, the white will always seem much nearer and the black further off. Hence when painters want something to look hollow, such as a well, a cistern, a ditch or a cave, they colour it black or brown. But when they want something to look prominent, such as the breasts of a girl, an outstretched hand, or the legs of a horse, they lay black on the adjoining areas in order that these will seem to recede and the parts between them will seem to come foreward.

Alkindi (beginning of 9th - c. 873)

Al-Farabi (870-950)

The science of optics studies the same things as geometry, that is, figures, sizes, sites, order, equality and inequality and others but deals with them as they are in lines, surfaces and bodies. Whence the speculation of geometry is more general than that of optics. But although eveything that is treated by the one is dealt with by the other, this one [optics] is not superfluous but necessary, as in the case of those things which Euclid proved were square. although at some distance they appear to converge and equal sizes appear unequal and conversely. Of those which are in one plane some appear lower, others appear higher and of those which seem closer some are further, and conversely. Hence this science was always necessary because it distinguishes between that which appears in the eye as other than it is and that which appears as it is. Thus this science assigns the causes of these [illusions] and with necessary demonstrations it shows the ways in which vision can err, in order that it does not err and we understand everything that we see as it is. For optics teaches how to take the heights of trees and walls, and the widths of rivers and depths and the heights of mountains after sight falls on their boundaries, then the distances of the heavenly bodies and their sizes....

Alhazen (c. 965-c.1040)

Kitab al manazir

Tzetzes (12th c.)

Cited in Junius, Painting of the Ancients, by Gombrich, 1960, 191.

The Athenians intending to consecrate an excellent image of Minerva upon a high pillar, set Phidias and Alcamenes to work, meaning to chuse the better of the two. Aclamenes being nothing at all skilled in Geometry and in the Optickes made the goddesse wonderfull faire to the eye of them that saw her hard by. Phidias on the contrary ... did consider that the whole shape of his image should change according to the height of the appointed place, and therefore made her lips wide open, her nose somewhat out of order and all the rest accordingly...when these two images were afterwards brought to light and compared, phidias was in great danger to have been stoned by the whole multitude, untill the statues were at length set on high. For Alcamenes his sweet and diligent strokes beeing drowned, and phidias his disfigured and distorted hardnesse being vanished by the height of the place, made Alcamenes to be laughed at, and Phidias to be much more esteemed.

Grosseteste (1168-1253)

Bacon, Roger (1214/20-1292)

Now I wish to present the...[purpose]... which concerns geometrical forms as regards lines, angles and figures both of solids and surfaces. for it is impossible for the spiritual sense to be known without a knowledge of the literal sense....But no one would be able to plan and arrange a representation of bodies of this kind, unless he were well acquainted with the books of the Elements of Euclid and Theodosius and Milleius and of other geometricians. For owing to ignorance of these authors on the part of theologians they are deceived in matters of greatest importance....Oh, how the ineffable beauty of the divine wisdom would shine and infinite benefit would overflow, if these matters relating to geometry, which are contained in Scripture, should be placed before our eyes in their physical forms!.... Therefore I count nothing more fitting for a man diligent in the study of God’s wisdom than the exhibition of geometrical forms of this kind before his eyes....And for the sake of all things in general let us recall to mind that nothing can be known concerning the things of this world without the power of geometry, as has already been proved. Also a knowledge of things is necessary in Scripture on account of the literal and spiritual sense, as has been set forth above. For without doubt the whole truth of things in the world lies in the literal sense, as has been said, and especially of things relating to geometry, because we can understand nothing fully unless its form is presented before our eyes, and therefore in the Scripture of god the whole knowledge of things to be defined by geometrical forms is contained and far better than mere philosophy could express it.

Witelo (1230/35-c. 1275)

Pec(k)ham (1230/35-1292)

Blasius of Parma (1345-1416)

Regiomontanus (1436-1476)

Maurolycus (1494-1575)

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Last Update: August 3, 1998