Mathematical Mirror

parts of perspective, just as there is the book on vision, and the book on mirrors, and others besides these. Alhaten, however, has treated it too superfluously, both in substance and in method. Ptolemy, however, proceeds quite moderately. Now, therefore, at your instance, I desire to collect certain essential points in a compendium from all the authors. But my treatise On the Generation of Species, and their multiplication, and action, and corruption, must always be kept at hand, without which nothing worthy regarding perspective can be understood. This science, however, is far more beautiful than others and more useful, and therefore more delightful, since our primary delight is in vision. And light and color have a special beauty beyond other things that are brought to our senses, and not only does their beauty become known, but greater utility and necessity arise from them. For Aristotle says in Book 1 of Metaphysics that vision alone shows us the differences of things: for through it we seek out certain experiences of all things that are in the heavens and on the earth. For those things which are in the celestial realms are considered through visual instruments, as Ptolemy and the other astronomers teach. And similarly those things which are generated in the air, such as comets and rainbows and the like. For their altitude above the horizon, and their size and figure, and multitude, and all things that are in them, are certified through the modes of seeing with instruments. Those things, however, which are here on earth, we experience through vision, because a blind person can experience nothing of this world that is worthy. And hearing makes us believe, because we believe the teachers, but we cannot experience what we learn except through vision. If, however, we allege taste and touch and smell, then we put on beastly wisdom. For the brutes are occupied about tastable and tangible things, and they exercise smell for the sake of taste and touch, but they are vile and few, and common to us and the brutes, concerning which these senses certify, and therefore they do not rise to the dignity of human wisdom. Furthermore, on account of necessity and utility and dignity, they are constituted