THE doctrines of mathematics are so necessary to and have such an affinity with magic, that they who profess it without them are quite out of the way, and labour in vain, and shall in no wise obtain their desired effect. For whatsoever things are, and are done in these inferior natural virtues, are all done and governed by number, weight, measure, harmony, motion, and light: and all things which we see in these inferiors have root and foundation in them; yet, nevertheless, without natural virtues of mathematical doctrines, only works like to naturals can be produced: as Plato saith--a thing not partaking of truth or divinity, but certain images akin to them (as bodies going, or speaking, which yet want the animal faculty), such as were those which, amongst the ancients, were called Dedalus's images, and αυτοματα, of which Aristotle makes mention, viz. the three-footed images of Vulcan and Dedalus moving themselves; which, Homer saith, came out of their own accord to the exercise; and which, we read, moved themselves at the feast of Hiarba, the philosophical exerciser. So there are made glasses (some concave, others of the form of a column) making the representation of things in the air seem like shadows at a distance; of which sort Apollonius and Vitellius, in their books, "De Prospectiva," and "Speculis," taught the making and the use. And we read that Magnus Pompeius brought a certain glass, amongst the spoils from the East, to Rome, in which were seen armies of armed men. And there are made certain transparent glasses, which (being dipped in some certain juices of herbs, and irradiated with an artificial light) fill the whole air round about with visions. And we know how to make reciprocal glasses, in which the sun shining, all things which were illustrated by the rays thereof are apparently seen many miles off. Hence a magician (expert in natural philosophy and mathematics, and knowing the middle sciences, consisting of both these, viz. arithmetic, music, geometry, optics, astronomy, and such sciences that are of