If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mat… - Roger Bacon

Everything in nature completes its action through its own force and species alone... as, for example, fire by its own force dries and consumes and does many things. Therefore vision must perform the act of seeing by its own force. But the act of seeing is the perception of a visible object at a distance, and therefore vision perceives what is visible by its own force multiplied to the object. Moreover, the species of the things of world are not fitted by nature to effect the complete act of vision at once, because of its nobleness. Hence these must be aided by the species of the eye, which travels in the locality of the visual pyramid, and changes the medium and ennobles it, and renders it analogous to vision, and so prepares the passage of the species itself of the visible object... Concerning the multiplication of this species, moreover, we are to understand that it lies in the same place as the species of the thing seen, between the sight and the thing seen, and takes place along the pyramid whose vertex is in the eye and base in the thing seen. And as the species of an object in the same medium travels in a straight path and is refracted in different ways when it meets a medium of another transparency, and is reflected when it meets the obstacles of a dense body; so is it also true of the species of vision that it travels altogether along the path of the species itself of the visible object.

I shall draw... a figure (which all these matters are made clear as far as possible on a surface, but the full demonstration would require a body like the eye... The eye of a cow, pig, and other animals can be used for illustration, if anyone wishes to experiment.

For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, since two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first … gives us definite information as to the number of the heavens and of the stars, whose size can be comprehended by means of instruments, and the shapes of all and their magnitudes and distances from the earth, and the thicknesses and number, and greatness and smallness, … It likewise treats of the size and shape of the habitable earth … All this information is secured by means of instruments suitable for these purposes, and by tables and by canons .. For everything works through innate forces shown by lines, angles and figures.