Book One

a 4

Book One presents considerations of the universal scope of the whole Earth in relation to the whole Heaven, which necessarily had to be presupposed. It also recounts the theorems that are presented for spherical demonstrations. It teaches the doctrine of chords and arcs. Finally, it investigates the ascensions of the right sphere. The "right sphere" refers to the celestial sphere as viewed from the equator, where the celestial equator passes through the zenith and the poles are on the horizon.

Large historiated initial 'R' decorated with elaborate foliate scrollwork and floral motifs.Rightly indeed, in my judgment, the more noble philosophers distinguished between the Theoretical and Practical parts of philosophy. For even if it happens that the theoretical must come before the practical, there is nonetheless a great difference between them: not only because we see that some of the moral virtues can exist in some people even without formal instruction, while the contemplation of the universe is impossible to attain without instruction; but most especially because in the former, all utility comes from frequent practice regarding the things themselves, whereas in the latter, it comes from contemplation. not The marginal "nō" (non/not) likely emphasizes the distinction being made in the text. Wherefore we also thought it right to say that our actions should be guided according to the considerations of those things that appear to us, so that we do not deviate too much from the best and most orderly arrangement of the universe, and that we should devote the greater part of our leisure to contemplations, which are many and beautiful.

For indeed, Aristotle appropriately divides contemplation itself into three primary types: namely, natural, mathematical, and theological. Since all beings consist of matter, form, and motion—each of which cannot be seen individually but can only be understood apart from the others—one would rightly consider the first cause of the universal motion to be God himself, invisible and immobile. He would deservedly name the investigation of this cause "theological science," and would place its operation upward among the more sublime parts of the world, entirely removed from the substance of sensible things Sensible things: objects that can be perceived by the five senses..

However, that science which investigates material and ever-moving quality, and which deals with white and hot, sweet and soft, and things of this sort, he would surely call "natural" This refers to "Physics" in the Aristotelian sense.; this is found for the most part among corruptible things and beneath the lunar orb.

But that science which manifests the species and local motions, and seeks after figure and quantity—both discrete and continuous—as well as place and time and similar things, he would justly call "mathematical." This occupies a place between the two previously mentioned sciences, not only because it can be perceived both through the senses and without the senses, but also because it applies to all beings simply, both mortal and immortal. For it is shared with those things that are always changing according to local motion, and with eternal things according to the immobility and immutability of their form.

Thus it happens that someone might call the other two types of contemplation "conjecture" rather than science: Theology, because of its extreme obscurity and incomprehensibility; and Natural science, because of the continuous and uncertain flux of matter. Because of this, one cannot observe even the philosophers being in agreement about it. Only Mathematics, if one approaches it with attentive signs, will be confessed to generate a certain and indelible science for its students. Indeed, its proofs proceed through the most certain methods of arithmetic and geometry.