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⸪ ...and mathematical science original: "metrieq; scientiã," likely completing "geometrie" from the previous page are achieved. For these reasons, we have been compelled, as far as possible, to engage in every kind of speculation speculation: from the Latin speculatio, meaning deep contemplation or theoretical study, but especially that which deals with divine and heavenly things. We do this because this science alone considers those things that always remain the same and in the same state; therefore, it is possible for it to be first in its own understanding, since nothing there is obscure or disordered, but always remains the same—which is the hallmark of true science. Furthermore, it assists no less in the understanding of other fields. For this science leads us most of all toward theological science In this context, "theology" refers to the Aristotelian study of the "Prime Mover" or the first cause of all things, which was considered the highest form of philosophy., as it alone can rightly consider the immobile and inseparable substance original: "substantiam" apart from their proximity to those things that happen to sensible, moving, and moved objects—being eternal and impassible substances—both regarding the reasons and the orders of their motions. Nor does it bring small benefit to natural science Natural science here refers to "physics," the study of the material, changing world.. For almost the entire property of material substance is manifested by the property of the local motion of heavenly things. Indeed, the "corruptible" and "incorruptible" Aristotle argued that things on Earth (the sublunary sphere) are corruptible (subject to decay), while the heavens are incorruptible (eternal). are distinguished by straight and circular motion, while heavy and light, or passive and active, are caused by motion toward the center and away from the center. And indeed, regarding the beauty of conduct and actions, this science above all others has made us diligent; since by the likeness of the order, commensurability, and modesty found in divine things, it makes those who follow it lovers of this beauty, and by a certain habit, it impels their minds toward a similarity with these arrangements as if by nature.

Therefore, by continually contemplating those things that remain always and similarly, we also strive to increase this love—both by learning those things skillfully and excellently discovered by our ancestors, and also by striving to add as much as the interval of time between them and us has been able to reveal. We will attempt to record in writing those things that we believe have become clearer to us at present, in as few words as possible, so that those who have tasted this science in any way may be able to follow. And so that there may be a continuity of progress, we will set forth in order everything useful for the contemplation of the heavens. But so that our discourse does not become too long, we will briefly run through those things that were completely stated by our ancestors; however, those things that were either not grasped at all or not sufficiently explained, we will pursue with a longer discourse.

⸪ { ¶ Therefore, this proposed composition of ours is preceded by a certain universal consideration of the extent original: "ambitus," referring to the circumference or scope of the whole Earth in relation to the whole Heaven.

¶ Of those things that are particular and follow after, the first will be to give an account of the oblique circle oblique circle: the ecliptic, or the path the sun appears to follow across the sky, and the location of our habitation, and the differences that occur between them according to each horizon due to inclination. For the study of these things first makes the consideration of others easier.

¶ Second, we will treat the motions of the Sun and Moon, and the accidents In philosophy, "accidents" are properties or characteristics (like an eclipse) that happen to a substance without changing its essential nature. that pertain to them. For without the knowledge of these, there will be no way for us to study the things that happen regarding the other stars.

¶ Since the final part of this treatise is to dispute concerning the stars, it is also right that the consideration of the sphere of the fixed stars sphere of fixed stars: the outermost shell of the universe where the stars do not move relative to one another precedes the pursuit of those called the wandering stars The planets, from the Greek planētēs meaning "wanderer.".

¶ We will attempt to prove each of these things, using as principles and foundations in our inquiry those things that are clearly apparent, based on the certain observations of both the ancients and those who lived in our own times, and subsequently adding geometric proofs original: "lineares p̃bationes," literally "linear proofs," referring to Euclidean geometry..

¶ What must be said generally is as follows: namely, that the Heaven is spherical and moves circularly; that the figure of the Earth itself is also spherical in sense, taken in its universal parts; that it is situated in the middle of the whole Heaven as a true center; that in magnitude and distance it has the ratio of a point relative to the sphere of fixed stars; and that it has no local motion of its own. We will say something briefly about each of these for the sake of remembrance.