Sphere into the length of the world through...?
...world into two parts...?
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COMPENDIUM of the SPHERE of the world happily begins.

For novice adolescents, who are obtaining an approach to the grasp of astronomy, by a short and direct path removed from the common track, the spherical little work of Joannes de Sacrobosco is dedicated, along with some additions marked here and there by the letter A; against the follies regarding the planetary theorica planetary models of Cremonensis refers to Gerard of Cremona, the disputes of Joannes de Monteregio Regiomontanus are added, being as accurate as they are useful. Also, the most accurate theorica of the planetary motions of the same [planets] by Georgius Purbachius is included, a work dedicated and woven in a useful series, beginning under a lucky star.

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Large ornamental drop-cap initial 'T' decorated with white foliage and vine motifs on a dark background.

We distinguish the treatise on the sphere into four chapters.
First, we will speak of the composition of the sphere, what the sphere is, what its center is, what the axis of the sphere is, what the pole of the world is, how many spheres there are, and what the form of the world is. In the second, of the circles from which the material sphere is composed and that celestial [sphere] which is understood to be composed through this imaginary one. In the third, of the rising and setting of the signs, and of the diversity of days and nights, which is for inhabitants in different places, and of the division of climates. In the fourth, of the circles and motions of the planets, and of the causes of eclipses.

Concerning the definition of the sphere and certain principles to be assumed, and the composition and convenience of the sphere. Chapter One.

Small woodcut initial 'N' within a square frame with floral decoration.

It is not in our power to go up to the heavens, to see with our own eyes their circles and degrees, and to revolve them from wherever and whenever it pleases. What has passed in them, man cannot view; nor would the life of man suffice to await what is to come; and what is happening in the present, while man is alive, no one can see all of it. Now elsewhere it is day, elsewhere it is night; for one the sun or a certain star rises, for another it sets; nor can it be for all places at the same time. To some, the sphere demonstrates itself as straight, to others as oblique, in many ways. For which reasons, it is good and convenient to have an artificial sphere, which one can revolve at will with one's hands, and be able to be looked at according to its common position and part, and all its degrees and circles perceived, at least those that are opportune, by means of which, as if by an example, we might be able to easily understand the present, the past, and the future, and what is natural of the sphere of heaven. Therefore, let us turn to memory those things which are said concerning the circles and points and the zodiac in the second chapter of this work, and let us construct it similarly to the likeness of the tenth, ninth, or eighth sphere. First, as is the custom, from circles made of subtle metal or suitable wood, well smoothed and secured in their roundness and positions, two great circles cutting each other orthogonally upon the points which are the poles. And another circle through the equinoctial, equidistant from those poles. Similarly, also two tropics, and two circles, the arctic and the antarctic, in their positions. And the zone of the zodiac divided in two by the ecliptic and the twelve signs, which are marked by degrees on the ecliptic and noted with their names according to order; and we shall separate each quarter of the equinoctial from colure to colure into 90 degrees. And let the quarters of the zodiac be similarly divided, so that one colure passes through the two solstices and the poles of the zodiac, and the other through the two points of the equinox. With these eight circles well secured and distinguished by their names and degrees, and knowing two round holes in two places diametrically opposite, where the two colure circles intersect each other, these are truly the points of the poles of the sphere itself; we shall pass through them a round axis of iron, very straight, from each...