The Sphere of the World (De Sphaera)

Note? the motion?.

That the heaven revolves from east to west is a sign: the stars that rise in the east are always elevated little by little and successively until they arrive at the middle of the sky; and they are always at the same proximity and distance from one another; and thus, always maintaining themselves, they tend toward the setting continuously and uniformly. There is also another sign. The stars that are near the arctic pole, which never set for us, move continuously and uniformly around the pole, describing their circles; and they are always at an unequal distance from one another and proximity. Whence, through these two continuous motions of the stars, both those tending toward the setting and those that do not, it is clear that the firmament moves from the east to the west. ON the roundness of the heaven.

A semi-circular diagram represents the celestial sphere with stars. The horizon is marked with "oriens" (East) and "occidens" (West). Stars are clustered at the top and sides to illustrate celestial motion.

Triple? reason? for the roundness? of the heaven?.

That the heaven is round: there is a triple reason, likeness, convenience, and necessity. Likeness, for the sensible world is made to the likeness of the archetype world, in which there is neither beginning nor end. Whence, to this likeness, the sensible world has a round form, in which it is not possible to assign a beginning or an end. Convenience, because of all body shapes, the sphere is the greatest, and of all shapes, the round is the most capacious; since, therefore, it is the greatest and round, it is the most capacious; whence, since the world contains all things, such a form was useful and convenient for it. Necessity: because if the world were of another form than round, namely three-sided or four-sided or multi-sided, two impossibilities would follow, namely that some place would be empty, and a body without a place, both of which are false, as is clear in elevated and convoluted angles. Likewise, as Al-Farghani a medieval Persian astronomer says, if the heaven were flat, some part of the heaven would be closer to us than another, namely that which is above our head; therefore, a star existing there would be closer to us than one existing in the rising or setting; but those that are closer to us appear larger. Therefore, the sun or another star existing in the middle of the sky ought to appear larger than one existing in the rising or setting, the contrary of which we see to happen. The sun or another star appears larger when existing in the east or west than in the middle of the sky; but since the truth of the matter is not so, the cause of this appearance is that in winter or rainy time certain vapors ascend between our sight and the sun or another star, and because those vapors are a diaphanous transparent body, they disperse our visual rays, so that they do not comprehend the thing in its natural and true quantity, as is clear regarding a denarius a coin thrown to the bottom of clear water, which appears larger than its true quantity due to a similar dispersal of rays. That the earth is round.

A circular diagram contains a triangle and a square inscribed within circles, illustrating geometric proofs regarding the sphericity of the heavens.

A diagram shows the Earth as a curved surface (labeled "Or." for Oriens and "Oc." for Occidens) with a person standing on it. To the right, a sun or star is shown rising over waves, illustrating the curvature of the Earth and the timing of sunrise/sunset.

roundness? of the earth?.

That the earth is also round is clear in this way. Signs and stars do not rise and set equally for all people existing everywhere; but they rise and set sooner for those who are toward the west or toward the east. And that they rise and set sooner and later for some, the cause is the bulge of the earth, which is well evident through those things which happen on high. One and the same lunar eclipse, which appears to us in the first hour of the night, appears to the easterners around the third hour of the night. Whence it is certain that it was night for them sooner and the sun set for them sooner than for us. The cause of this thing is only the bulge of the earth. That the earth also has a roundness from the north to the south, and conversely, is thus clear. For those existing toward the north, certain stars are always appearing, namely those which are near...