The Sphere of the World (De Sphaera)

Three circular diagrams illustrate the geometric properties of a sphere.
1. The top circle displays basic divisions, labeled "Polus" (Pole) at the top and "Diameter spere" (Diameter of the sphere) across the horizontal center line.
2. The middle circle illustrates parallel circles and sections. Labels include "Polus" at the top and bottom, "Sector" for a segment, "Portio maior" (Greater portion) for the largest segment, and a "zona" (zone) identified between parallel lines. Cursive annotations appear to the right of this diagram.
3. The bottom circle shows a wedge-shaped section labeled "scinda" (sector) cut from the sphere, with the horizontal diameter labeled "linea per centrum" (line through the center).

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A portion of a sphere is that which is bounded by a sector and a part of the surface of the sphere. When this exists as half of a sphere, it is called a half-portion or hemisphaerium hemisphere. But if it is more than a hemisphere, it is called the greater portion of the sphere. And if it is less, it is called the lesser portion, just as was said concerning the portions of a circle.

... intercepta? intercepted

When two semicircles of the greater circles of the sphere meet upon some straight line that passes through the center of the sphere, forming an angle, the part of the sphere intercepted, which is bounded by those two surfaces and a part of the surface of the sphere, is called by many a scinda sphaerae sector of a sphere.

Zona Zone
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Parallel circles in a sphere are said to be those which have the same axis, are cut orthogonally by each, and have the same poles. Therefore, they are called parallels, because all points of them are equidistant from each other. Finally, the part of the surface of the sphere taken between any two of them is called a zone. A circle in a sphere is said to be inclined over another when it is not equidistant to it or intersects it at unequal angles. Furthermore, when two circles, equal or unequal, intersect each other on the surface of the sphere in such a way that all four angles caused around the point of common intersection are equal—which happens only with great circles, or when two collateral angles on one side and the remaining two on the other are made equal, which is not accustomed to happen unless from unequal circumferences—then those two circles are said to intersect each other orthogonally. And conversely, if there are circumferences or circles in a sphere intersecting each other orthogonally, it is necessary that the angles be equal, as we have said. And these four angles are named right spherical angles, when all are equal to each other. But if only opposite angles are found to have equality, or none equals another, those circles and their circumferences intersect each other obliquely and deviate from one another. Furthermore, it is understood that all circumferences of a circle, whether great or small in a sphere, are divided into three hundred and sixty equal parts, and each of them is called one degree. Wherefore, since the diameter of a circle is nearly a third part of the length of the circumference—which they did not define precisely—they established the diameter itself to be one hundred and twenty degrees. Likewise, every degree is separated into sixty equal parts, and each is called a minute; and every minute is similarly divided into sixty parts, of which each is a second. Thus, dividing successively by sixty, every second is divided into a third, every third into a fourth, every fourth into a fifth, every fifth into a sixth, and so on. From which it is clear that not all degrees are equal, but only those that are of one or equal circles; and those of larger circles are larger, and those of smaller circles are smaller.

... sphaeralis? spherical

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... diameter?
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