The Sphere of the World

For young novices seeking entry into the astronomical republic via a short and direct path, set apart from common tracks: the little work on the sphere by Johannes de Sacrobosco. Along with the most accurate and useful disputations of Johannes Regiomontanus Johannes Regiomontanus (1436–1476) was a German mathematician and astronomer who greatly influenced the Renaissance scientific revolution. against the "deliriums" original: "delyramenta" — Regiomontanus was notoriously critical of earlier medieval translations and theories he considered mathematically unsound. of Gerard of Cremona regarding the theories of the planets. Also the very accurate theory of Georg von Peuerbach Georg von Peuerbach (1423–1461) was the teacher of Regiomontanus and a pioneer in observational astronomy. on the same planetary motions; this dedicated work, woven in a useful sequence, begins.

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WE DIVIDE the treatise on the sphere into four chapters. Speaking first: what a 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 shape of the world is. ¶ In the second, about the circles from which the material sphere is composed, and that super-celestial sphere which is understood to be composed by these imaginary circles. ¶ In the third, about the rising and setting of the zodiacal signs, the variation of days and nights for those living in different places, and the division of climates. ¶ In the fourth, about the circles and motions of the planets, and the causes of eclipses.

Chapter One

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The sphere is thus described by Euclid Euclid of Alexandria (c. 300 BCE) was a Greek mathematician, often called the "father of geometry.": A sphere is the passage of the circumference of a half-circle when it is rotated around a fixed diameter until it returns to its place. That is, a sphere is such a round and solid object that is described by the arc of a semicircle being turned around. A sphere is also described by Theodosius Theodosius of Bithynia (c. 160–100 BCE) was a Greek astronomer and mathematician who wrote Sphaerics, a book on the geometry of the sphere. thus: A sphere is a certain solid contained by one surface, in the middle of which is a point from which all lines drawn to the circumference are equal. And that point is called the center of the sphere. A straight line passing through the center of the sphere and touching the circumference at both ends on either side is called the axis of the sphere. The two points terminating the axis are called the poles of the world. ¶ The sphere, however, is divided in two ways: according to substance and according to accident. According to substance, it is divided into nine spheres: namely, the ninth sphere, which is called the first motion or the first movable Primum Mobile In the medieval geocentric system, the Primum Mobile is the outermost moving sphere that carries all other spheres around the Earth once every 24 hours., and into the sphere of the fixed stars, which is called the firmament firmamentum.

A circular library stamp at the bottom center. The outer ring reads "Central National Library of Florence" original: "BIBLIOTECA NAZIONALE CENTRALE FIRENZE". The center of the stamp features the Roman numerals "XV".