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On Sizes and Distances (of the Sun and Moon) (Greek: Περὶ μεγεθῶν καὶ ἀποστημάτων [ἡλίου καὶ σελήνης], romanized: Peri megethon kai apostematon) is a text by the ancient Greek astronomer Hipparchus (c. 190 – c. 120 BC) in which approximations are made for the radii of the Sun and the Moon as well as their distances from the Earth.
Hipparchus was born in Nicaea (Ancient Greek: Νίκαια), in Bithynia.The exact dates of his life are not known, but Ptolemy attributes astronomical observations to him in the period from 147 to 127 BC, and some of these are stated as made in Rhodes; earlier observations since 162 BC might also have been made by him.
Mihalis Dafermos (born 1976) - Professor of Mathematics at Princeton University and Lowndean Chair of Astronomy and Geometry at the University of Cambridge [17] Apostolos Doxiadis (born 1953) - Australian born Mathematician. [18] Athanassios S. Fokas (born 1952) - Contributor in the field of integrable nonlinear partial differential equations. [19]
IV. The earliest Greek geometry V. Pythagorean geometry VI. Progress in the Elements down to Plato's time ("the formative stage in which proofs were discovered and the logical bases of the science were beginning to be sought" [6]) VII. Special problems ("three famous problems" of antiquity [6]) VIII. Zeno of Elea IX. Plato X.
Book 6 combines the theory of the sun and the moon to produce a theory that predicts eclipses. Books 7 and 8 start freshly; they lay out the theory and practice when working with fixed stars and conclude with a catalogue of 1,022 stars. Books 9 to 13 are dedicated to the five visible (and thus, at the time, the five known) planets.
Hipparchus is purported to have written a twelve-volume work on chords, all now lost, so presumably, a great deal was known about them. In the table below (where c is the chord length, and D the diameter of the circle) the chord function can be shown to satisfy many identities analogous to well-known modern ones:
The major accomplishment of Hippocrates is that he was the first to write a systematically organized geometry textbook, called Elements (Στοιχεῖα, Stoicheia), that is, basic theorems, or building blocks of mathematical theory. From then on, mathematicians from all over the ancient world could, at least in principle, build on a common ...
Aristarchus's 3rd century BCE calculations on the relative sizes of, from left, the Sun, Earth and Moon, from a 10th-century CE Greek copy. On the Sizes and Distances (of the Sun and Moon) (Ancient Greek: Περὶ μεγεθῶν καὶ ἀποστημάτων [ἡλίου καὶ σελήνης], romanized: Perì megethôn kaì apostēmátōn [hēlíou kaì selḗnēs]) is widely accepted ...