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More generally, if the quadrilateral is a rectangle with sides a and b and diagonal d then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then d 2, the right hand side of Ptolemy's relation is the sum a 2 + b 2.
A famous papyrus published at the end of the 19th century by Bernard Pyne Grenfell, the papyrus Revenue Laws is a comprehensive set of regulations on farm taxes in the reign of Ptolemy II Philadelphus (283–246), more precisely for the year –259/–258. This document contains tax regulations for the understanding of how Ptolemy II ...
Ptolemy began a process of hellenization and commissioned numerous constructions, building the massive Musaeum institution, which was a leading center of education. [15] [g] Euclid is speculated to have been among the Musaeum's first scholars. [22] Euclid's date of death is unknown; it has been speculated that he died c. 270 BC. [22]
The Ptolemaic system of celestial motion as depicted in the Harmonia Macrocosmica (1661). Science in classical antiquity encompasses inquiries into the workings of the world or universe aimed at both practical goals (e.g., establishing a reliable calendar or determining how to cure a variety of illnesses) as well as more abstract investigations belonging to natural philosophy.
An edition in Latin of the Almagestum in 1515. The Almagest (/ ˈ æ l m ə dʒ ɛ s t / AL-mə-jest) is a 2nd-century mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy (c. AD 100 – c. 170) in Koine Greek. [1]
Some Greek astronomers (e.g., Aristarchus of Samos) speculated that the planets (Earth included) orbited the Sun, but the optics (and the specific mathematics – Isaac Newton's law of gravitation for example) necessary to provide data that would convincingly support the heliocentric model did not exist in Ptolemy's time and would not come ...
Ibn Sahl is the first Muslim scholar known to have studied Ptolemy's Optics, and as such an important precursor to the Book of Optics by Ibn Al-Haytham (Alhazen), written some thirty years later. [8] Ibn Sahl dealt with the optical properties of curved mirrors and lenses and has been described as the discoverer of the law of refraction (Snell's ...
Three important textbooks, written shortly before Ptolemy's time, were written by Cleomedes, Geminus, and Theon of Smyrna. Books by Roman authors like Pliny the Elder and Vitruvius contain some information on Greek astronomy. The most important primary source is the Almagest, since Ptolemy refers to the work of many of his predecessors. [3]