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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.
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:
By the 2nd century BC Hipparchus was using a systematic coordinate system, based on dividing the circle into 360°, to uniquely specify places on Earth. [2]: 31 So longitudes could be expressed as degrees east or west of the primary meridian, as is done today (though the primary meridian is different). He also proposed a method of determining ...
Apollonius of Perga (c. 240 – c. 190 BC) is known for his work on conic sections and his study of geometry in 3-dimensional space. He is considered one of the greatest ancient Greek mathematicians. Hipparchus (c. 190 – c. 120 BC) is considered the founder of trigonometry [9] and also solved several problems of spherical trigonometry.
The most famous successors of the tradition begun by Thales were Plato and Aristotle; while much thought continued to rely on intuition, the lasting legacy of this work was that it offered non-supernatural explanations for the normal operations of the universe; mathematics (especially geometry) was significantly developed and applied on the ...
This page was last edited on 17 December 2024, at 15:13 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.
The lune of Hippocrates is the upper left shaded area. It has the same area as the lower right shaded triangle. In geometry, the lune of Hippocrates, named after Hippocrates of Chios, is a lune bounded by arcs of two circles, the smaller of which has as its diameter a chord spanning a right angle on the larger circle.