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For the Moon, Ptolemy began with Hipparchus' epicycle-on-deferent, then added a device that historians of astronomy refer to as a "crank mechanism": [28] he succeeded in creating models for the other planets, where Hipparchus had failed, by introducing a third device called the equant. Ptolemy wrote the Syntaxis as a textbook of mathematical ...
[8] [9] Elements was a descriptive summary of Ptolemy's Almagest that included the findings and revised values of earlier Islamic astronomers. [10] Among the revisions included in the book were corrections to calculations of the circumference of the Earth , the Earth's axial tilt , and the apsides of the Sun and the Moon. [ 10 ]
The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, [1] a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function.
The basic elements of Ptolemaic astronomy, showing a planet on an epicycle (smaller dashed circle), a deferent (larger dashed circle), the eccentric (×) and an equant (•). Equant (or punctum aequans) is a mathematical concept developed by Claudius Ptolemy in the 2nd century AD to account for the observed motion of the planets. The equant is ...
The Canon of Kings was a dated list of kings used by ancient astronomers as a convenient means to date astronomical phenomena, such as eclipses.For a period, the Canon was preserved by the astronomer Claudius Ptolemy, and is thus known sometimes as Ptolemy's Canon.
The Almagest is primarily a work on astronomy, and astronomy relies on trigonometry. Ptolemy's table of chords gives the lengths of chords of a circle of diameter 120 as a function of the number of degrees n in the corresponding arc of the circle, for n ranging from 1/2 to 180 by increments of 1/2. [20]
Ptolemy did not predict the relative sizes of the planetary deferents in the Almagest. All of his calculations were done with respect to a normalized deferent, considering a single case at a time. This is not to say that he believed the planets were all equidistant, but he had no basis on which to measure distances, except for the Moon.
Ptolemy's Handy Tables (Ancient Greek: πρόχειροι κανόνες, romanized: Procheiroi kanones) is a collection of astronomical tables that second century astronomer Ptolemy created after finishing the Almagest. The Handy Tables elaborated the astronomical tables of the Almagest and included usage instructions, but left out the ...