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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": [30] 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 ...
Ptolemy was the name of several pharaohs of the Ptolemaic dynasty who ruled Hellenistic Egypt for nearly 300 years, from 305 BC to 30 BC. The Greco-Egyptian pharaonic dynasty of Macedonian origin was established by Ptolemy I Soter (303–282 BC), and the male dynastic successors were all also named Ptolemy. Dynasty members who ruled Egypt include:
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 ...
In Ptolemy's era the boundaries of the zodiac signs were close to those of the visible constellations whose names they bear, but Ptolemy demonstrates the theoretical distinction between the two frames of reference in describing the starting point of the zodiac as fixed, not to the stars, but to the mathematically calculated vernal equinox. [57]
The angular rate at which the epicycle traveled was not constant unless he measured it from another point which is now called the equant (Ptolemy did not give it a name). It was the angular rate at which the deferent moved around the point midway between the equant and the Earth (the eccentric) that was constant; the epicycle center swept out ...
Unfortunately, the system that was available in Ptolemy's time did not quite match observations, even though it was an improvement over Hipparchus' system. Most noticeably the size of a planet's retrograde loop (especially that of Mars) would be smaller, or sometimes larger, than expected, resulting in positional errors of as much as 30 degrees.
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 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.