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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.
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A 16th-century engraving of Ptolemy. Ptolemy's Optics is a 2nd-century book on geometrical optics, dealing with reflection, refraction, and colour. The book was most likely written late in Ptolemy's life, after the Almagest, during the 160s. [1] The work is of great importance in the early history of optics. The Greek text has been lost completely.
The works of Ptolemy (astronomy) and Galen (medicine) were found not always to match everyday observations. Work by Vesalius on human cadavers found problems with the Galenic view of anatomy. [187] The discovery of Cristallo contributed to the advancement of science in the period as well with its appearance out of Venice around 1450.
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]
This planetary concept allowed Ptolemy to keep the theory of uniform circular motion alive by stating that the path of heavenly bodies was uniform around one point and circular around another point. Ptolemy does not have a word for the equant – he used expressions such as "the eccentre producing the mean motion". [1]
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.
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]