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- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 authorLink "Carl Benjamin Boyer".
- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 chapter "Greek Trigonometry and Mensuration".
- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 first "Carl Benjamin".
- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 isCitedBy History_of_trigonometry.
- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 last "Boyer".
- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 pages "164–166".
- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 quote "The theorem of Menelaus played a fundamental role in spherical trigonometry and astronomy, but by far the most influential and significant trigonometric work of all antiquity was composed by Ptolemy of Alexandria about half a century after Menelaus. [...] Of the life of the author we are as little informed as we are of that of the author of the Elements. We do not know when or where Euclid and Ptolemy were born. We know that Ptolemy made observations at Alexandria from AD. 127 to 151 and, therefore, assume that he was born at the end of the 1st century. Suidas, a writer who lived in the 10th century, reported that Ptolemy was alive under Marcus Aurelius .Ptolemy's Almagest is presumed to be heavily indebted for its methods to the Chords in a Circle of Hipparchus, but the extent of the indebtedness cannot be reliably assessed. It is clear that in astronomy Ptolemy made use of the catalog of star positions bequeathed by Hipparchus, but whether or not Ptolemy's trigonometric tables were derived in large part from his distinguished predecessor cannot be determined. [...] Central to the calculation of Ptolemy's chords was a geometric proposition still known as "Ptolemy's theorem": [...] that is, the sum of the products of the opposite sides of a cyclic quadrilateral is equal to the product of the diagonals. [...] A special case of Ptolemy's theorem had appeared in Euclid's Data : [...] Ptolemy's theorem, therefore, leads to the result sin = sin α cos β − cos α sin Β. Similar reasoning leads to the formula [...] These four sum-and-difference formulas consequently are often known today as Ptolemy's formulas.It was the formula for sine of the difference – or, more accurately, chord of the difference – that Ptolemy found especially useful in building up his tables. Another formula that served him effectively was the equivalent of our half-angle formula.".
- 829e6a1625187b83fe8dfda1f628c01aeb4c61b0b8b470fc8d4d03632af0f671 year "1991".