Hipparchus

Topics: Trigonometry, Trigonometric functions, Mathematics Pages: 4 (1226 words) Published: June 20, 2013
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Hipparchus
"Even if he did not invent it, Hipparchus is the first person of whose systematic use of trigonometry we have documentary evidence." (Heath 257) Some historians go as far as to say that he invented trigonometry. Not much is known about the life of Hipp archus. It is believed that he was born at Nicaea in Bithynia. (Sarton 285) The town of Nicaea is now called Iznik and is situated in northwestern Turkey. Founded in the 4th century BC, Nicaea lies on the eastern shore of Lake Iznik. He is one of the g reatest astronomers of all time. We know from Ptolemy's references that he made astronomical observations from 161 to 127 BC. (Sarton 285) Unfortunately, nearly all of his works are lost, and all that remains is his commentary on the Phainomena of Eudoxos of Cnidos, and a commentary on an astronomical poem by Aratos of Soloi. (Sarton 285) Most of what we know about Hipparchus comes from Ptolemy's Almagest and a few remarks by other writers. The sole trigonometric function used by the ancient Greeks is the chord, which is closely related to the sine function (Toomer 7). What is known from Ptolemy is that Hipparchus produced a table of chords, which were an essential tool in the early development of trigonometry. According to Theon of Alexandria, who worked in Alexandria as a teacher of mathematics and astronomy, Hipparchus wrote a treatise in twelve books on chords in a circle, which has been lost (Sarton 286) . It is believed that this treatise contained some general trigonometric theory together with some tables. Hipparchus is believed to be the first person to determine exactly the times of the rising and setting of the zodiacal signs. Pappus of Alexandria, who was a teacher of mathema tics in the fourth century, observed that "Hipparchus in his book on the rising of the twelve signs of the zodiac shows by means of numerical calculations that equal arcs of the semicircle beginning with Cancer which set...