Hipparchus, Menelaus, Ptolemy And Greek Trigonometry

1350 words - 5 pages

Hipparchus of Nicaea (c. 190 – c. 120 B.C.) was a Greek astronomer, geographer, and mathematician of the Hellenistic period. Many credit him as the founder of trigonometry. Hipparchus was born in Nicaea, Bithynia (now Iznik, Turkey) and most likely died on the island of Rhodes. He flourished during 162 to 127 B.C. as a working astronomer and is considered by many to be the greatest ancient astronomical observer and, by some, the greatest overall astronomer of antiquity. Utilizing the observations and mathematical techniques accumulated over the centuries by the Babylonians and other Mesopotamians, he was the first person whose quantitative and accurate models for the motion of the Sun and Moon still survive to this day. He developed trigonometry, constructed trigonometric tables, and solved several problems of spherical trigonometry. He may have been the first to develop a reliable method to predict solar eclipses, compiled the first comprehensive star catalog of the western world, and possibly invented the astrolabe and armillary sphere. He is most famous for his incidental discovery and measurement of Earth’s procession (Wikipedia). It is also believed that Hipparchus introduced Greece to the concept of the division of a circle into 360 degrees and Theon of Alexandria credits Hipparchus with a twelve-book treatise on chords. However, this work has been lost to history. It is believed Ptolemy’s famous table of chords was based on a Hipparchus’ treatise (History of Mathematics 175-177).

Menelaus of Alexandris (c. 70 – 140 A.D) was a Greek mathematician and astronomer. Little is known of Menelaus’s life. After spending his youth in Alexandria, he most likely moved to Rome. Both Pappus of Alexandria and Proclus referred to him as Menelaus of Alexandria. Ptolemy, in his work Almagest, mentions two astronomical observations made by Menelaus of Rome. These observations were occultations of the stars Spica and Beta Scorpii by the moon, a few nights apart. Ptolemy used these observations to confirm procession of the equinoxes, which, as mentioned above, was discovered by Hipparchus in the 2nd century B.C. The only work of Menelaus that has survived to the present day is an Arabic translation of his book Sphaerica. This work deals with the geometry of a sphere and its application to astronomical measurements and observations and introduces the concept of a spherical triangle (Wikipedia). In this book, Menelaus deduced and proved the spherical case of a proposition know in plane geometry as Menelaus’ theorem. Menelaus assumes that the plane case of Menelaus’ theorem is well known and uses it to prove the spherical case. Many spherical trigonometry concepts can be deduced from this theorem (History of Mathematics 175-177).
Claudius Ptolemy (c. 90 – c. 168 A.D.) was a Greco-Roman writer of Alexandria, known as a mathematician, astronomer, geographer, and astrologer. Few reliable details of his life are known but...

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