Ptolemy Claudius Ptolemaeus

PTOLEMY (CLAUDIUS PTOLEMAEUS), of Alexandria, the celebrated mathematician, astronomer and geographer, was, ac cording to the Byzantine Theodorus Meliteniota (c. 1361), born at Ptolemais Hermii, a Grecian city of the Thebaid. All that is known for certain about him is that he observed at Alexandria during the reigns of Hadrian and Antoninus Pius, between the years A.D. I27 and 141 or 151. Olympiodorus, a philosopher of the Neoplatonic school, who lived in the reign of the emperor Justinian, relates in his scholia on the Phaedo of Plato that Ptolemy devoted his life to astronomy and lived for 4o years in the so-called Hrepa ro0 Ka.vcoi3ov, probably elevated terraces of the temple of Serapis at Canopus, near Alexandria, where they raised pillars with the results of his astronomical discoveries en graved upon them. Arabian traditions say that Ptolemy lived to the age of 78 years, and give some details about his personal appearance, to which too much weight must not be attached.

His Work as a Mathematician.

Ptolemy's work as a geographer is discussed below, and an account of the discoveries in astronomy of Hipparchus and Ptolemy is given in the article ASTRONOMY : History. Their contributions to pure mathematics, however, require to be noticed here. Of these the chief is the foundation of trigonometry, plane and spherical, including the formation of a table of chords, which served the same purpose as our table of sines. This branch of mathematics was created by Hipparchus for the use of astronomers, and its exposition was given by Ptolemy in a form so perfect that for 1,400 years it was not surpassed. The doctrine as to the motion of the heavenly bodies known as the Ptolemaic system, was paramount for about the same period of time. The astronomical and trigonometrical systems are contained in the great work of Ptolemy, or The Mathematical Collection. Later it came to be known as the or alternatively as '0 ,t&yas aorpovoyos, the Great Astronomer, to distinguish it from another collection called '0 or Iturpovo,uoN.tcvos, the

Little Astronomer, comprising some works of Autolycus, Euclid, Aristarchus, Theodosius, Hypsicles and Menelaus. To designate the great work of Ptolemy, the Arabs used the superlative 12E-y1,0771 from which, the article al being prefixed, the hybrid name Almagest, by which it has ever since been known, is derived.

We proceed now to consider the trigonometrical work of Hip parchus and Ptolemy. In the ninth and tenth chapters of the first book of the Almagest Ptolemy shows how to form a table of chords. He supposes the circumference divided into 36o equal parts or degrees). Further, he divides the diameter into 120 equal parts. Then, for the subdivision both of the degrees and of the parts of the diameter, he uses sexagesimal fractions or, as we say, "minutes," "seconds," etc. It must not be supposed, however, that these sexagesimal divisions are due to Ptolemy; Babylonian in origin, they must already have been used by Hip 'The Ptolemies were not in antiquity distinguished by the ordinal numbers affixed to their names by modern scholars and represented according to the usual convention by Roman figures. This is merely done for our convenience. In the case of the later Ptolemies different systems of notation prevail according as the problematic Eupator and Philopator Neos are reckoned in or not.

parchus. Nor did the formation of the table of chords originate with Ptolemy; indeed, we know that Hipparchus wrote a treatise in 12 books on straight lines (chords) in a circle, while Menelaus (c. A.D. 00) wrote another in six books. Ptolemy shows how the calculation of chords is based on a few simple theorems in geometry (including the well-known "Ptolemy's theorem" relating to a quadrilateral inscribed in a circle), and these he gives in a form which for conciseness and elegance could not be surpassed; Hipparchus' method was no doubt the same, though his exposition would run to greater length.