Introduction to Arithmetic

So far as the origin of the signs of the zodiac and the star-symbols is concerned, Oriental and Occidental contributions are not separable, and the same is true of other scientific ideas.¹ Franz Boll, Sphaera, New Greek Texts and Investigations on the History of Constellations (Leipzig, 1903), p. 461. Astrology was born and bred in the temples of the Babylonians. The desire to forecast the future and equally the desire to establish a connection between the marvels of the beautiful heavens of the East and the events on the mundane sphere resulted in the cultivation of astrology. The devotion to the art constituted the first scientific study of the stars.² Cumont, Oriental Religions in Roman Paganism (Paris, 1909). See also his Astrology and Religion among the Greeks and Romans (New York, 1912). "The observations which the priests of the ancient Orient gathered with indefatigable patience inspired the first physical and astronomical discoveries, and just as in the period of scholasticism, the occult sciences [astrology and magic] led to the exact sciences. But these, by making evident later the vanity of the marvellous illusions by which they were nourished, destroyed the foundations of astrology and magic to which they owed their birth."³ Cumont, Oriental Religions in Roman Paganism, p. 235.

The observations of the Egyptian and, more particularly, of the Babylonian astronomers, furnished a mass of material which was used by the Greeks.⁴ Heath, Aristarchus of Samos, The Ancient Copernicus, A History of Greek Astronomy to Aristarchus (Oxford, 1913), Chapter III. Ptolemy and Hipparchus utilized the observations and the computations of the Chaldeans, mentioning specifically certain eclipses observed;⁵ Ptolemy, Mathematical Composition of Claudius Ptolemy (Almagest), ed. Halma (Paris, 1813), vol. I, Book IV, pp. 216, 244-247, 267. Theon of Smyrna discusses the different types of treatment of astronomical problems by Egyptians as compared with the Babylonians;⁶ Theon of Smyrna, p. 177, 9 ff., Hiller. Diodorus Siculus notes that both the Egyptian priests and the Chaldeans were skilled in the prediction of eclipses.⁷ Diodorus Siculus, Historical Library, I. 50; II. 30. As scientific observers of celestial phenomena the Babylonians compare favorably with the greatest of the Greek astronomers. Further than this, the evidence of their ability to use the data intelligently is indisputable. The determination of the period and mean motion of the moon, the determination of the lengths of the seasons and of the year, the determination of the period of eclipses and the periods (ephemerides tables of planetary positions) of the planets, and a host of minor deductions were derived by the scientists of the Orient from their data. The most