SEXAGESIMAL FRACTIONS Nature and Origin.-Fractions written on the scale of 6o (Latin, sexaginta) are called sexagesimal fractions (from the Latin sexagesimus, both). Since the Babylonians wrote their numbers on a combined scale of io and 6o, in which the character for I represented any power of 6o, they naturally used 6o as a radix in certain systems of measure, as in the case of 6o maneh making a talent. The statement that 6o seconds make a minute was probably looked upon quite as our statement that 12 inches make a foot, the idea of sexagesimal fractions, as we have it, not being present. The Greek astronomers no doubt received the scale of 6o from the Babylonians or their successors, and it seems to have been they who developed sexagesimal fractions on a large scale. When they decided to take 120 units as the length of the diameter of their standard circle (probably because its numerous factors, 2, 3, 4, 5, 6, io, 12, 15, 20, 30, 40 and 6o made the rep resentation of fractions easy), the circle (using the old value 3 for 7r) became 36o units. To each of these units they gave the name yoipa (mof'ra), which became (either through the Latin de+gradus, step, or the Arabic daraja, step, scale, ladder) our "degree." They then called of a degree a first part (7rp& ra E 17KOQTb,, pro'ta hexekostd; Latin, pars minuta prima, first small part), whence our "minute"; and a second part (8EvTEpa deu'tera hexekosta; Latin, pars minuta secunda), whence our "second," and so on. Since these fractions were used in astronomy, they were called "astronomical fractions" in the middle ages. They were also known as "physical fractions," and so we find Gemma Frisius (c. 1540) writing De Fractionibus .4stronomicis, sine de minutiis Pbysieis, to distinguish them from the fractiones vulgares. He wrote : S. g. m. 2. 3. 4.