SEXAGESIMALS

, or Sexagesimal Fractions, are fractions whose denominators proceed in a sexagecuple ratio; that is, a prime, or the first minute = 1/60, a second = 1/3600, a third = 1/216000.

Anciently there were no other than Sexagesimals used in astronomical operations, for which reason they are sometimes called astronomical fractions, and they are still retained in many cases, as in the divisions of time and of a circle; but decimal arithmetic is now much | used in the calculations. Sexagesimals were probably first used for the divisions of a circle, 360, or 6 times 60 making up the whole circumference, on account that 360 days made up the year of the Ancients, in which time the sun was supposed to complete his course in the circle of the ecliptic.

In these fractions, the denominator being always 60, or a multiple of it, it is usually omitted, and the numerator only written down: thus, 3° 45′ 24″ 40‴ &c, is to be read, 3 degrees, 45 minutes, 24 seconds, 40 thirds, &c.