A history of Greek mathematics - Wilbourhall.org

214 SUCCESSORS OF THE GREAT GEOMETERS
work in which we find the division of the ecliptic circle
into
360 parts ' ' or degrees. The author says, after the preliminarypropositions,
'The circle of the zodiac having been divided into 360 equal
circumferences (arcs), let each of the latter be called a degree
in space (fiolpa tottiktj, 'local' or 'spatial part'). And similarly,
supposing that the time in which the zodiac circle
returns to any position it has left is divided into 360 equal
times, let each of these be called a degree in time (/ioipa
XpOVLKTj)'
From the word KaXeiaOco (' let it be called ') we may perhaps
infer that the terms were new in Greece. This brings us to
the question of the origin of the division (1) of the circle of
the zodiac, (2) of the circle in general, into 360 parts. On this
question innumerable suggestions have beerf made. With
reference to (1) it was suggested as long ago as 1788 (by Formaleoni)
that the division was meant to correspond to the
number of days in the year. Another suggestion is that it
would early be discovered that, in the case of any circle the
inscribed hexagon dividing the circumference into six parts
has each of its sides equal to the radius, and that this would
naturally lead to the circle being regularly divided into six
parts ; after this, the very ancient sexagesimal system would
naturally come into operation and each of the parts would be
divided into 60 subdivisions, giving 360 of these for the whole
circle. Again, there is an explanation which is not even
geometrical, namely that in the Babylonian numeral system,
which combined the use of 6 and 10 as bases, the numbers 6,
60, 360, 3600 were fundamental round numbers, and these
numbers were transferred from arithmetic to the heavens.
The obvious objection to the first of these explanations
(referring the 360 to the number of days in
the solar year) is
that the Babylonians were well acquainted, as far back as the
monuments go, with 365-2 as the number of days in the year.
A variant of the hexagon- theory is the suggestion that a
natural angle to be discovered, and to serve as a measure of
others, is the angle of an equilateral triangle, found by drawing
a star # like a six-spoked wheel without any circle. If
the base of a sundial was so divided into six angles, it would be