Leonardo, making use of fractions of the sexagesimal scale, gives X = I° 221 7 42" i 33 iv 4v 40 vi, after having demonstrated, by a discussion founded on the 10th book of Euclid, that a solution by square roots is impossible.
The Babylonian system was sexagesimal, thus (18) --
This whole class seems to cling to sites of Phoenician trade, and to keep clear of Greece and the north -- perhaps a Phoenician form of the 129 system, avoiding the sexagesimal multiples.
- The Egyptian notation was purely denary, the only separate signs being those for 1, io, too, &c. The ordinary notation of the Babylonians was denary, but they also used a sexagesimal scale, i.e.
The Babylonians adopted 60 for both these purposes, thus giving us the sexagesimal division of angles and of time.
The Greeks originally used unit-fractions, like the Egyptians; later they introduced the sexagesimal fractions of the Babylonians, extending the system to four or more successive subdivisions of the unit representing a degree.
In the sexagesimal system the numerators of the successive fractions (the denominators of which were the successive powers of 60) were followed by', ", "', ", the denominator not being written.
There was, however, no development in the direction of decimals in the modern sense, and the Arabs, by whom the Hindu notation of integers was brought to Europe, mainly used the sexagesimal division in the ' " "' notation.
Even where the decimal notation would seem to arise naturally, as in the case of approximate extraction of a square root, the portion which might have been expressed as a decimal was converted into sexagesimal fractions.
The sexagesimal system of division was originally used by the ancient Babylonian astronomers, was adopted by Ptolemy; and the sixtieth part of a degree, and its further subdivision into sixty parts, was called in Latin pars minutae prim'ae, and pars minutae secundae respectively, hence the English "minute" and "second."