By Florian Cajori
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Is to fre be Doubtless because the decimal division of weights and measures seemed unnatural. In everyday affairs the division of units into 2, 3, 4, 6 equal parts is the commonest, and duodecimal fractions In duodecimals the give easier expressions for these parts. in decimals these of the whole above parts are -fa, T%, -f% ^ 5 parts are ^ 31 21 -|, 1-^ ^, ^. ; Unlike the Greeks, the Eomans dealt The Eoman as, originally a copper coin weighing one pound, was divided into 12 uncice. The abstract fraction was expressed concretely by deunx (= de with concrete fractions.
By . , the system may be sufficiently extended to enable one to count the very Assuming 10,000 grains of sand to fill the space of a poppy-seed, he finds a number which would exceed the number sands. 1 2 CAKTOE, Vol. , p. 132. What the Archimedean and, in general, the Greek method of root- extraction really was, has "been a favourite subject of conjecture. See for example, H. WEISSENBOEN'S Berechnung des JKreisumfanges bei Archi medes und Leonardo Pisano, Berlin, 1894. ject, For bibliography of this sub see S.
Such as expert Greek mathematicians of classical time may have used. 1 some While among the Sophists computation received it was pronounced a vulgar and childish attention, by Plato, who cared only for the philosophy of arithmetic. Greek writers did not confine themselves to unit-fractions as Unit-fractions were designated closely as did the Egyptians. art by simply writing the denominator with a double 1 accent. specimens of such multiplications see CANTOR, JBeitrage z. JTulturl. HANKEL, p. 56 Gow, p.
A History of Elementary Mathematics by Florian Cajori