# A History of Elementary Mathematics by Florian Cajori

By Florian Cajori

This scarce antiquarian ebook is a range from Kessinger Publishings Legacy Reprint sequence. as a result of its age, it could possibly comprise imperfections reminiscent of marks, notations, marginalia and wrong pages. simply because we think this paintings is culturally very important, we've made it to be had as a part of our dedication to conserving, keeping, and selling the worlds literature. Kessinger Publishing is where to discover millions of infrequent and hard-to-find books with whatever of curiosity for everybody!

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**Extra resources for A History of Elementary Mathematics**

**Example text**

See HEATH, op. , pp. 133- GREECE 35 divorced from geometry, his treatment is purely analytical. " is number to be subtracted gives a applied to differences, like (2 x to be 3) (2 x 3), the product of which he finds without resorting to geometry. 2 Identities like (a -f 6) 2 a2 -f 2 ab 5 , which are elevated = + rank of geometric theorems, with Diophantus are the simplest consequences of algebraic laws of operation. Diophantus represents the unknown quantity x by by Euclid to the exalted U v V the square of the unknown a?

1 2 Gow, p. 69. For their definitions see Gqw, 2 p. 70, or CAJOEI, op. The Pythagcit,, p. 68. A HISTOEY OF MATHEMATICS 30 oreans paid much attention to the subject of proportion. Tha,, quantities a, b, c, d, were said to be in arithmetical proportion, when a b=cd; in geometrical proportion, when a b = c d : : ; in har/nojiic proportion, when a "proportion, : -| when a (a -f &) &:& c=a:c; = 2 ab/(a + b):b. in musical lamblichus says that the last was introduced from Babylon. The 7th, 8th, and 9th books of Euclid's Elements are on the science of number, but the 2d and 10th, though professedly geometrical and treating of magnitudes, are applicable to numbers.

Historical importance of this translation lies in the extended use made of it later in Western Europe. The Roman laws of inheritance gave rise to numerous arith metical examples. The following is of interest in itself, and also because its occurrence elsewhere at a later period assists us in tracing the source of arithmetical knowledge in Western with child, dying man wills, that if his wife, being Europe : A shall receive f, and she -| of his gives birth to a son, the son is if a but estate born, the daughter shall receive daughter ; |, a and happens that twins are born, a boy as to so be divided shall the estate satisfy the and the wife f girl.