By James Gow
James Gow's a quick historical past of Greek arithmetic (1884) supplied the 1st complete account of the topic to be had in English, and it this day is still a transparent and thorough consultant to early mathematics and geometry. starting with the origins of the numerical approach and continuing in the course of the theorems of Pythagoras, Euclid, Archimedes etc, the quick heritage bargains in-depth research and valuable translations of person texts in addition to a huge ancient review of the improvement of arithmetic. elements I and II crisis Greek mathematics, together with the beginning of alphabetic numerals and the nomenclature for operations; half III constitutes a whole heritage of Greek geometry, from its earliest precursors in Egypt and Babylon via to the strategies of the Ionic, Sophistic, and educational faculties and their fans. specific awareness is given to Pythagorus, Euclid, Archimedes, and Ptolemy, yet a number of lesser-known thinkers obtain deserved consciousness besides.
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Additional resources for A Short History of Greek Mathematics
The facts to be now stated are in any case of great importance, since they furnish the only compact mass of evidence concerning the difficulties which beset ancient arithmetic and the way in which they were surmounted. 16 EGYPTIAN ARITHMETIC. 12. Quite recently a hieratic papyrus, included in the Rhind collection of the British Museum, has been deciphered and found to be a mathematical handbook, containing problems in arithmetic and geometry1. The latter will be treated on a later page. C. but it was founded on and follows, not always correctly, an older work.
Different positions of the left hand on the left breast and hip gave the numbers from 10,000 to 90,000: the same motions with the right hand gave the hundred thousands and the hands folded together represented a million. 20. The finger-symbolism here described was in use, in practically the same form, in Greece and Italy and throughout the East certainly from the beginning of our era2, but there is unfortunately no evidence as to where or when it was invented. By far the oldest passage in which any reference to it may be supposed to occur is Aristophanes, Vespae, 11.
31, 32, and 41. ' In these examples a pair of legs walking, so to say, with or against the stream of the writing, are used as mathematical symbols of addition and subtraction. ' Cantor, pp. 32, 33. Eisenlohr, pp. 22—26. EGYPTIAN ARITHMETIC. 19 See -=- = 19: divides 19 by 8 and multiplies the quotient ( 2 | ^) by 7 and so finds the desired number 16J £, but he has also various other methods of treating the two sides. For instance, in no. e. of divisions according to different rates of profit. The examples are ' Divide 100 loaves so that 50 go to 6 and 50 to 4 persons,' and ' divide 100 loaves among 5 persons, so that the first 3 get 7 times as much as the other 2.