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A Short History of Greek Mathematics by James Gow

By James Gow

James Gow's a brief background of Greek arithmetic (1884) supplied the 1st complete account of the topic to be had in English, and it this present day is still a transparent and thorough advisor to early mathematics and geometry. starting with the origins of the numerical process and continuing during the theorems of Pythagoras, Euclid, Archimedes and so on, the fast heritage bargains in-depth research and worthwhile translations of person texts in addition to a extensive historic evaluate of the advance of arithmetic. elements I and II quandary Greek mathematics, together with the foundation of alphabetic numerals and the nomenclature for operations; half III constitutes an entire historical past of Greek geometry, from its earliest precursors in Egypt and Babylon via to the options of the Ionic, Sophistic, and educational faculties and their fans. specific realization is given to Pythagorus, Euclid, Archimedes, and Ptolemy, yet a bunch of lesser-known thinkers obtain deserved recognition in addition.

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After this, the writer passes to geometry, but he recurs at the end of the book to these algebraical problems and gives about twenty more examples of the same kind. Most of them are simple, but in at least three Cantor sees evidence that Ahmes was acquainted with the theory of arithmetical and geometrical series. The solution which he gives of the second problem above quoted is as follows: 'the difference is 5J : 23, 17J, 12, 6J, 1. ' The series first given amounts only to 60, and each of its terms must be multiplied by If, in order to produce8 the requisite sum 100.

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. ' After this, the writer passes to geometry, but he recurs at the end of the book to these algebraical problems and gives about twenty more examples of the same kind.

He begins with a series of exercises in reducing fractions, with 2 for numerator, to submultiples. ' Divide 2 by 5' or ' express 2 divided by 7 ' etc. is his mode of stating the proposition and he gives immediately a table of answers, for all fractions 2 of the form ^ =• up to $$. He does not state, however, why he confines himself to 2 as a numerator or how he obtains, in each case, the series of submultiples which he selects. It is possible that numerators higher than 2 were subdivided2, but the second question is the more interesting and has been very carefully discussed8.

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