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

**Example text**

P. 66. Ahmes papyrus Sylvester (then in Baltimore) material for a paper " the Theory of Yulgar Fractions," pp. 32 and 388. suggested to a Point in On Am. , 1880. EGYPT cation in arithmetics of the 23 century and fifteenth later, namely, that of aliquot parts, used largely in Practice. In the second of the above examples aliquot parts are taken of -fa. This process seen again in Ahmes's calculations to verify is the identities in the table of unit-fractions. A limes then proceeds to eleven problems leading to simple equations with one unknown quantity.

According to Philolaus, 5 is the cause and light, 8 of love and of colour, 6 of cold, 7 of mind, health, Even Plato and Aristotle refer the virtues to While these speculations in themselves were fan and barren, lines of fruitful mathematical inquiry were 1 friendship. numbers. tastic suggested by them. numbers into odd and even, and observed that the sum of the odd numbers from 1 to 2 n -f- 1 was always a perfect square. Of no particular value were their classifications of numbers into heteromecic, trian The Pythagoreans classified gular, perfect, excessive, defective, amicable.

Evidently this subject was one of Simultaneous changes in both numerator and denominator were usually avoided. Fractions are found among theBabvlonians. ISFot only had they sexagesimal divisions of great difficulty. weijipts *fr3erions and measures, but also sexagesimal fractions. pt the denominators constant, but equal to 12. The Egyptians and Greeks, on the other hand, kept the numerators constant stood, , ancLdgajt with variable denominators. fractions of a special class, namely unit-fractions, Em- having unity for their numerators.