A History of Elementary Mathematics by Florian Cajori

By Florian Cajori

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The same story of death in the sea is ~~ "" was owing to told of the Pythagorean Hip* pasus for divulging the knowledge of the dodecaedron. ) of this theorem embraced three to the base. different cases: that of equilateral, that of isosceles, and, finally, that of scalene triangles. , 28, 29. They could also construct a polygon equal in area to a given polygon and similar to another. In a general way it may be said that the Pythago rean plane geometry, like the Egyptian, was much concerned with areas.

From them rules, it but this would be easy, by induction, to obtain general not done. When we remember that only one is hundred years ago it was the practice of many English arith metical writers to postpone the discussion of fractions to the end of their books, it is surprising to find that this hand-book of 4000 years ago begins with exercises in fractions, and pays but little attention to whole numbers. G-ow probably is right in his conjecture that Ahmes wrote for the 4lite mathematicians of his day.

Par PAUL TAKKEBY, Paris, 1887, p. 92 ; Le ; A HISTOBY OF MATHEMATICS 48 The Eudernian Summary ascribes to Thales the invention of the theorems on the equality of vertical angles, the equality of the base angles in isosceles triangles, the bisection of the by any diameter, and the congruence of two triangles having a side and the two adjacent angles equal respectively. circle Famous his application of the last theorem to the deter is the distances of ships from the shore. The all angles inscribed in a semicircle are right attributed by some ancients to Thales, by others to mination of theorem that angles is Thales thus seems to have originated the geome Pythagoras.

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