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Additional resources for A History of Elementary Mathematics
90), Bretschneider, Tannery, Loria, are inclined to deny Thales a knowledge of similitude of figures. See Die Geometrie und die Geometer vor Euklides. 1889, p. 14. , p. Historischer Versuch, von C. A. BEETSCHXEIBER, Leipzig, 1870, p. 46 Geometrie Grecque . . 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.
Is down IffiSETingenuity has been expended in conjectures as to its nature. Bretschneider's sur mise, that the Pythagorean proof was substantially the same to "as: as the one of Bhaskara (given elsewhere), has been well received by Hankel, Allman, Grow, Loria. 1 Cantor thinks it not improbable that the early proof involved the consideration of special cases, of which the isosceles right triangle, perhaps the first, may have been proved in the manner indi by the cated The 2 adjoining figure. four lower triangles together equal the four upper.
TV], what is the remainder? : Come, you can tell. e. ' take care of your property. " what does it make ? ' the Romans unconsciously hit upon a fine in their concrete treatment of fractions. idea pedagogical fractions in connection with money, learned Roman boys Doubtless weights, and measures. meant more " broken We conjecture than what was that to them fractions conveyed by the definition, number," given in old English arithmetics. 524), who a work, is to be mentioned in this connection as the author of De Institutione Arithmetica, essentially a translation of the One Roman of the last writers was Boethius (died arithmetic of I^icomachus, although some of the most beau tiful arithmetical results in the original are omitted by The Boethius.