By Prof. Dr. Bartel Leenert van der Waerden (auth.)

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Luckey: Die Rechenkunst des Gamsld b. Mas'üd al-Kasl (Wiesbaden 1951). G. Horner (1819). See F. Cajori: A History of Mathematics, p. 271. In 1240, the republic of Pisa awarded the "serious and learned Master Leonardo Bigolli" a yearly salary of 20 pounds silver "in addition to the usual From Leonardo da Pisa 10 Luca Pacioli 35 allowances, in recognition of his usefulness to the city and its citizens through his teaching and devoted services". We shall now discuss the extant works of Leonardo. 1.

In the case N = 2 this is just the wellknown Greek problem of "doubling the cube". Hippokrates of Chios had proved that this problem can be reduced to the problem of finding two mean proportionals x and y between two given line segments a and b. Omar Khayyam proceeds just so. He solves the auxiliary problem (3) with a = e and b = Ne, and he proves that the first intermediate x is the side of the required cube. All this is well-known from Greek texts. According to Eutokios, the solution of (3) by means of the intersection of two parabolae is due to Menaichmos.

353-365, Euler presents four more examples, aH of the form apq and ar. For more information about amicable numbers see the survey of Edward B. Escott in Scripta Mathematica 12, p. 61-72 (1946). 24 Chapter 1. Three Muslimic Authors Part C Omar Khayyam The Persian poet, philosoph er, mathematician, and astronomer Omar ben Ibrahim al-Hayyam, usually called Omar Khayyam, lived in the second half of the eleventh century. His farne in the western world is mainly based on the very free translation of his nearly 600 short poems of four lines each ( Ruba'iyat) by E.