# Read e-book online A History of Algebra: From al-Khwārizmī to Emmy Noether PDF

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

ISBN-10: 3642515991

ISBN-13: 9783642515996

ISBN-10: 3642516017

ISBN-13: 9783642516016

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Extra info for A History of Algebra: From al-Khwārizmī to Emmy Noether

Sample text

Omar knows very weIl that earlier authors sometimes equated geometrical magnitudes with numbers. He avoids this logical inconsistency by a trick, introdueing a unit of length. He writes: Every time we shall say in this book "a number is equal to a rectangle", we shall understand by the "number" a rectangle of which one side is unity, and the other a line equal in measure to the given number, in such a way that each of the parts by which it is measured is equal to the side we have taken as unity.

Descartes formulated Tabit's rule explicitely and presented a third example: 9363584=2 7 x 191 x 383 9437056=2 7 x 73727 (Rene Descartes, Oeuvres II, p. 93-94 and p. 148). Now the question arises: How did Tabit find his rule? The weIl known pair 220 and 284 has a factorization of the form in which p, q, and rare primes. So let us see whether we can find a pair such that M is the sum of the proper divisors of N and conversely. I suppose that Tabit knew that the sum of all divisors of N (including N itself) is (1+2+ ...

As compared with Fibonacci, Luca has a simpler algebraic notation. He denotes the square root by R or R2, the cube root by R3, the fourth power root by R4 or RR (Radix Radix). The unknown in an equation is denoted by co. (cosa), its square by ce. (censo), its cube by cu. (cubo), its fourth power by ce. ce. (censo censo). If a second unknown is introduced, it is called "quantita". For addition and subtraction the signs p and mare used. Thus, RV40mR320 V V means 40 - 320. The letter V indicates that the root has to be extracted from the whole expression that follows (V= U = Universale).