A History of Mathematical Notations (Dover Books on Mathematics)

A History of Mathematical Notations (Dover Books on Mathematics)

Florian Cajori

Language: English

Pages: 820

ISBN: 0486677664

Format: PDF / Kindle (mobi) / ePub


This classic study notes the first appearance of a mathematical symbol and its origin, the competition it encountered, its spread among writers in different countries, its rise to popularity, its eventual decline or ultimate survival. The author's coverage of obsolete notations — and what we can learn from them — is as comprehensive as those which have survived and still enjoy favor. Originally published in 1929 in a two-volume edition, this monumental work is presented here in one volume.

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cubo, censo de censo, primero relato, censo y cubo, segundo relato, censo de censo de censo, cubo de cubo. The second plan was not to use a symbol for the unknown quantity itself, but to limit one’s self in some way to simply indicating by a numeral the power of the unknown quantity. As long as powers of only one unknown quantity appeared in an equation, the writing of the index of its power was sufficient. In marking the first, second, third, etc., powers, only the numerals for “one,” “two,”

second “measure” or “part,” but had no contracted sign for them. Later still al-Qalasâdî used a sign for unknown (§ 124). An early European sign is found in Regiomontanus (§ 126), later European signs occur in Pacioli (§§ 134, 136), in Christoff Rudolff (§§ 148, 149, 151),1216 in Michael Stifel who used more than one notation (§§ 151, 152), in Simon Stevin (§ 162), in L. Schoner (§ 322), in F. Vieta (§§ 176–78), and in other writers (§§ 117, 138, 140, 148, 164, 173, 175, 176, 190, 198). Luca

W. Chauvenet, Faà de Bruno, P. Appell, C. Jordan, J. Bertrand, W. Fiedler, A. Clebsch. Of course, I am not prepared to say that these writers never used n! or ; I claim only that they usually avoided those symbols. These considerations are a part of the general question of the desirability of the use of symbols in mathematics to the extent advocated by the school of G. Peano in Italy and of A. N. Whitehead and B. Russell in England. The feeling against such a “scab of symbols” seems to be strong

sin.sin. x, x for log. log. log. x. Just as we write , we may write similarly sin.−1 x = arc (sin. = x), log.−1 x. = cx. Some years later Herschel explained that in 1813 he used fn(x), f−n(x), sin.−1x, etc., “as he then supposed for the first time. The work of a German Analyst, Burmann, has, however, within these few months come to his knowledge, in which the same is explained at a considerably earlier date. He [Burmann], however, does not seem to have noticed the convenience of applying this

perhaps to suggest improvements of its own. The experience of history suggests that at any one congress of representative men only such fundamental symbols should be adopted as seem imperative for rapid progress, while the adoption of symbols concerning which there exists doubt should be discussed again at future congresses. Another advantage of this procedure is that it takes cognizance of a disinclination of mathematicians as a class to master the meaning of a symbol and use it, unless its

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