Volume 2

A history of mathematical notations / by Florian Cajori.

  • Cajori, Florian, 1859-1930.
Date:
[1928-1929]
Catalogue details

Licence: In copyright

Credit: A history of mathematical notations / by Florian Cajori. Source: Wellcome Collection.

    34/396 (page 10)
    Ceulen’s Number, or that in Art. 64.38. mav be Examin’d with all desirable Ease and Dispatch.” Then he writes “d = c-c7r” and “C = dX7T.” This was not the first appearance of the letter 7r in Jones’s book of 1706. But in earlier passages the meanings were different. On page 241 it was used in lettering a geometric figure where it represented a point. On page 243 one finds “Periphery (7r),” as previously found in Wallis. Nor did the appearance of t = 3.14159 .... on the stage attract general attention. Many mathematicians continued in the old way. In 1721 P. Varignon1 wrote the ratio S.7r, using for ratio the dot of Oughtred. 397. Eider’s use of 7r.—In 1734 Euler2 employed p instead of 7r and g instead of . In a letter of April 16, 1738, from Stirling to Euler, as well as in Euler’s reply, the letter p is used.3 But in 1736 he4 desig¬ nated that ratio by the sign 1: ir and thus either consciously adopted the notation of Jones or independently fell upon it. Euler says: “Si enim est m — J terminus respondens inuenitur - denotante 1:7r ratio- nem diametri ad peripheriam.” But the letter is not restricted to this use in his Mechanica, and the definition of 7r is repeated when it is taken for 3.1415.He represented 3.1415 . . . . again by 7r in 17375 (in a paper printed in 1744), in 1743,6 in 1746,7 and in 1748.8 Euler and Goldbach used 7r = 3.1415 . . . . repeatedly in their corre¬ spondence in 1739. Johann Bernoulli used in 1739, in his correspond¬ ence with Euler, the letter c (circumferentia), but in a letter of 1740 1 Pierre Varignon, Histoire de VAcademic r. des sciences, annee 1721 (Paris, 1723), Memoires, p. 48. 2 Euler in “De summis serierum reciprocarum,” Comm. Acad. Petr., Vol. VII (1734-35), p. 123 ff. See von Braunmtihl, Vorlesungen uber Geschichte der Trigo¬ nometric, Vol. II (Leipzig, 1903), p. 110. 3 Charles Tweedie’s James Stirling (Oxford, 1922), p. 179, 180, 185, 188. 4 L. Euler, Mechanica sive motus scientia analytice exposita, Vol. I (Petrograd, 1736), p. 119, 123; Vol. II, p. 70, 80. 5 L. Euler in Comm. Acad. Petr, ad annum 1737, IX (1744), p. 165. See A. von Braunmuhl, op. cit., Vol. II, p. 110. Euler says: “Posito ir pro peripheria circuli, cuius diameter est 1, ... . ” 6 L. Euler in Miscellanea Berolinensia, Vol. VII (1743), p. 10, 91, 136. 7 L. Euler in Histoire de Vacademie r. des sciences, et de belles lettres, annee 1745 (Berlin, 1746), p. 44. 8 L. Euler, op. cit., annee 1748 (Berlin, 1750), p. 84.