Calcul
Mot attesté en français depuis le XVe siècle (Nicolas Chuquet, 1484). Il provient du latin calculus, qui veut dire "caillou" et, par extension, "boule", "jeton" et "pion".
Ifrah G. 1994
Calculus.
In Latin calculus means "pebble." It is the diminutive of calx, meaning a piece of limestone.
In Latin, persons who did counting were called calculi. Teachers of calculation were known as calculones if slaves, but calculatores or numerarii if of good family (Smith vol. 2, page 166).
The Romans used calculos subducere for "to calculate."
In Late Latin calculare means "to calculate." This word is found in the works of the poet Aurelius Clemens Prudentius, who lived in Spain c. 400 (Smith vol. 2, page 166).
Calculus in English, defined as a system or method of calculating, is dated 1666 in MerriamWebster's Collegiate Dictionary, Tenth Edition.
The earliest citation in the Oxford English Dictionary, Second Edition for calculus in the sense of a method of calculating, is in 1672 in Phil. Trans. VII. 4017: "I cannot yet reduce my Observations to a calculus."
The restricted meaning of calculus, meaning differential and integral calculus, is due to Leibniz.
A use by Leibniz of the term appears in the title of a manuscript Elementa Calculi Novi pro differentiis et summis, tangentibus et quadraturis, maximis et minimis, dimensionibus linearum, superficierum, solidorum, allisque communem calculum transcendentibus [The Elements of a New Calculus for Differences and Sums, Tangents and Quadratures, maxima and minima, the measurement of lines, surfaces and solids, and other things which transcend the usual sort of calculus]. The manuscript is undated, but appears to have been compiled sometime prior to 1680 (Scott, page 157).
Newton did not originally use the term, preferring method of fluxions (Maor, p. 75). He used the term Calculus differentialis in a memorandum written in 1691 which can be found in The Collected Correspondence of Isaac Newton III page 191 [James A. Landau].
Webster's dictionary of 1828 has the following definitions for calculus, suggesting the older meaning of simply "a method of calculating" was already obsolete:
1. Stony; gritty; hard like stone; as a calculous concretion.
2. In mathematics; Differential calculus, is the arithmetic of the infinitely small differences of variable quantities; the method of differencing quantities, or of finding an infinitely small quantity, which, being taken infinite times, shall be equal to a given quantity. This coincides with the doctrine of fluxions.
3. Exponential calculus, is a method of differencing exponential quantities; or of finding and summing up the differentials or moments of exponential quantities; or at least of bringing them to geometrical constructions.
4. Integral calculus, is a method of integrating or summing u moments or differential quantities; the inverse of the differential calculus.
5. Literal calculus, is specious arithmetic or algebra.
The 1890 Funk & Wagnalls Standard Dictionary has: "While calculus is sometimes used in this wide sense, it is commonly used, when without a qualifying word, for the infinitesimal calculus, and includes differential calculus and integral calculus."
The use of calculus without the definite article has become common only in the twentieth century. Some early titles in which "the" appears not to occur are Robinson's Differential and Integral Calculus for High Schools and Colleges (1868), Treatise on Infinitesimal Calculus by Price (1869), Differential Calculus with Numerous Examples by B. Williamson (1872), Calculus of Finite Differences by G. Boole (1872), Integral Calculus by W. E. Byerly (1898), The discovery of Calculus by A. C. Hathaway (1919).
Jeff Miller et
Mathématiques, Université de York
