English

Noun

infinitesimal analysis ‎(uncountable)

1. (archaic, calculus) calculus

   1816: John Playfair, Dissertation on the Progress of Mathematical and Physical Science since the Revival of Letters in Europe

   • "Of the new or infinitesimal analysis, we are to consider Sir Isaac Newton as the first inventor, Leibnitz, a German philosopher, as the second; ..."
   • "The fluxionary and differential calculus may be considered two modifications [in the matter of notation] of one general method, aptly distinguished by the name of the infinitesimal analysis."

2. (mathematics, analysis) a systematic employment of infinitesimals that reduces calculus to algebra; nonstandard analysis.

   1998: John L. Bell, A Primer of Infinitesimal Analysis.

   2002: E.I. Gordon, A.G. Kusraev, S.S. Kutateladze, Infinitesimal Analysis

References

• Professor Playfair's "Dissertation on the Progress of Mathematical and Physical Science"

as quoted by John Spare, The Differential Calculus, Bradley, Dayton and Co., 1865, pp. 1-2.

• Infinitesimal analysis is "an archaic term for calculus."

• "In 1816, he published, in the Supplement to the Encyclopaedia Britannica, a "Dissertation on the Progress of Mathematical and Physical Science since the Revival of Letters in Europe," a work of great erudition and research.", biography of PLAYFAIR, JOHN.

• "The supplement was published in half-volume parts from December 1816 to April 1824. It formed six volumes 4to, containing 4933 Pages, 125 plates, 9 maps, three dissertations and 669 articles, of which a list is given at the end. ... The second dissertation,"On the progress of mathematics and physics,"was by Playfair, who died 19th July 1819, when he had only finished the period of Newton and Leibnitz.", article on Encyclopaedia from the eleventh edition of the Encyclopaedia Britannica, first published in 1911.