Taylor, Brook | Methodus incrementorum directa & inversa, London, 1715, first edition

Taylor, Brook

Methodus incrementorum directa & inversa. London: by Pearson, for William Innys, 1715

First edition of the first treatise dealing with the calculus of finite differences; containing the earliest printing of the celebrated formula now known as Taylor's theorem—which was the "first general expression for the expansions of functions of a single variable in infinite series"—and containing also the first statement of "the differential equation of the path of a ray of light when traversing a heterogeneous medium" (E. I. Carlyle, DNB).

By the time of publication of Methodus, Taylor had already been elected a member of the Royal Society for three years and would hold the position of Secretary of the Society for four years. Though Taylor would encounter priority controversies of his own, most notably with Bernoulli over his discoveries within calculus, Taylor served on the committee in charge of ruling the claim of priority of Leibniz over Newton.

4to (220 x 160mm). Roman types with italic and greek, numerous woodcut diagrams, woodcut ornament on title, tailpiece, and passe-partout initial borders; title soiled, some minor repairs to marginal tears, leaves variously browned, foxing predominately to last . Contemporary quarter calf marbled boards, spine in six compartments with red morocco gilt lettering-piece in fifth, plain endpapers and single flyleaves, all edges stained red; worn and rubbed, spines scuffed with some loss at head, upper joints and foot, upper flyleave nearly detached, edges dust-soiled.

REFERENCES

DNB 19:404: DSB 13:265–67; Honeyman sale 7:2968; Newton/Harrison The Library of Isaac Newton 248 , no. 1597; Smith History of Mathematics 1:451; Sotheran/Zeitlinger Bibliotheca chemico-mathematica 4762; Wallis British Mathematics 1701–1760 35, no. 708TAY151

PROVENANCE

Hugh Blackburn, professor of mathematics at Glasgow 1849–73 — thence by descent — Sotheby's, 10 October 1993, lot 781