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[Sir Isaac NEWTON (1642-1727)]. - Isaac BARROW (1630-1677). The Usefulness of Mathematical Learning explained and demonstrated: Being Mathematical Lectures read in the publick schools at the University of Cambridge. To which is prefixed, the oratorical preface of our learned author, spoke before the University on his being elected Lucasian Professor of the Mathematics. Translated by the Revd. Mr. John Kirkby. London: printed for Stephen Austen, 1734. Octavo (7 ½ x 4 3/4in; 190 x 121mm). Pp. [i-]iii-xxxii, 1-440, [i-xvi]. Engraved portrait frontispiece, 1 folding engraved plate. (Neat repair to outer margin of A4 just touching nine characters [see image], some spotting to first and last few leaves). 19th-century half calf (rubbed, chipped, old strengthening to joints [see images]). Provenance: early indistinct signature to title.
First edition in English. “Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for proof of the fundamental theorem of calculus. His work centered on the properties of the tangent… He is also notable for being the inaugural holder of the prestigious Lucasian Professorship of Mathematics, a post later held by his student, Isaac Newton.” (wikipedia). “As a mathematician Barrow is well-known as a pioneer in the development of calculus. Barrow also presented, although in geometrical form, the fundamental theorem of the calculus, in which integration and differentiation are shown to be inverse operations. His preference for geometrical proofs over algebraic manipulations could well have had some influence on the young Newton [who was one of his students], who later expressed his own distaste for the new techniques introduced into mathematics by Descartes and his followers." (Gjertsen, p. 55).