STIRLING EXPANDS NEWTON'S WORK ON CUBICS. STIRLING, JAMES. 1692-1770. Lineae tertii ordinis Neut...

STIRLING EXPANDS NEWTON'S WORK ON CUBICS. STIRLING, JAMES. 1692-1770. Lineae tertii ordinis Neutonianae, sive illustratio tractatus D. Neutoni de enumeratione linearum tertii ordinis. Oxford: at the Sheldonian Theatre, 1717. 8vo (xxx x xxx mm). Engraving of the Sheldonian Theater to title page; woodcut diagrams in text. 19th-century morocco, gilt arms of William Stirling-Maxwell to upper cover. Provenance: 'G.M.' (inscription to title page); Sir William Stirling Maxwell (armorial binding, his bookplate to pastedown). RARE FIRST EDITION OF THE FIRST SYSTEMATIC TREATMENT OF NEWTON'S CUBICS, AND THE AUTHOR'S FIRST BOOK—THE STIRLING FAMILY COPY. Newton's classification of cubic curves first appeared in 1704, as an appendix to his Optics, Lineae tertii ordinis Neutonianae ('Newton's Enumeration Of Lines Of The Third Order'). Newton showed that all cubics can be generated by the projection of the five divergent cubic parabolas, but his classification of cubics was incomplete (including only 72 out of 78 possible types). While Newton defined the cubic curves geometrically, Stirling provided proofs using the emerging calculus, and identified 4 more (Nicole and Bernoulli would complete the classification). Stirling also provides the proof for solving Leibniz's problem of orthogonal trajectories, which he had solved while still an undergraduate at Oxford in 1715 (see John Keill to Isaac Newton, June 24, 1715). 'Stirling's influence as a mathematician of profound analytical skill has been a notable feature within the inner circle of mathematicians. Witness, for example, the tribute of praise rendered by Laplace in his papers on Probability and on the Laws of Functions of very large numbers. Binet, in a celebrated memoir on Definite Integrals, has shown Stirling's place as a pioneer of Gauss' (Tweedle, James Stirling, 1922, 'Preface'). Stirling was the cousin of the Stirlings of Keir, from which William Stirling-Maxwell descended. James Stirling's only daughter, Christian, married her cousin Archibald Stirling, of Garden. Of the two known books from James Stirling's library, one was given to Bernoulli in 1719, and the other, on Geometry ended up at Garden, presumably through his daughter. It seems likely that this volume, not generally representative of William Stirling-Maxwell's vast library, also descended from James Stirling through his daughter. For further information on this lot please visit Bonhams.com For further information about this lot please visit the lot listing