history of the exact sciences

Newton and Leibniz on the relativity of motion”, for the Oxford Handbook of Newton, ed. Chris Smeenk and Eric Schliesser, 2015 (www.oxfordhandbooks.com), [preprint]. 

On the mathematization of free fall: Galileo, Descartes and a history of misconstrual”, for The Mathematization of NatureMinnesota Studies in Philosophy of Science, 2015 [preprint].

Leibniz's Actual Infinite in Relation to his Analysis of Matter”, forthcoming in Leibniz on the interrelations between mathematics and philosophy, (Springer: Archimedes Series), ed. Norma Goethe, Philip Beeley and David Rabouin, 2015. [preprint]

Leibniz's Syncategorematic Infinitesimals, Smooth Infinitesimal Analysis, and Second Order Differentials”, Archive for History of Exact Sciences, 67: 553–593, April 2013 [preprintThe final publication will be available at link.springer.com.

The Labyrinth of the Continuum”, in Maria Rosa Antognazza (ed.), Oxford Handbook of Leibniz; published online at (www.oxfordhandbooks.com), Oxford: Oxford University Press, December 2013.  [preprint]

Leery Bedfellows: Newton and Leibniz on the Status of Infinitesimals,” pp. 7-30 in Infinitesimal Differences: Controversies between Leibniz and his Contemporaries, ed. Ursula Goldenbaum and Douglas Jesseph, Berlin and New York: De Gruyter, 2008.  [preprint]

Leibniz’s Archimedean Infinitesimals,” Proceedings of the Canadian Society for History and Phil. of Mathematics, 21, 1-10, 2008—a preliminary version of the paper below to be published by the Royal Academy.  [preprint]

‘x + dx = x’: Leibniz’s Archimedean infinitesimals”, supposed to appear as a chapter in Structure and Identity, ed. Karin Verelst, Royal Academy, Brussels (unpublished; written 2007)  [preprint]

"The transcendentality of π (pi) and Leibniz's philosophy of mathematics", Proceedings of the Canadian Society for History and Philosophy of Mathematics, 12, 13-19, 1999. Here I show that in an unpublished paper of 1676 (A VI iii N69) Leibniz conjectured that π (pi) cannot be expressed even as the irrational root "of an equation of any degree", thus anticipating Legendre's famous conjecture of the transcendentality of π by some 118 years.  [preprint]

"The remarkable fecundity of Leibniz's work on infinite series": a review article on 2 Akademie volumes of Leibniz's writings, VII, 3: 1672-76: Differenzen, Folen Reihen, and III, 5: Mathematischer, naturwissenschaftlicher und technischer Briefwechsel . [preprint]

© Richard Arthur 2012