Unknown manuscript material of Christiaan Huygens (Q1057249)

The hitherto unknown manuscripts of Christiaan Huygens reported in this paper have come to light in the early stages of the author's project of composing an inventory of seventeenth century mathematical manuscripts in the Netherlands. One important find is Huygens' reconstruction of a proof of a proposition of J. van Heuraet on centres of gravity, where Huygens uses recursion and similarity of two systems of weights to conceal a limit transition. A detailed account of this proof, including text and analytical commentary, has already been given by the author in another publication [Centaurus 27, 218-279 (1984)]. Besides sketches of an artistic nature scattered through the drafts of several of Huygens' letters to Sluse, there are marginal notes in one of Huygens' copies of the Opera of Archimedes, which the author has been able to identify as the copy he received from van Schooten in 1648. These evidently include some references to Leibniz's arithmetical quadrature of the circle, which would repay study, since Leibniz regarded this as one of the finest results he had obtained using his new infinitesimal calculus. Another manuscript contains a summary of Sluse's Mesolabum. In the expectation that the planned inventory will reveal yet more manuscripts of Huygens, the author points to the need for a concordance between the Huygens collection in the Leiden University Library and the Oeuvres complètes.