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Cartesian - Springer Nature

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Last Updated: 03 January 2023

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Henry More’s Epistola H. Mori ad V.C. and the Cartesian Context of Newton’s Early Cambridge Years

I argue that Henry More contributed to a climate of receptivity toward Descartes in Cambridge at the time when Newton first encountered Cartesianism as a student there. Although we can't be certain that Moreu2019s views on Newton may have had on Newton, this more optimistic review of Moreu2019's participation in Cartesian natural philosophy makes us reconsider the common belief that More rejected Cartesianism in his later years.

Source link: https://doi.org/10.1007/978-3-031-09722-5_11


Fractional Helly Theorem for Cartesian Products of Convex Sets

Local intersection patterns influence global intersection patterns for a family of convex sets in Euclidean space, according to Helly's theorem and its variations. We generalize Eckhoff's results to Cartesian convex sets in all dimensions, answering a question raised by B'u00e1ny and Kalai, as well as Lew. We provide examples showing that adding an additional (p,d+1) - condition, although not surprisingly, has no effect on increasing the quantitative limits in neither the fractional Helly theorem for convex sets nor Cartesian convex sets.

Source link: https://doi.org/10.1007/s00454-022-00468-8

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions

* Please keep in mind that all text is summarized by machine, we do not bear any responsibility, and you should always check original source before taking any actions