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Euler: “A baby on his lap, a cat on his back — that’s how he wrote his immortal works” (orig...

undoubtedly Dieudonné Thiébault, as the anecdote is reported in his personal recollections of his stay in Berlin, published in Mes souvenirs de vingt ans de séjour à Berlin, vol. 5, (Paris, 1804): [Euler
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Exact source that Descartes had observed that $V-E+F=2$ for planar graphs

The reconstruction of the story is dealt with in the volume Descartes on Polyhedra: A Study of the "De solidorum elementis". Long story short: while in Paris in 1675-1676, Leibniz copied a manuscript …
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