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To deny, to believe, and to doubt well are to a man as the race is to a horse.
W. H. Auden and L. Kronenberger (eds.) The Viking Book of Aphorisms, New York: Viking Press, 1966.
Loci: Convergence
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Mathematical Treasures
Seki Kowa's Essentials of Mathematics
This is the title page of Seki Kowa’s (1642-1708) Katsuyo sampo [Essentials of Mathematics], 4 vols., published posthumously in 1712. It is a collection of Seki’s discoveries including: an accurate value of π to 10 decimal places and the computation of the volume of a sphere using a “method of circles”, enri; “Newton’s” interpolation formula; properties of spirals and ellipses; derivation of “Bernoulli” numbers and the “Pappus-Guldin “ theorem.
These are two pages in vol I showing the table employed to obtain “Bernoulli” numbers. They are given in the right column and were obtained by a technique called Ruisai Shosa-ho.