# Mathematical Treasures - Seki Kowa's Essentials of Mathematics

Author(s):
Frank J. Swetz and Victor J. Katz

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 $$\pi$$ to 10 decimal places and the computation of the volume of a sphere using enri, which was a “method of circles”;
• “Newton’s” interpolation formula;
• properties of spirals and ellipses;
• derivation of “Bernoulli” numbers; and
• the “Pappus-Guldin” theorem.

These are two pages in Volume 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.

Index to Mathematical Treasures