Shuki sanpo [trans.: Selected Jewels of Mathematical Method] by [ARIMA, Yoriyuki]

Many woodcut illus. & diagrams in the text. 43; 44; 39; 49; 55 folding leaves. Five vols. 8vo, orig. patterned blue wrappers, orig. block-printed title labels on upper covers, new stitching. Edo: Suharaya Mohei, 1769. First edition of this important and influential mathematical book. "The Seki school was the most popular of the many schools of mathematics in Japan. Yoriyuki Arima (1714-1783), Lord of Kurume, was one of its leaders and was the first to publish its secret theories of algebra. Arima personifies the anomaly of a member of a hereditary warrior class drawn, in a time of enforced peace, to mathematics of the mostly highly abstract and purely aesthetic sort; he, too, had been a pupil of Yamaji, and he took Fujita under his protection and assisted him in the publication of Seiyo sampo. Arima's own Shuki sampo was as popular in its time as Fujita's work, and Aida drew heavily upon both books."-D.S.B., I. p. 83. In this work, Arima "described 150 problems chosen from all fields of wasan research in the Seki tradition. Included were problem-solving procedures - though he gave no theoretical explanations of them. This was the first printed book in which one could find, for instance, a detailed description of Seki's written algebra, called tenzanjutsu. Thenceforth tenzanjutsu became a standard working tool of wasan students in general - almost a full century after its invention by Seki."-Sugimoto & Swain, Science & Culture in Traditional Japan, pp. 365-66. In this work, Arima gave the value of pi which was correct to 29 decimal places. The problems relate to indeterminate equations, the various roots of an equation, the application of algebra to geometry, the inscription of spheres within spheres, maxima and minima, binomial series, and stereometry. While this book was published under the name of Bunkei Toyota, it was actually written by Arima. ❧ Smith, History of Mathematics, Vol. I, pp. 536-37.