## A History of Japanese Mathematics |

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Great book to wrap up Wansan and envision the future of Japan after western math being introduced.

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abacus Aida Ajima ancient appeared arithmetic astronomy Book calculation celestial element century Ch'in Chiu-shao chapter China Chinese Chinese mathematics chord circle contemporaries diameter Dutch early edition ellipse Endo entitled equation Europe European figures follows formula Fujita given gives Hartsingius Hatono Hayashi Honcho Sugaku Hoyen inscribed Isomura Japan Japanese mathematics Jinko-ki jitsu Josephus problem jutsu Katsuyo Kawakita Ketsugi-sho known Kurushima Kwatsuyo Sampo later learning Literally magic squares manuscript mathe mathematicians matics Matsunaga measures mentioned method middle circle Mori multiplied Muramatsu Nakane native period polygon problems published pupil regular polygon result rods roku root Sakabe Sampo samurai Sangaku sangi Sankyo scholars seems segment Seiyo Seki school Seki's Shinan Shogun Shuki side Siigaku solution solved soroban sphere swan-pan Takebe Takebe's Tengen tenzan algebra Tetsujutsu theory Tokyo treatise triangle Uchida volume Wada wasan writers written wrote Yamaji Yedo yendan yenri Yoshida

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Page 10 - Given an unknown number, which when divided by 3, leaves a remainder of 2 ; when divided by 5, it leaves 3 ; and when divided by 7, it leaves 2 ; what is the number? Ans. 23. This is followed by a special rule for working out the problem in terms sufficiently concise and elliptical, to elude the comprehension of the casual reader ; — Dividing by 3 with a remainder of 2...

Page 141 - ... was able to correct an error in the computation of an eclipse of the sun as recorded in the official calendar.2 Hayashi was executed in 1646.

Page 15 - Less than all things," says a current precept, " men must grudge money : it is by riches that wisdom is hindered." Hence children were brought up with utter disregard of economy. It was considered bad taste to speak of it, and ignorance of the value of different coins was a token of good breeding.

Page 83 - Now that the elimination has proceeded to this stage, let us reverse the order, beginning with the child I choose. The husband agreed again, and the counting proceeded in the reverse order, with the unexpected result that all of the second wife's children were stricken out and there remained only the step-child, and accordingly he inherited the property.

Page 13 - ... (minus). In a series of 18 problems, it gives the method of ascertaining the value of unknown quantities, from certain conditions of combination, depending on the number of terms in the equation. The following is one of the simplest examples : — If 5 oxen and 2 sheep cost 10 taels of gold, and 2 oxen and 8 sheep cost 8 taels ; what are the prices of the oxen and sheep respectively ? — Ans., each ox, 1 tael and \^-\ each sheep, f- £ of a tael.

Page 4 - XIV, p. 38; hereafter referred to as Knott. Another interesting form of counting is still in use in Japan, and is more closely connected with the ancient one than is the common form above given. It is as follows: (I) hitotsu, (2) futatsu, (3) mittsu, (4) yottsu, (5) itsutsu, (6) muttsu, (7) nanatsu, (8) yattsu, (g] kokonotsu, (lo) to.

Page 122 - So (An incomplete treatise on the volume of a sphere). by considering the volume of a ring1 generated by the revolution of a segment of a circle about a diameter parallel to the chord of the segment.

Page v - It is the hope of the authors that this brief history may serve to show to the West the nature of the mathematics that was indigenous to Japan, and to strengthen the bonds that unite the scholars of the world through an increase in knowledge of and respect for the scientific attainments of a people whose progress in the past four centuries has been one of the marvels of history. It is only just to mention at this time the generous assistance rendered by Mr.

Page 15 - A crude theology, a purposeless logic, a feeble literature,— these had some standing; but mathematics save for calendar purposes was ever an outcast in the temple and the church, save as it occasionally found some eccentric individual to befriend it In the period of the Ashikaga shoguns it is asserted that there hardly could be found in all Japan a man who was versed in the art of division.

Page 5 - Algebra, with Arithmetic and Mensuration, from the Sanscrit of Brahmegupta and Bhascara. London 1817, p. 4; TAYLOR, J., Lilawati. Bombay 1816, p. 5. 8 WILLIAMS, SW, The Middle Kingdom.