KO May Medallist Ganita Bharati INDIAN JOURNAL OF HISTORY OF SCIENCE centor by Li Chunfeng 602 ID: 817690
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The Continuation of Ancient Mathematics:
The Continuation of Ancient Mathematics: Wang Xiatongs Jigu Century China by Tina SuLyn Lim and Donald B Wagner, NIAS Press, Nordic Instituteof Asian Studies, Copenhagen, Denmark, Pages, xii+220*K.O. May Medallist, Ganita Bharati INDIAN JOURNAL OF HISTORY OF SCIENCE cent.)or by Li Chunfeng (602670) or by both. They (official History of the Sui Dynasty).mentions that Zu Chongzhis (which isnot extent now) contained Zus calculation of the calendricalmentions reviewers paper which was first 27, (Tenthe works with great difficulty. Out of the severaleditions of Wangs Dynasty (1644-1911), that of Li Huang (1832) isYanqu
an translated the text in modern Chinese
an translated the text in modern Chinese inStudy of the work (Taiwan, 2001). So theLim and Wagner is most welcome.Wang in his Jigu which has 20 problems (called or method). The first problem istriangles. These problems may be considered as a (no. 2 in thelist). For example Wang used = 3 (used in invariablyas an intermediary state in nearly all of the Wangsproblems. Appendix 1 (p.205) lists all the cubicequations along with their real roots. They are ofbe 0 also). Such equations have been shown toHow Wang solved such equations is notHorners or rather Ruffini-Horner method forequations and named after Paolo Ruffini (1
803)and William George Horner (1819). It
803)and William George Horner (1819). It may be thatWang did not include details of the methodHappily, Lim and Wagners presentationand exposition of Wangs problems in Part II isvery simple, clear and explanatory. A large numberBOOK REVIEW: THE CONTINUATION OF ANCIENT MATHEMATICSsteps easily. The illustrative diagrams are neatlyAs a sample of Wangs formation of histhe first part of his problem 7. This is related to a i.e. a truncatedsquare pyramid. We first give a convenient modernexposition using modern symbology. Let are given or known. To find from (6) into (7) to get = 6, = 468, = 360 (10)which is exactly what Wan
g got (p.169). He solves12 easily. In fa
g got (p.169). He solves12 easily. In fact he had also arrived atWang.of Wangs reasoning is not found in and Wagner have correctly concluded that thesquare pyramid (of height (whose points A, B, C and D merge to form the(p.168): Difference of sides,To find values of is the problem. per view, Wangs problem amounts to finding of (i)a b = x, say (5)(ii)h b = y, say (6)Fig. 2INDIAN JOURNAL OF HISTORY OF SCIENCEcommon vertex T). Now we brief by describe theexposition of Lim and Wagner in our symbolsYangma is/3 (11) does not corresponds to actually representsthe Éffective area of the combined corner YangmaSimilarly
, the combined volume of the four latera
, the combined volume of the four lateral (13)Finally the volume of the remaining central solid + + ) is equal to V, we get the requiredexpose and explain Wangs problems. Authors century Chinese skill inas to whether Wangs reasoning aboutcalculations should be called algebra. G.H.Frhetorical and algebra.Wang is seemingly fit for the first category butActually, symbolic algebra is a powerfultool. We used it to derive equation (10) for = 432 (15) = 9. However (14) involvesnegative coefficients and is not of the type (1)problems 18, 19 and 20 are incomplete. What haswith suitable comments (p.104). Significantly, the