A History of Mathematics From Mesopotamia to Modernity

86 A History ofMathematics 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 2 1 1 Fig. 1Rod numbers. Fig. 260390 as a rod number As in our system, ...

ChineseMathematics 87 [i] [ii] [iii] [v] [vi] [vii] [iv] Fig. 3The stages in calculating 81×81 by rod numbers. constitutes an ‘i ...

88 A History ofMathematics favoured medium for writing numbers, and in this sense we could think of a two-stage ‘invention’ of t ...

ChineseMathematics 89 Here is the text of chapter 8, problem 1, together with the ‘Array Rule’ which solves it. Now given 3 bund ...

90 A History ofMathematics These are details. The method, it could be said, has not changed even if questions about different gr ...

ChineseMathematics 91 Fig. 4Li Zhi’s ‘round town’ form theCeyuan haijing. Qin Jiushao(c.1202–61), who worked in the south, and ...

92 A History ofMathematics 208 B C 15 E 135 South D (centre) A (the tree) Fig. 5Following Chinese convention, south is at the to ...

ChineseMathematics 93 Fig. 6Illustration from theShushu jiuzhang, p. 167. We have, as often in the early history of mathematics, ...

94 A History ofMathematics Exercise 5.Find the equation which solves Li’s problem, and check that x= 240 is a root. A note on ‘e ...

ChineseMathematics 95 8. On ‘transfers’—when, and how? Seek knowledge, even as far as China. (The Hadith) Aside from the unusual ...

96 A History ofMathematics a=39 a=39 b=25 c=30 h 2 h 1 b=25 Fig. 8The ‘pointed field’, from Qin Jiushao’s problem. takes the num ...

ChineseMathematics 97 p. 91ff for the Islamic one). Still less are we about to discuss the priority, on which the evidence is sl ...

98 A History ofMathematics numbers as examples (cf. Høyrup 1994); then one can suppose that there is a common source, though the ...

ChineseMathematics 99 Solutions to exercises (a) We would probably call the original cerealx. Then after the three taxes have b ...

100 A History ofMathematics This (ifzis the yield of low-grade) gives us 36z=99 from the first column, soz=^9936 = (^234) as req ...

5. Islam, neglect and discovery 1. Introduction It should be clear from the present chapter that the traditional view of the Ara ...

102 A History ofMathematics in Western Europe has gone through a variety of transformations. In the early Middle Ages, from the ...

Islam,Neglect andDiscovery 103 what is once again a dauntingly long historical period. It should be easy for the student to appr ...

104 A History ofMathematics (Khayyam 1931). This, however, is long out of print and far from easy to find. Again, there are good ...

Islam,Neglect andDiscovery 105 Fig. 1MS, page from al-K ̄ash ̄i. And many of the out-of-print studies and aricles of the past hu ...