A History of Mathematics- From Mesopotamia to Modernity

110 A History ofMathematics translated. In fact, with such disparate sources, the idea that the Islamic work could be simple bor ...

Islam,Neglect andDiscovery 111 This may seem less than clear to us, but it enables a description—the first—of what a general qua ...

112 A History ofMathematics a b a b c e f d Fig. 3Al-Khw ̄arizm ̄i’s first picture for the quadratic equation. ‘It is necessary’ ...

Islam,Neglect andDiscovery 113 A KL EGF HM CBD Fig. 4The diagram for Euclid proposition II.6. The line AB is bisected at C(AC=CB ...

114 A History ofMathematics What Th ̄abit does next is equally interesting; he goes through his method and shows, stage by stage ...

Islam,Neglect andDiscovery 115 6. Algebra—the next steps We have heard the great eastern mathematicians have extended the algebr ...

116 A History ofMathematics been vastly extended, without this ever being made explicit. The earlier author never said that numb ...

Islam,Neglect andDiscovery 117 he came to a startlingly pragmatic conclusion. We should think, he says, of a quantity not as a l ...

118 A History ofMathematics Fig. 5Table from al-Samaw’al. In al-Samaw’al’s famous phrase, from his introduction, his aim is to p ...

Islam,Neglect andDiscovery 119 where he can. Sometimes an example (such as( 10 /a^3 )(a^2 +a)=( 10 /a)+( 10 /a^2 ))is set out an ...

120 A History ofMathematics by 2x^3 + 5 x+ 5 +( 10 /x). This is far from being the hardest such sum which will be tackled; in pa ...

Islam,Neglect andDiscovery 121 uses them simply and with facility. In some sense, his introduction of them seems to be a claim t ...

122 A History ofMathematics learners that al-K ̄ash ̄i wroteThe Calculator’s Key, a very diverse collection of arithmetic, algeb ...

Islam,Neglect andDiscovery 123 the obvious high culture of his milieu, one would like more information on what preceded it and w ...

124 A History ofMathematics should be made: Islam did certainly differ from Christianity (for example) in the value placed on k ...

Islam,Neglect andDiscovery 125 of Mecca where the faithful should turn for prayer. As he says: [L]et us point out the great need ...

126 A History ofMathematics A simple number is any number which may be pronounced by itself without reference to root or square. ...

Islam,Neglect andDiscovery 127 G b H a c e fd Fig. 7Al-Khw ̄arizm ̄i’s second picture. AB F E CD G Fig. 8The figure for Th ̄abit ...

128 A History ofMathematics then the product ofEAwithABtogether with the square onBFare equal to the square onAF. But the produc ...

Islam,Neglect andDiscovery 129 Fig. 10Al-K ̄ash ̄i’s table. (Numbers are written using Arabic letters, cf fig. 5.) value 42 25 3 ...