A History of Mathematics From Mesopotamia to Modernity

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 ...

130 A History ofMathematics Solutions to exercises Clearly ‘Is’ denotes an odd place (counting from the end); and the point is ...

Islam,Neglect andDiscovery 131 Obviously for a positive solution we want the positive root, and a slight rearrangement of the ex ...

132 A History ofMathematics It is easy to check that the vertices given are distant 2 √ 2 from each other; which establishes ( ...

6. Understanding the ‘scientific revolution’ 1. Introduction Philosophy is written in that vast book which stands forever open b ...

134 A History ofMathematics inspiration of Plato or Archimedes, saw the transformation in terms of the introduction of ‘math- em ...

Understanding the‘ScientificRevolution’ 135 as a discipline in the eighteenth and nineteenth centuries. One historian changed th ...

136 A History ofMathematics other than ‘revolution’. For mathematicians, it is likely to be the relatively early period when the ...

Understanding the‘ScientificRevolution’ 137 reasoning ridiculed by Galileo and Descartes, for example. Dijksterhuis makes the ca ...

138 A History ofMathematics say that, however learned Albert was, he did not know very much about Greek geometry; it also shows ...

Understanding the‘ScientificRevolution’ 139 is given by Nicolas Oresme. Oresme has been considered the originator of graphical ( ...

140 A History ofMathematics This is, at any rate, my interpretation of the way Oresme describes the summation of geometric serie ...

Understanding the‘ScientificRevolution’ 141 history—because it focuses not on the work in its context with its proper connexions ...

142 A History ofMathematics Fig. 1German arithmetic book from Holbein’s ‘The Ambassadors’ (National Gallery, London). catalogue ...

Understanding the‘ScientificRevolution’ 143 ‘algebra’ of the al-Khw ̄arizm ̄i kind and the extraction of square and cube roots w ...

144 A History ofMathematics A realization that the Greek writings were—depending on the author’s particular take—too difficult, ...

Understanding the‘ScientificRevolution’ 145 The remainder then as a general rule Of their cube roots subtracted Will be equal to ...