A History of Mathematics- From Mesopotamia to Modernity

150 A History ofMathematics considered Descartestherevolutionary who had freed them from bondage to the tedious methods of the a ...

Understanding the‘ScientificRevolution’ 151 1.5 1 0.5 0 –0.5^0 –1 –1 –0.5 0.5 1 –1.5 0 0 Fig. 2Graph of a cubic curve. Europe, e ...

152 A History ofMathematics in these early stages of what later becomes the calculus, there is a general sense of exploration, o ...

Understanding the‘ScientificRevolution’ 153 C G K K D V F A R R P L M X P E J O N Fig. 3Kepler’s diagram from ‘Astronomia Nova’. ...

154 A History ofMathematics dialogue form, and full of artful reasoning and rhetoric. (Misleadingly, the Dover edition of the se ...

Understanding the‘ScientificRevolution’ 155 Appendix A (From Oresme,Quaestiones super Euclidem) Next we inquire whether an addit ...

156 A History ofMathematics For example: in the above the second part, which is a third of the first, differs from the first by ...

Understanding the‘ScientificRevolution’ 157 If I wish to find out to what class this curve belongs, I choose a straight line, as ...

158 A History ofMathematics Fig. 5Kepler’s picture of the circle, the straight line, and the infinitely small subdivisions. Theo ...

Understanding the‘ScientificRevolution’ 159 A BCC
Fig. 6Archimedes’ idea: ABC is the triangle whose base is the circumference a ...

160 A History ofMathematics Let us translate Euclid’s statement into algebra. You start with a quantitya. You subtract from thi ...

7. The calculus 1. Introduction By the help of this new Analysis Mr Newton found out most of the propositions in thePrincipia Ph ...

162 A History ofMathematics than their share of attention in history of mathematics courses, they are either ignored or grossly ...

TheCalculus 163 on extremely short intervals of time, so that the question of whether Leibniz received three communications abou ...

164 A History ofMathematics acknowledging the debt, its circulation was certainly more restricted. And yet the circle ofsavants ...

TheCalculus 165 3. The priority dispute We shall not discuss the shamefully bitter controversy as to the priority and independen ...

166 A History ofMathematics Modern scholars (see particularly Hall 1980) are agreed that Newton’s communication was both too lat ...

TheCalculus 167 A y C R O B b a Fig. 1Indian calculation of the arc. Ifyis the arc AC,a=AB is the ‘Sine’ of the angle AOC, BO th ...

168 A History ofMathematics Here ‘Sine’ and ‘Cosine’ mean the lines AB, BO in the diagram (Fig. 1.)—sine and cosine multiplied b ...

TheCalculus 169 the Indian work as, precisely,nota version of the (later) European ‘method of infinite series’, let alone that b ...