A History of Mathematics- From Mesopotamia to Modernity

170 A History ofMathematics separately. This is how Newton’s first private draft of his ideas begins, if with no explanation of ...

TheCalculus 171 T qo po AA' BCB' x y Fig. 3A and A′are infinitely close on the curve (a parabola, represented as a polygon with ...

172 A History ofMathematics integration—finding the fluent—is established as the central problem; so is the fact that you can fi ...

TheCalculus 173 was in no hurry to publish—it took nine years from his discovery of the method in 1675 to his first paper, which ...

174 A History ofMathematics However, it is only after three pages of this exposition of ‘rules’ for the calculus, which tells yo ...

TheCalculus 175 we have claiming pride in the discovery, such as the one which opens this section, come in the main from some ti ...

176 A History ofMathematics Leibniz’s manuscript notes). However, none of this matters in terms of the impact such a solution wo ...

TheCalculus 177 are complicated. As has been pointed out for example, by Hall, the work would have been doubly unfamiliar to its ...

178 A History ofMathematics Fig. 5Newton’s picture forPrincipiaI, proposition 1. This argument does not use Newton’s version of ...

TheCalculus 179 Leibniz was in Italy and did not reply to this crawling letter (there is more in the same vein). However, the br ...

180 A History ofMathematics showed that it worked because two errors in calculation happened to cancel. (It just happened that o ...

TheCalculus 181 –0.5 0.5 2 4 6 8 2 –1.5 –1 1 1.5 A C B T W T 0 c Fig. 6The catenaryy=acosh(x/a)=(a/ 2 )(ex/a+e−x/a). [Jakob Bern ...

182 A History ofMathematics And it is now time to return to a version—if possible updated—of Boris Hessen’s thesis: that the who ...

TheCalculus 183 du 5 –5 55 r Fig. 7A cardioid,r= 2 ( 1 +cosθ); and an element of area. which (you can either believe this or w ...

184 A History ofMathematics T ABb E D d c Fig. 8Newton’s picture of the tangent to a curve. T F D BLA M E G e C Fig. 9Newton’s ‘ ...

TheCalculus 185 In consequence, sinceBDis equal toy,BTwill bez−x−(by+yy)/z. This is−BT=AL+(BD× GM/BL). Here the sign−prefixed to ...

186 A History ofMathematics AX, cut off from the axis is calledx. Let the tangents beVB,WC,YD,ZE, intersecting the axis respecti ...

TheCalculus 187 therefore also to the triangleSAB. By the like argument, if the centripetal force acts successively in C,D,E, &a ...

188 A History ofMathematics The simplest method of solution is to divide bywand multiply byx(so all like terms are together): d ...

8. Geometries and space 1. Introduction Most people are unaware that around a century and a half ago a revolution took place in ...