A History of Mathematics- From Mesopotamia to Modernity

30 A History ofMathematics to ruin their overseers to the greater profit of the state.) Of course, we still sometimes face probl ...

BabylonianMathematics 31 Solutions to exercises I shall not answer, while exercise 2 is answered in the text. If the number in ...

32 A History ofMathematics We now have to subtract. This time again, it is more correct to borrow along the line. However, sinc ...

2. Greeks and ‘origins’ Socrates: Then as between the calculating and measurement employed in building or commerce and the geome ...

34 A History ofMathematics Fig. 1TheMenoargument. The large square has side 4 feet (area 16 square feet), the four small squares ...

Greeks and‘Origins’ 35 whole number, or even a ‘rational’ number (a fractionp/q, wherep,qare whole numbers). You can approximate ...

36 A History ofMathematics quite easy to spectacularly difficult. This will give some idea of the achievements of Greek mathe- m ...

Greeks and‘Origins’ 37 AD BC EF G Fig. 2The diagram for Euclid proposition I.35. an example of the approach, is a single short p ...

38 A History ofMathematics have worried commentators, but they are not—perhaps you will agree—very important unless you suppose ...

Greeks and‘Origins’ 39 with a historicist sense of difference. The classical works were using methods which are alien to us to a ...

40 A History ofMathematics Although he has been criticized since for the way in which he used his often unreliable sources, Tann ...

Greeks and‘Origins’ 41 of mathematicians scattered among other writers. While Plato and Aristotle date from the fourth-centurybc ...

42 A History ofMathematics be illuminating; but, unless a document which confirms the reconstruction turns up, it must necessari ...

Greeks and‘Origins’ 43 inFor Marxgave a naive version (‘Thales opened up the “continent” of mathematics for scientific knowledge ...

44 A History ofMathematics or dogmatic assertion. To be more cautious, to insist as Lloyd does on how little we know, is to risk ...

Greeks and‘Origins’ 45 Pythagoras at all.^8 That he did exist is a reasonable assumption, since he is referred to by Herodotus a ...

46 A History ofMathematics Octahedron Cube [Hexahedron] Tetrahedron Icosahedron Dodecahedron Fig. 3The five regular (‘Platonic’) ...

Greeks and‘Origins’ 47 should naturally also come across a theory of proportions, in which no arithmetical parts remain. (Hasse ...

48 A History ofMathematics how they can be so sure; for example, there is nothing to suggest this in theElements. (Fowler, contr ...

Greeks and‘Origins’ 49 challenge is to reconstruct what the two did. The main fact known about Democritus is that he was an ‘ato ...