The History of Mathematics: A Brief Course

142 6. CALCULATION Therefore, the two numbers are 8.5 + 4.5 = 13 and 8.5-4.5 = 4. The two techniques just illustrated occur cons ...

EUROPE 143 7 8 3 4 2 5 FIGURE 3. Multiplication with Hindu-Arabic numerals. be inclined to think that the phrase myrias diploo ...

144 6. CALCULATION For computations these cumbersome numerals were supplanted centuries ago by the Hindu-Arabic place-value deci ...

THE VALUE OF CALCULATION 145 and engineering, and he made no attempt to show how to calculate with an actually infinite decima ...

146 6. CALCULATION 9. Mechanical methods of computation Any study of the history of calculation must take account of the variety ...

MECHANICAL METHODS OF COMPUTATION 147 The problem here is to find the fourth proportional x, satisfying r : a = b : x, where r ...

148 6. CALCULATION S ï a b c d FIGURE 4. Geometric basis of logarithms. The first point sets out from Ô at the same time and wit ...

!). MECHANICAL METHODS OF COMPUTATION 149 improvements consist of scaling in such a way that the logarithm of 1 is 0 and the log ...

150 6. CALCULATION depended on turning a crank a certain number of times in order to find a sum. Leibniz used a variant of this ...

MECHANICAL METHODS OF COMPUTATION 151 Top: Leonardo da Vinci's design for an adding machine. Cen- ter: model of the machine. B ...

L52 fi. CALCULATION The future of calculation, as depicted in the April 17, 1944 issue of Newsweek. The potential of mechanical ...

MECHANICAL METHODS OF COMPUTATION 153 further than Babbage had envisioned. Babbage's assistant Augusta Ada Lovelace (1815-1852 ...

154 6. CALCULATION this book for your own reference library. You will need it many times in years to come. That book remains on ...

QUESTIONS AND PROBLEMS 155 6.7. Verify that the solution to Problem 71 (2 3) is the correct pesu of the diluted beer discussed i ...

156 6. CALCULATION an algorithm amounts to the drama that results when these roles are acted. That is why it is so important tha ...

QUESTIONS AND PROBLEMS 157 6.21. Compare the pond-filling problem (Problem 26 of Chapter 6) of the Jiu Zhang Suanshu (discussed ...

158 6. CALCULATION Year 0 1 2 3 4 5 6 Full Moon Apr. 14 Apr. 3 Mar. 23 Apr. 11 Mar. 31 Apr. 18 Apr. 8 Year 7 8 9 10 11 12 13 Ful ...

Chapter 7. Ancient Number Theory The impossibility of getting square roots to come out even, in connection with appli- cations o ...

160 7. ANCIENT NUMBER THEORY Plimpton 322. © Rare Book and Manuscript Library, Columbia University. Width Diagonal [...] 15 1,59 ...

PLIMPTON 322 161 We should therefore keep in mind that the reciprocals of these numbers may play a role in the construction of ...