By D. J. Struik
These chosen mathematical writings hide the years while the principles have been laid for the idea of numbers, analytic geometry, and the calculus.
Originally released in 1986.
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Extra resources for A Source Book in Mathematics, 1200-1800
This is done simply by the subtraction of the given sine from radius. For (by 29) the logarithm of the sine 9996700 lies between the limits 3300 and 3301; and these limits, since they differ from each other by unity only, cannot 6 The modern theorem for the logarithm of a product does not hold, since the logarithm of unity is not zero. Hence Arts. 37 and 38, to express special cases. 1 This is proved by the principle of proportion and of Article 36. This rule is used first in Arts. 5000300. Articles 41 to 45 illustrate the fact that one may now calculate the logarithms of all the "proportionals" in the First, Second, and Third tables, as well as of the sines or natural numbers not proportionals in these tables but near or between them.
6. 6 FERMAT. TWO FERMAT THEOREMS AND FERMAT NUMBERS Pierre de Fermat (1601-1665) was a lawyer attached as councilor to the provincial parlia ment (that is, law court) of Toulouse. 7, 8. D. C. 250 by Claude Bachet in 1621, together with a Latin translation. Fermat communicated his results in letters to his friends or kept them to himself in notes, 8 This means that jPj, = ^ 9 Some of this is translated in Smith, Source book, pp. 76-79. ^^ ^ — = Oj Ili -2; hence C1J = Pj+5 + 1, where t 1 1· Z · • * \/C — 1) ml C5p = of p.
1], I say that when the geo metrically moving point G is at T,its velocity is as the distance TS, and when Fie. 1 6 ι T l 1 G 2 3 4 56 1—ι—ΓΤΊ G G 1 S G is at 1 its velocity is as I S , and when at 2 its velocity is as 2 S , and so of the others. , to one another, will be the same. 16 I ARITHMETIC I For we observe that a moving point is declared more or less swift, according as it is seen to be borne over a greater or less space in equal times. Hence the ratio of the spaces traversed is necessarily the same as that of the velocities.