Synopsis
Excerpt from The First Three Sections of Newton's Principia: With an Appendix, and the Ninth and Eleventh Sections
Now since the quantities or ratios tend continually to equality, the ratio of their difference to either of them must always be greater than that of the difference of their limits to either of the limits, that is than D L or D L D, either of which is a finite ratio. But by the hypothesis the ratio of their difference to either of them may be made less than any finite ratio, which is absurd; therefore the limits are not unequal, that is, they are equal.
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About the Author
I. Bernard Cohen (1914-2003) was Victor S. Thomas Professor (Emeritus) of the History of Science at Harvard University. Among his recent books are "Benjamin Franklin's Science" (1996), "Interactions" (1994), and "Science and the Founding Fathers" (1992). Anne Whitman was coeditor (with I. Bernard Cohen and Alexander Koyre) of the Latin edition, with variant readings, of the "Principia" (1972). Julia Budenz, author of "From the Gardens of Flora Baum" (1984), is a multilingual classicist and poet.
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