 | Colin Macfarquhar, George Gleig - Encyclopedias and dictionaries - 1797 - 450 pages
...tiuretore, by km. i. the figures infrrited nnd circumlenbed become ultimately eq'.ial the one to ihe other ; and much more will the intermediate curvilinear figure be ultimately equal to either. L EM. N I. The fame ultimate ratios are alfo ratios of equality, when the brcadtl.s AB, BC, CD, &c.... | |
 | Isaac Newton - Celestial mechanics - 1803 - 344 pages
...becomes lefs than any given fpace. And therefore (by Lem. 1) the figures infcribed and circumfcribed become ultimately equal one to the other; and much...be ultimately equal to either. QED LEMMA III. The fame ultimate ratios are aljo ratios of equality, when the breadths AB, BC, DC, fyc. of the parallelograms... | |
 | John Mason Good - 1819 - 788 pages
...space. And therefore by lem. 1. the figures inscrioed and circumscribed become ultimately equal the one to the other; and much more will the intermediate...curvilinear figure be ultimately equal to either. Le.v III. The same ultimate ratios arc also ratios of equality, when the breadths AB, BC, CD, &c. of... | |
 | Encyclopedias and dictionaries - 1816 - 778 pages
...fpace. And therefore, by lem. i. the figures infcribed and circumfcribed become ultimately equal the one to the other ; and much more will the intermediate...curvilinear figure be ultimately equal to either. LEM. III. The fame ultimate ratios are alfo ratios of equality, when the breadths AB, BC, CD, &c. of... | |
 | Harvey Goodwin - Mathematics - 1846 - 500 pages
...figures, and a fortiori the curvilinear figure which is intermediate to the two, become ultimately equal. QED LEMMA III. The same ultimate ratios are also ratios of equality, when tke breadths of the parallelograms AB, BC, CD, are unequal, and all are diminished indefinitely. For... | |
 | Harvey Goodwin - Mathematics - 1849 - 588 pages
...figures, and a fortiori the curvilinear figure which is intermediate to the two, become ultimately equal. QED LEMMA III. The same ultimate ratios are also ratios of equality, when the breadths of the parallelograms AB, BC, CD, are unequal, and all are diminished indefinitely. D is For let AF... | |
 | Sir Isaac Newton - Curves, Plane - 1863 - 316 pages
...figures, and, a fortiori, the curvilinear figure, which is intermediate, become ultimately equal. NEWT. c LEMMA III. The same ultimate ratios are also ratios of equality, when the breadths of the parallelograms AB, BC, CD, are unequal, and all are diminished indefinitely. JL JJ FC For, let... | |
 | Florian Cajori - Mathematics - 1919 - 320 pages
...supposed diminished in infinitum, becomes less than any given space. And therefore (by Lem. I) the figures inscribed and circumscribed become ultimately equal...curvilinear figure be ultimately equal to either. OED " Principia, Book I, Section /, Lemma XI, Scholium (first part omitted) 10. ". . . Quae de curvis... | |
 | Z. Bechler - Biography & Autobiography - 1982 - 264 pages
...figure he nonchalantly asserted that because their difference becomes "less than any given" the figures inscribed and circumscribed become ultimately equal...curvilinear figure be ultimately equal to either, (ibid., p. 30) The Principia opens with a preface which does two things: it first differentiates between... | |
 | Michael Spivak - Mathematics - 2006 - 682 pages
...supposed diminished in infinitum, becomes less than any given space. And therefore (by Lem. 1) the figures inscribed and circumscribed become ultimately equal...curvilinear figure be ultimately equal to either. QED *21. Suppose that / is increasing. Figure 16 suggests that FIGURE 16 22. (a) If P = {t0,...,tn} is... | |
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M inscribed and circumscribed become ultimately equal one to the other, and much more will the intermediate curvilinear figure be ultimately equal to either. QED 