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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Paperback. Condizione: New. Print on Demand. This book is an extensive exploration of the principles and applications of conic sections, regarded as a foundational work in the history of mathematics. The author begins with essential definitions and lemmas about curves and tangents and develops the theory of conic sections from the ground up. Drawing on the work of Apollonius, the author derives the fundamental properties of ellipses, parabolas, and hyperbolas from a single definition based on the distance to a fixed point and a fixed straight line. The book also explores the motion of bodies in conic sections under the influence of a central force and discusses the relationship between the force and the shape of the orbit. Through a meticulous and insightful examination of conic sections, this book provides a comprehensive understanding of these geometric forms and their applications in the study of motion and forces. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Codice articolo 9781331882978_0
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Condizione: New. KlappentextrnrnExcerpt from The First Three Sections of Newton s Principia: With an Appendix, and the Ninth and Eleventh SectionsNow since the quantities or ratios tend continually to equality, the ratio of their difference to either of . Codice articolo 2147902969
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