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Sinopsis
The Principles of Elliptic and Hyperbolic Analysis is a book written by Alexander Macfarlane and published in 1894. The book is a comprehensive study of the principles of elliptic and hyperbolic analysis, which are two branches of mathematics that deal with the study of curves and surfaces.The book begins with an introduction to the basic concepts of elliptic and hyperbolic geometry, including the definition of curves and surfaces, and the properties of circles and ellipses. It then goes on to explore the theory of elliptic and hyperbolic functions, including their properties, their applications in geometry and physics, and their relation to other mathematical concepts.The book also covers the theory of differential equations, including the methods of solving them, and their applications in physics and engineering. It includes a detailed discussion of the Laplace equation, which is a fundamental equation in the study of elliptic and hyperbolic functions.Throughout the book, Macfarlane provides numerous examples and exercises to help readers understand the concepts and techniques presented. The book is written in a clear and concise style, making it accessible to both students and professionals in the field of mathematics.Overall, The Principles of Elliptic and Hyperbolic Analysis is a valuable resource for anyone interested in the study of elliptic and hyperbolic functions, and their applications in mathematics, physics, and engineering.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.
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Reseña del editor
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone!
Reseña del editor
which we denote by Let OPA (Fig. 1) represent aA and OAQ represent B; then OPQ, the third side of the spherical triangle, represents the product aAB. To prove that aAB = cos A cos B - sin A sin B cos a + {cos B sin A a+cos A sin B - sin A sin B sin a}. The first part of this proposition, namely, that cos aAB = cos A cos B - sin A sin B cos a, is equivalent to the well-known fundamental theorem of Spherical Trigonometry; the only difference is, that a denotes, not the angle included by the sides, but the angle between the planes; or, to speak more accurately, the angle between the axes a and. It is more difficult to prove the complementary proposition, namely, that Sin aAB = cos B sin A a + cos A sin B - sin A sin B sina a, for it is necessary to prove, not only that the magnitude of the right-hand member is equal to - cos2aAB, but also that its direction coincides with the axis normal to the plane of OPQ At page 7 of Fundamental Theorems, I have proved the above statement as regards the magnitude, but I was then unable to give a general proof as regards the axis. Now, however, I am able to supply a general proof, and it will be found of the highest importance in the further development of the analysis. In Fig. 1, OP is the initial line of aA, and OQ the terminal line of B; let OR be drawn equal to cos B sin A a + cos A sin B - sin A sin B sina a; it is required to prove that OR is perpendicular to OP and to OQ. Now, OP = a-A = (cos A - sin A). About the Publisher Forgotten Books is a publisher of historical writings, such as: Philosophy, Classics, Science, Religion, History, Folklore and Mythology. Forgotten Books' Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the aged text.
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- EditorialKessinger Publishing
- Año de publicación2010
- ISBN 10 1165069822
- ISBN 13 9781165069828
- EncuadernaciónTapa blanda
- IdiomaInglés
- Número de páginas52
- Contacto del fabricanteno disponible
(Ningún ejemplar disponible)
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