Hyperbolic Functions |
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Common terms and phrases
a₁ Alternating Currents ANTI-HYPERBOLIC FUNCTIONS AREAS OF CORRESPONDING axis b₁ catenary central conic characteristic ratios circular functions complex numbers conjugate radii constants corresponding points cosh 82 cosh a sinh cosh iy cosh mx cosh u cosh cosh-¹ coth csch curve d(sinh DERIVATIVES differential elliptic functions elliptic sector exponential expressions find cosh FUNCTIONAL RELATIONS gd-¹ gd-¹v geometrical given gudermanian angle HARVARD COLLEGE OBSERVATORY hyperbolic functions hyperbolic sector hyperbolic sine hyperbolic trigonometry identities integral interpolation intrinsic equation inverse log cosh log sinh lowest point m₁ MANSFIELD MERRIMAN numerical values Prob Prove pure imaginary radian radius S₁ sech sector AOP sectorial measure Show singly periodic functions sinh a cosh sinh iy solution tables tabulated tangent tanh tanhu terminal theory tions tractory triangle values of cosh variable x₁ y₁ Επ
Popular passages
Page 3 - EDITORS' PREFACE. THE volume called Higher Mathematics, the third edition of which was published in 1900, contained eleven chapters by eleven authors, each chapter being independent of the others, but all supposing the reader to have at least a mathematical training equivalent to that given in classical and engineering colleges. The publication of that volume was discontinued in 1906, and the chapters have since been issued in separate Monographs, they being generally enlarged by additional articles...
Page 3 - ... former presentation or record recent advances. This plan of publication has been arranged in order to meet the demand of teachers and the convenience of classes, but it is also thought that it may prove advantageous to readers in special lines of mathematical literature. It is the intention of the publishers and editors to add other monographs to the series from time to time, if the call for the same seems to warrant it. Among the topics which are under consideration are those of elliptic functions,...
Page 3 - ... order to meet the demand of teachers and the convenience of classes, and it was also thought that it would prove advantageous to readers in special lines of mathematical literature. It is the intention of the publishers and editors to add other monographs to the series from time to time, if the demand seems to warrant it. Among the topics which are under consideration are those of elliptic functions, the theory of quantics, the group theory, the calculus of variations, and non-Euclidean geometry;...
Page 3 - ... readers in special lines of mathematical literature. It is the intention of the publishers and editors to add other monographs to the series from time to time, if the demand seems to warrant it. Among the topics which are under consideration are those of elliptic functions, the theory of quantics, the group theory, the calculus of variations, and non-Euclidean geometry; possibly also monographs on branches of astronomy, mechanics, and mathematical physics may be included. It is the hope of the...
Page 48 - The tension at any point of the catenary is equal to the weight of a portion of the string whose length is equal to the ordinate of the point.
Page 51 - But, by definition, PM = SP, л TS = PS. 50. Theorem.— To prove that the tangent FT bisects the angle SPM. Since ST = SP (proved), ¿STP = ¿SPT. But PM is parallel to TS, Л ¿STP = ¿MPT (alt ¿4 ie the tangent at P bisects /.SPM.
Page 33 - ... to be noted that the variables x, y are numbers, or ratios, and that the equation y = cosh x merely expresses that the relation between the numbers x and y is taken to be the same as the relation between a sectorial measure and its characteristic ratio. The numerical values of cosh...
Page 7 - The elliptic integrals, and thence the elliptic functions, derive their name from the early attempts of mathematicians at the rectification of the ellipse.