Uniplanar Algebra: Being Part I of a Propædeutic to the Higher Mathematical AnalysisBerkeley Press, 1893 - 141페이지 |
도서 본문에서
13개의 결과 중 1 - 5개
55 페이지
... cosh , tanh , coth , sech , csch , are defined by the following identities : e − u ) , sinh u = } ( * —e ... cosh o = 1 . ( 2 ) . cosh2 u sinh u = I. ( 3 ) . sech u + tanhu = I . ( 4 ) . coth2 u csch2 u = 1 . ( 5 ) . sinh 2 u = 2 sinh a ...
... cosh , tanh , coth , sech , csch , are defined by the following identities : e − u ) , sinh u = } ( * —e ... cosh o = 1 . ( 2 ) . cosh2 u sinh u = I. ( 3 ) . sech u + tanhu = I . ( 4 ) . coth2 u csch2 u = 1 . ( 5 ) . sinh 2 u = 2 sinh a ...
56 페이지
... cosh u has 1 for its smallest and for its largest value corresponding to u = 0 and ∞ respectively , and if the variations of x / a be confined to the right hand branch of the hyperbola its range of values is likewise between 1 and + ...
... cosh u has 1 for its smallest and for its largest value corresponding to u = 0 and ∞ respectively , and if the variations of x / a be confined to the right hand branch of the hyperbola its range of values is likewise between 1 and + ...
57 페이지
... cosh u = ON , distance from centre to foot of NP , a tanh u = AH , distance along a tangent from A to OP , a coth u ... ( cosh ù — sech u ) · = a sinh a / ( cosh ? t −1 ) = a csch a . u applied to the six analogues of the goniometric ...
... cosh u = ON , distance from centre to foot of NP , a tanh u = AH , distance along a tangent from A to OP , a coth u ... ( cosh ù — sech u ) · = a sinh a / ( cosh ? t −1 ) = a csch a . u applied to the six analogues of the goniometric ...
62 페이지
... cosh u and y│a = = sinh u , ph : - eu . n a2 ... Area of OAP , .. P = ( eu In ― e - u / n ) 4 a u sinh ( u in ) 2 ... cosh u + cosh a sinh v . ( 2 ) . cosh ( u + v ) = cosh a cosh a + sinh u sinh tanh u + tanh v ( 3 ) . tanh ( u + v ) ...
... cosh u and y│a = = sinh u , ph : - eu . n a2 ... Area of OAP , .. P = ( eu In ― e - u / n ) 4 a u sinh ( u in ) 2 ... cosh u + cosh a sinh v . ( 2 ) . cosh ( u + v ) = cosh a cosh a + sinh u sinh tanh u + tanh v ( 3 ) . tanh ( u + v ) ...
63 페이지
... cosh u the ratios NP / a and ON a . [ Burn- side : Messenger of Mathematics , vol . xx , pp . 145-148 . ] I ( 5 ) . In the figure of Art . 53 show that the trapezoids SAP1S1 , SP 、 P2S2 , etc. , are equal in area to the corre- sponding ...
... cosh u the ratios NP / a and ON a . [ Burn- side : Messenger of Mathematics , vol . xx , pp . 145-148 . ] I ( 5 ) . In the figure of Art . 53 show that the trapezoids SAP1S1 , SP 、 P2S2 , etc. , are equal in area to the corre- sponding ...
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a+ib addition and subtraction Addition Theorem affix Agenda amplitude angle AOQ arc AVQ arc-ratio assumed base CALIFORNIA circular sector co-ordinates commutative law complex quantities corresponding cosh COSK csch defined definition direction distance equal equation equilateral hyperbola expm exponential expressed factors formula functions geometric addition Goniometric Ratios Hence hyperbolic functions Hyperbolic Ratios hyperbolic sector imaginary indeterminate form integer inverse law of indices law of involution law of metathesis length logarithmic spiral logm metathesis modular normal modulus natural logarithms negative nth roots orthomorphosis parallel path plane polynomial positive Prop proportion PROPOSITION Prove the following quotient radius real axis real magnitudes real quantities reciprocal represent respectively roots sech sector sinh speed straight line tanh tensor tion triangle unit circle x+iy z-plane zero