The Applications of Elliptic FunctionsMacmillan and Company, 1892 - 357 sider |
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Side viii
... obtain a working knowledge of the subject of Elliptic Functions , such as he would probably never acquire from a study of a treatise like Jacobi's Fundamenta Nova , where the formulas are established and the subject is developed in ...
... obtain a working knowledge of the subject of Elliptic Functions , such as he would probably never acquire from a study of a treatise like Jacobi's Fundamenta Nova , where the formulas are established and the subject is developed in ...
Side 1
... obtained by taking moments about O is d2o W ( h2 + k2 ) dt2 Wgh sin 0 , since the impressed force of gravity is Wg poundals , acting vertically through G ; so that or , on putting G.E.F. 0 ( h + ) = − g sin 0 ; h + k2 / h = l , ¿ d20 ...
... obtained by taking moments about O is d2o W ( h2 + k2 ) dt2 Wgh sin 0 , since the impressed force of gravity is Wg poundals , acting vertically through G ; so that or , on putting G.E.F. 0 ( h + ) = − g sin 0 ; h + k2 / h = l , ¿ d20 ...
Side 19
Sir George Greenhill. 19. The time of moving from A to E is obtained by putting 47 , and is therefore Kk / n ; and therefore the period , or time of a complete revolution , is 2KÊ / n ( not 4Kk / n ) . With the series for K as given in ...
Sir George Greenhill. 19. The time of moving from A to E is obtained by putting 47 , and is therefore Kk / n ; and therefore the period , or time of a complete revolution , is 2KÊ / n ( not 4Kk / n ) . With the series for K as given in ...
Side 23
... ) / k , where the Landen point L is obtained by drawing a circle with centre D , cutting the circle AE orthogonally , and the vertical AD in L. We shall prove subsequently that any straight line through L THE ELLIPTIC FUNCTIONS . 23.
... ) / k , where the Landen point L is obtained by drawing a circle with centre D , cutting the circle AE orthogonally , and the vertical AD in L. We shall prove subsequently that any straight line through L THE ELLIPTIC FUNCTIONS . 23.
Side 28
... obtained by multiplying Euler's equations respectively by ( i . ) p , q , r , and adding , ( ii . ) by Ap , Bq , Cr , and adding ; and then integrating . Comparing these equations with the equations of § 7 , cn'u = sn u dn u , sn'u = cn ...
... obtained by multiplying Euler's equations respectively by ( i . ) p , q , r , and adding , ( ii . ) by Ap , Bq , Cr , and adding ; and then integrating . Comparing these equations with the equations of § 7 , cn'u = sn u dn u , sn'u = cn ...
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1+cos Addition Theorem algebraical angular velocity axes axis c₁ catenary Catenoid centre circle cn a dn confocal constant corresponding cosh cubic curve d₁ denoting differential relation do² du² e₁ e₂ Elastica electrodes elliptic functions elliptic integral expressed factors formulas given herpolhode hyperbola hyperbolic functions II(u imaginary infinite invariable plane Jacobi's notation Landen's Transformation Legendre Legendre's linear Messenger of Mathematics modular angle Modular Equation modulus momental ellipsoid motion negative obtain oscillations pendulum period polhode positive Prove quadric quartic radius rectangle sinh sn²u spherical Spherical Pendulum suppose tangent tanh transformation triangle u₁ U₂ v₁ values vector function vertical w₂ Weierstrass's writing X₁ συ