The Quarterly Journal of Pure and Applied Mathematics, Volum 11J.W. Parker, 1871 |
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Resultat 1-5 av 13
Side 15
... ellipsoid . ,, parallel surface of an ellipsoid . I propose to consider these surfaces , not at present in any detail , but merely for the purpose of presenting them in connexion with each other and with the present theory . It will be ...
... ellipsoid . ,, parallel surface of an ellipsoid . I propose to consider these surfaces , not at present in any detail , but merely for the purpose of presenting them in connexion with each other and with the present theory . It will be ...
Side 21
... ellipsoid at right angles to the radius vectors from the centre . This is given in my paper " Sur la Surface , & c . " in the Annali di Matematica , t . II . , ( 1859 ) , as the envelope of the quadric surface x2 0 y3 + θ 0 θω = 0 . The ...
... ellipsoid at right angles to the radius vectors from the centre . This is given in my paper " Sur la Surface , & c . " in the Annali di Matematica , t . II . , ( 1859 ) , as the envelope of the quadric surface x2 0 y3 + θ 0 θω = 0 . The ...
Side 22
... ellipsoid . Writing the equation of the ellipsoid in the form y " 22 ― + + w = 0 , the centro - surface is given as the b2 c2 envelope of the quadric surface b2y a2x2 + Cz2 ( 0 + a2 ) 2 + ( 0 + b2 ) 2 + ( 0 + c2 ) 2 - - — w2 = 0 ...
... ellipsoid . Writing the equation of the ellipsoid in the form y " 22 ― + + w = 0 , the centro - surface is given as the b2 c2 envelope of the quadric surface b2y a2x2 + Cz2 ( 0 + a2 ) 2 + ( 0 + b2 ) 2 + ( 0 + c2 ) 2 - - — w2 = 0 ...
Side 23
... ellipsoid . This is given , Salmon , p . 148 , as the envelope of the quadric surface y2 + + z2 a2 + 0 b2 + 0 c2 + 0 - ( 1 + 1 / 2 )だ@ 2 = 0 . Ө The reciprocal quartic is thus the envelope of ( a2 + 0 ) X2 + ( b2 + 0 ) Y2 + ( c2 + 0 ) ...
... ellipsoid . This is given , Salmon , p . 148 , as the envelope of the quadric surface y2 + + z2 a2 + 0 b2 + 0 c2 + 0 - ( 1 + 1 / 2 )だ@ 2 = 0 . Ө The reciprocal quartic is thus the envelope of ( a2 + 0 ) X2 + ( b2 + 0 ) Y2 + ( c2 + 0 ) ...
Side 24
... ellipsoid , but real for either of the hyper- boloids , and its existence in the case of the hyperboloid is readily perceived . Reverting to the equation a y 22 2 a2 + 0 + b2 +0 + c + 0 ( 1 + 20o ) 202 = 0 , or say า ( a2 + 0 ) ( b2 + 0 ) ...
... ellipsoid , but real for either of the hyper- boloids , and its existence in the case of the hyperboloid is readily perceived . Reverting to the equation a y 22 2 a2 + 0 + b2 +0 + c + 0 ( 1 + 20o ) 202 = 0 , or say า ( a2 + 0 ) ( b2 + 0 ) ...
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The Quarterly Journal of Pure and Applied Mathematics, Volum 6 James Joseph Sylvester,James Whitbread Lee Glaisher Uten tilgangsbegrensning - 1864 |
Vanlige uttrykk og setninger
a+b+c action af-g angle angular velocities axes body Cayley centre circle coefficient columns common tangent concyclic cone confocal conic conicoids conjugate coordinates corresponding cubic curvature cusps denote differential dt dt elements ellipsoid envelope equal equation Euler's equations evectant evolute expression fixed point formulæ given curve greatest value Hence inflexion instantaneous axis integral intersection line IJ log mv magic square nodal normal obtain pairs parallel curve perpendicular points of contact pole quadric quartic surface radius reciprocal respectively shewn solenoid solution stationary tangent suppose tangent planes theorem torse triads unlike signs vertex w₁ whence WILLIAM WALTON zero square
Populære avsnitt
Side 187 - On the small oscillations of a Rigid Body about a Fixed Point under the action of any Forces, and more particularly when gravity is the only force acting," Transactions of the Boyal Irish Academy, vol.
Side 59 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Side 188 - ... to these directions are at right angles. III. A Free Rigid Body. 4. A free rigid body may receive any displacement by being screwed along an axis in space, the distance it travels along the axis when turned through the unit of angle being termed the pitch of the screw.
Side 50 - Д0 be the area of the triangle formed by joining the points of contact of the...
Side 189 - ... of these axes, as about a fixed axis, and its motion is always compounded of vibrations about these axes. 15. The length of the simple pendulum isochronous with the vibration about each normal axis is proportional to the square of the ratio of the corresponding diameter in the ellipsoid of equal energy to that of the momental ellipsoid.
Side 6 - I)2 = 0 ; and by reason of this property it is very easy to find the equations of the reciprocal surfaces, or plane-equations of the quartic surfaces in question. And, in the same paper, it is noticed that the surfaces of the form in question include the reciprocals of several interesting surfaces of the orders 6, 8, 9, 10, and 12 ; viz., order 6, parabolic ring : order 8, elliptic ring : order 9, centrosurface of paraboloid : order 10, parallel surface of paraboloid ; envelope of planes through...
Side 189 - A body rotating about a fixed point has throe degrees of freedom; its motion is compounded of vibrations about three normal screws whose pitch is zero, and whose directions pass through the point. NB — The screws in this case may be conveniently called the normal axes. V.
Side 9 - General Solution and Extension of the Problem of the 15 School Girls,
Side 309 - On the summation by definite integrals of geometrical series of the second and higher orders.