The Quarterly Journal of Pure and Applied Mathematics, Volum 11J.W. Parker, 1871 |
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Resultat 1-5 av 26
Side 16
... variable parameter . The equation of the sphere therefore is ( x − að3w ) 2 + ( y − 2a0w ) 2 + z2 — k2w2 = 0 , - - and the ring is the envelope of this sphere . The reciprocal of the sphere is k2 ( X2 + Y2 + Z3 ) - ( a0 X + 2a0 Y + W ) ...
... variable parameter . The equation of the sphere therefore is ( x − að3w ) 2 + ( y − 2a0w ) 2 + z2 — k2w2 = 0 , - - and the ring is the envelope of this sphere . The reciprocal of the sphere is k2 ( X2 + Y2 + Z3 ) - ( a0 X + 2a0 Y + W ) ...
Side 17
... variable sphere is ( x - aw cos ) 2 + ( y − bw sin 0 ) 2 + za — k3w2 = 0 . The reciprocal of this is - - k2 ( X2 + Y2 + Z ) - ( aX cos + bY sin @ + W ) 2 = 0 . viz . writing this under the form aX cose + by sine + W + k √ ( X ' + Y2 + ...
... variable sphere is ( x - aw cos ) 2 + ( y − bw sin 0 ) 2 + za — k3w2 = 0 . The reciprocal of this is - - k2 ( X2 + Y2 + Z ) - ( aX cos + bY sin @ + W ) 2 = 0 . viz . writing this under the form aX cose + by sine + W + k √ ( X ' + Y2 + ...
Side 18
... variable sphere is - ( x − aw ) 2 + ( y — Bw ) 2 + z2 − k3w2 = 0 , - - where ( a , B ) vary subject to the condition have therefore a2 B2 + a2 b2 = 1. We аго х -aw - λ - = 0 , and thence aw = βιο = a * βω -βιο - λ = 0 , b2 a2x x -aw ...
... variable sphere is - ( x − aw ) 2 + ( y — Bw ) 2 + z2 − k3w2 = 0 , - - where ( a , B ) vary subject to the condition have therefore a2 B2 + a2 b2 = 1. We аго х -aw - λ - = 0 , and thence aw = βιο = a * βω -βιο - λ = 0 , b2 a2x x -aw ...
Side 20
... variable sphere which generates the ring . Centro - surface of a paraboloid . X * Y For the paraboloid + – 2ZW = 0 , it may be shewn a b that the centro - surface is the envelope of the quadric ax2 by2 ( a + 0 ) 2 + ( b + 0 ) 2 ̄ - 2zw ...
... variable sphere which generates the ring . Centro - surface of a paraboloid . X * Y For the paraboloid + – 2ZW = 0 , it may be shewn a b that the centro - surface is the envelope of the quadric ax2 by2 ( a + 0 ) 2 + ( b + 0 ) 2 ̄ - 2zw ...
Side 22
... variable plane is the inverse of the point on the ellipsoid . The quartic surface has the nodal conic W = 0 , X2 + Y + Z2 = 0 ; and also the node X = 0 , Y = 0 , Z = 0 ; there is consequently in the order of the reciprocal surface a ...
... variable plane is the inverse of the point on the ellipsoid . The quartic surface has the nodal conic W = 0 , X2 + Y + Z2 = 0 ; and also the node X = 0 , Y = 0 , Z = 0 ; there is consequently in the order of the reciprocal surface a ...
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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.