Cambridge Senate-house Problems and Riders for the Year 1860: With SolutionsMacmillan, 1860 - 198 páginas |
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Página 58
... differential equations d2x dz d2z + ds2 = 0 , dx ds2 = + .. x d2x ds2 d'y , dz d'z ds * dy ds " d'y d2z = 0 ; dz dz + y + ds * ds " x dx + y = 0 . dy In a conoidal surface if the axis coincide with the 58 [ Jan. 17 , SENATE - HOUSE ...
... differential equations d2x dz d2z + ds2 = 0 , dx ds2 = + .. x d2x ds2 d'y , dz d'z ds * dy ds " d'y d2z = 0 ; dz dz + y + ds * ds " x dx + y = 0 . dy In a conoidal surface if the axis coincide with the 58 [ Jan. 17 , SENATE - HOUSE ...
Página 80
... differential equations of conical and conoidal surfaces respectively when referred to any system of rectangular axes . d x ax Generally the operation a f ( x ) is equivalent to writing ax for x in f ( x ) . See Carmichael's Calc . Op ...
... differential equations of conical and conoidal surfaces respectively when referred to any system of rectangular axes . d x ax Generally the operation a f ( x ) is equivalent to writing ax for x in f ( x ) . See Carmichael's Calc . Op ...
Página 81
... differential equa- tions of conical surfaces , or df dx df ( x − a ) 1 x + ( y − B ) 1/4 + ( z − y ) - dy df = 0 . dz Again , in conoidal surfaces . If a , B , y be any point on the axis , l , m , n the direction - cosines of the ...
... differential equa- tions of conical surfaces , or df dx df ( x − a ) 1 x + ( y − B ) 1/4 + ( z − y ) - dy df = 0 . dz Again , in conoidal surfaces . If a , B , y be any point on the axis , l , m , n the direction - cosines of the ...
Página 87
... differential equation of the trajectory on the plane is d2u do μ ' μ + u1 + = h2 h2 ( 1 ) , μ and μ ' being the absolute intensities of the attractive and repulsive forces respectively . Its polar equation is therefore м n2h2 u = + A ...
... differential equation of the trajectory on the plane is d2u do μ ' μ + u1 + = h2 h2 ( 1 ) , μ and μ ' being the absolute intensities of the attractive and repulsive forces respectively . Its polar equation is therefore м n2h2 u = + A ...
Página 95
... differential equation of the disturbance is d ? dť2 = a2 d2 & dx2 . For which we may assume the integral § = A sin m ( at + x ) + A ' sin m ( at — x ) . - pressure Now measuring x from the bottom of the cylinder we must have the ...
... differential equation of the disturbance is d ? dť2 = a2 d2 & dx2 . For which we may assume the integral § = A sin m ( at + x ) + A ' sin m ( at — x ) . - pressure Now measuring x from the bottom of the cylinder we must have the ...
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Términos y frases comunes
acceleration angular velocity Arabic numbers asymptotes attraction axes axis bisects Cambridge centre of force centre of gravity chord circle circular cloth co-ordinates cone conic conic section constant cos² Crown 8vo curvature cylinder described diameter differential equation direction directrix distance drawn dt dt ellipse ellipsoid equal angles equiangular spiral equilibrium extremity Fcap fixed point fluid foci focus given point Hence horizontal hyperbola inclined intersection latus rectum length locus MACMILLAN & CO.'S meridian motion normal parabola parallel particle perpendicular point of contact position pressure prove ratio respectively right angles Roman numbers SENIOR MODERATOR shew sides sin² singular solution smooth sphere spherical straight line string subtend surface tangent tension triangle Trinity College uniform vertex vertical Vis Viva weight аф
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