Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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Page vii
... remarkable functions known as Laplace's Co- efficients . There can be but one opinion as to the beauty and utility of this analysis of Laplace ; but the manner in which it has been hitherto presented has seemed repulsive to the ablest ...
... remarkable functions known as Laplace's Co- efficients . There can be but one opinion as to the beauty and utility of this analysis of Laplace ; but the manner in which it has been hitherto presented has seemed repulsive to the ablest ...
Page 26
... remarkable theorems to which it led him is that of § 38 . Since the radius - vector of the hodograph represents the velocity at each instant , it is evident ( § 27 ) that an elementary arc represents the velocity which must be ...
... remarkable theorems to which it led him is that of § 38 . Since the radius - vector of the hodograph represents the velocity at each instant , it is evident ( § 27 ) that an elementary arc represents the velocity which must be ...
Page 133
... remarkable corollary that three pure strains produced one after another , in any piece of matter , each without rotation , may be so adjusted as to leave the body unstrained , but rotated through some angle about some axis . We shall ...
... remarkable corollary that three pure strains produced one after another , in any piece of matter , each without rotation , may be so adjusted as to leave the body unstrained , but rotated through some angle about some axis . We shall ...
Page 142
... remarkable proposition , and its converse , that if F ( x , y , z ) denote any function of the co - ordinates of any point of a body , and if every such point be displaced from its given position ( x , y , z ) to the point whose co ...
... remarkable proposition , and its converse , that if F ( x , y , z ) denote any function of the co - ordinates of any point of a body , and if every such point be displaced from its given position ( x , y , z ) to the point whose co ...
Page 144
... remarkable that fjas { 1 ( dy - de ) + m ( da - dy ) + n ( de da ) } dz dz - dx dy is the same for all surfaces having common curvilinear boundary ; and when a , ẞ , y are the components of a displacement from x , y , z , it is the ...
... remarkable that fjas { 1 ( dy - de ) + m ( da - dy ) + n ( de da ) } dz dz - dx dy is the same for all surfaces having common curvilinear boundary ; and when a , ẞ , y are the components of a displacement from x , y , z , it is the ...
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Common terms and phrases
acceleration action algebraic angular velocity anticlastic application arbitrary axis Cambridge centre of inertia circle co-ordinates coefficients component configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dt dy dx dy dy dy dy dz ellipsoid equal equations of motion equilibrium expression finite fixed force formula function give given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy Lagrange's linear mass measured momentum moving negative P₁ parallel particle path perpendicular polygon position principal axes principle quadratic quadratic function quantity radius rectangular resultant rigid body rolling roots rotation round simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values variable whole Y₁ αξ λ² аф
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