Treatise on Natural Philosophy, Volume 1, Part 1At the University Press, 1879 - Mechanics, Analytic |
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Page v
... denote the investigation of laws in the material world , and the deduction of results not directly observed . Observation , classification , and description of phenomena necessarily precede Natural Philosophy in every department of ...
... denote the investigation of laws in the material world , and the deduction of results not directly observed . Observation , classification , and description of phenomena necessarily precede Natural Philosophy in every department of ...
Page 3
... denote Curvature the inclination of its tangent , at any point x , y , to OX . Hence curve . of a plane dy 0 = tan - 1 ; dx and , by differentiation with reference to any independent variable t , we have de . = Also , dy d dx dx d'y ...
... denote Curvature the inclination of its tangent , at any point x , y , to OX . Hence curve . of a plane dy 0 = tan - 1 ; dx and , by differentiation with reference to any independent variable t , we have de . = Also , dy d dx dx d'y ...
Page 7
... denote the direction cosines of the osculating plane , given by the preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is ...
... denote the direction cosines of the osculating plane , given by the preceding formulæ . Curvature and tortu- osity . curvature ( compare 10. The integral curvature , or whole change of direction of Integral an arc of a plane curve , is ...
Page 17
... denote by f the resultant acceleration . Hence the direction cosines of the plane of these two lines are dyd'z - dzd'y { ( dyd3z — dzd3y ) 2 + ( dzd2x − dxď3z ) 2 + ( dxd3y— dyd3x ) " } } ' - etc. These ( 9 ) show that this plane is ...
... denote by f the resultant acceleration . Hence the direction cosines of the plane of these two lines are dyd'z - dzd'y { ( dyd3z — dzd3y ) 2 + ( dzd2x − dxď3z ) 2 + ( dxd3y— dyd3x ) " } } ' - etc. These ( 9 ) show that this plane is ...
Page 55
... denotes any positive or negative integer . Consider the integral F ( x ) dx a2 + x2 c where a , c , c ' denote any three given quantities . dx less than F ( 2 ) [ a2 + a2 ro Its value is dx and greater than F ( ) a2 + x2 , if z and denote ...
... denotes any positive or negative integer . Consider the integral F ( x ) dx a2 + x2 c where a , c , c ' denote any three given quantities . dx less than F ( 2 ) [ a2 + a2 ro Its value is dx and greater than F ( ) a2 + x2 , if z and denote ...
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Common terms and phrases
acceleration action algebraic altered angular velocity anticlastic application axis Cambridge centre of inertia circle co-ordinates coefficients component condition configuration constant corresponding course curvature curve cycloidal cylinder denote determined differential equation direction cosines displacement distance dt dt dx dy dy dy dy dz ellipsoid elongation equal equations of motion equilibrium expression finite fixed force formula function geometrical given gyrostatic harmonic motions Hence impulse infinitely small instant integral kinetic energy length linear momentum moving negative osculating plane P₁ parallel particle perpendicular polygon position principal axes quadratic quadratic function quantity radius ratio rectangular resultant right angles rigid body rolling roots rotation round shear simple harmonic simple harmonic motions solution spherical harmonic spherical surface St John's College strain suppose tangent plane theorem tion values whole Y₁ λ² аф
Popular passages
Page 241 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it may be compelled by impressed forces to change that state.