Treatise on Natural Philosophy, Volume 1, Issue 1University Press, 1879 - Calculators |
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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 . 0 = tan- dy ; dx and , by differentiation with reference to any independent variable t , we have d do dy dx = 1 + ( dy dx d'y - dy d'x dx2 + dy ...
... denote Curvature the inclination of its tangent , at any point x , y , to OX . Hence curve . 0 = tan- dy ; dx and , by differentiation with reference to any independent variable t , we have d do dy dx = 1 + ( dy dx d'y - dy d'x dx2 + dy ...
Page 5
... denote the angle LOL ' . We have , by the elements of analytical geometry , cos 80 = aa ' + bb ' + cc ' . ( 3 ) ; = ( a + a ' ) cos 80 m = , 1/2 ( b + b ' ) cos 80 ( c + c ' ) n = cos , 80 . ( 4 ) ; a ' @ = - a 2 sin 80 ' B = = b ' - b ...
... denote the angle LOL ' . We have , by the elements of analytical geometry , cos 80 = aa ' + bb ' + cc ' . ( 3 ) ; = ( a + a ' ) cos 80 m = , 1/2 ( b + b ' ) cos 80 ( c + c ' ) n = cos , 80 . ( 4 ) ; a ' @ = - a 2 sin 80 ' B = = b ' - b ...
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 - dzd3y { ( dyd3z — dzd3y ) 2 + ( dzď2x − dxd3z ) 2 + ( dxd3y— dyd3x ) 3 } * - 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 - dzd3y { ( dyd3z — dzd3y ) 2 + ( dzď2x − dxd3z ) 2 + ( dxd3y— dyd3x ) 3 } * - etc. " These ( 9 ) show that this plane is ...
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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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