Treatise on Natural Philosophy, Volume 1, Issue 1At the University Press, 1879 - Mechanics, Analytic |
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Page xvii
... Length , founded on artificial Metallic Standards - Measures of Length , Surface , Volume , Mass . and Work Clock - Electrically controlled Clocks - Chronoscope - Diagonal Scale Vernier - Screw Screw - Micrometer - Sphero- meter ...
... Length , founded on artificial Metallic Standards - Measures of Length , Surface , Volume , Mass . and Work Clock - Electrically controlled Clocks - Chronoscope - Diagonal Scale Vernier - Screw Screw - Micrometer - Sphero- meter ...
Page 2
... length of the curve according to the notation below ) , is called the curvature . To exemplify this , suppose two tangents drawn to a circle , and radii to the points of contact . The angle between the tangents is the change of ...
... length of the curve according to the notation below ) , is called the curvature . To exemplify this , suppose two tangents drawn to a circle , and radii to the points of contact . The angle between the tangents is the change of ...
Page 3
... length of the arc or path described by a point as the independent variable . On this supposition we have 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d ̧3x + dy d ̧3y ) , where we denote by the suffix to the letter d , the independent ...
... length of the arc or path described by a point as the independent variable . On this supposition we have 0 = d ( ds2 ) = d ( dx2 + dy3 ) = 2 ( dx d ̧3x + dy d ̧3y ) , where we denote by the suffix to the letter d , the independent ...
Page 4
... length of the curve . To express the radius of curvature , the direction cosines of the osculating plane , and the tortuosity , of a curve not in one plane , in terms of Cartesian triple co - ordinates , let , as before , So be the ...
... length of the curve . To express the radius of curvature , the direction cosines of the osculating plane , and the tortuosity , of a curve not in one plane , in terms of Cartesian triple co - ordinates , let , as before , So be the ...
Page 5
... length ds . We have 80 2 sin 80 sin 80 1 = δε P 88 when ds is infinitely small ; and in the same limit . ( 7 ) dx 1 = m = ds dy ds ' dz n == ; ds dx dy dz a ' - a = d b ' b = d c'c d . ( 8 ) ; ds ds ' ds bc ' - b'c = dy , dz d ds ds ...
... length ds . We have 80 2 sin 80 sin 80 1 = δε P 88 when ds is infinitely small ; and in the same limit . ( 7 ) dx 1 = m = ds dy ds ' dz n == ; ds dx dy dz a ' - a = d b ' b = d c'c d . ( 8 ) ; ds ds ' ds bc ' - b'c = dy , dz d ds ds ...
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Common terms and phrases
acceleration according action actual altered amount angle angular velocity application axes axis becomes body called Cambridge centre circle co-ordinates coefficients complete component condition configuration consider constant corresponding course curvature curve denote described determined differential direction displacement distance edition equal equations equilibrium Example expression finite fixed force function give given harmonic Hence inertia infinitely small instant integral kinetic energy length less mass matter mean measured motion moving natural negative observations parallel particle particular path period perpendicular plane position present principle problem produced proved quantity radius reference relative remain remarkable respectively resultant rigid rolling roots rotation round side simple solution space spherical strain suppose surface tangent theorem tion turn unit University values whole
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.