Elements of Natural Philosophy |
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Page 9
... equal increments in successive equal periods of time . It is then measured by the increment of velocity , which would have been generated in a unit of time had the acceleration remained throughout that unit the same as at its ...
... equal increments in successive equal periods of time . It is then measured by the increment of velocity , which would have been generated in a unit of time had the acceleration remained throughout that unit the same as at its ...
Page 10
... equal ( to V ) , and there- fore PQS is a circle whose centre is O. The direction of acceleration at A is parallel to the tangent at P , that is , is per- pendicular to OP , i.e. to Aa , and is therefore that of the radius AC . Now P ...
... equal ( to V ) , and there- fore PQS is a circle whose centre is O. The direction of acceleration at A is parallel to the tangent at P , that is , is per- pendicular to OP , i.e. to Aa , and is therefore that of the radius AC . Now P ...
Page 13
... equal to OBD . Hence the sum of the two half - moments together with half the area of the parallelogram is equal to AOB together with BOD , that is to say , to the area of the whole figure OABD . But ABD , a part of this figure , is equal ...
... equal to OBD . Hence the sum of the two half - moments together with half the area of the parallelogram is equal to AOB together with BOD , that is to say , to the area of the whole figure OABD . But ABD , a part of this figure , is equal ...
Page 14
... equal areas in equal times . III . The square of the periodic time [ in an elliptic orbit ] is pro portional to the cube of the major axis . Sections 45-47 , taken in connexion with the second of these laws , show that the acceleration ...
... equal areas in equal times . III . The square of the periodic time [ in an elliptic orbit ] is pro portional to the cube of the major axis . Sections 45-47 , taken in connexion with the second of these laws , show that the acceleration ...
Page 22
... equal to the diagonal of a parallelogram de- scribed on lengths equal to their am- plitudes measured on lines meeting at an angle equal to their difference of epochs ; and of epoch differing from their epochs by angles equal to those ...
... equal to the diagonal of a parallelogram de- scribed on lengths equal to their am- plitudes measured on lines meeting at an angle equal to their difference of epochs ; and of epoch differing from their epochs by angles equal to those ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called centimetre centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant corresponding cosine couple curvature curve cylinder denote density described diagram displacement distance ellipse ellipsoid elongation equal equations equilibrium external point finite fixed point flexure fluid forces acting formulae friction geometrical given force Hence hodograph horizontal inclined infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section P₁ parallel parallelogram particle path pendulum perpendicular plane perpendicular portion position pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular relative right angles rigid body rotation round shear shell sides simple harmonic motion solid angle space spherical surface spiral square straight line strain stress suppose tangent theorem tion torsion uniform unit vertical vibrations weight whole wire