Elements of Natural Philosophy, Part 1 |
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Page 3
... considering the curve as a polygon whose sides are indefinitely small . Any two consecutive sides , of course , lie in a plane - and in that plane the curvature is measured as above ; but in a curve which is not plane the third side of ...
... considering the curve as a polygon whose sides are indefinitely small . Any two consecutive sides , of course , lie in a plane - and in that plane the curvature is measured as above ; but in a curve which is not plane the third side of ...
Page 5
... consider the invo- lutes described by different points of the string ; and these will , in general , be different curves . But the following section shows that there is but one evolute . P 22. Let AB be any curve , PQ a portion of an ...
... consider the invo- lutes described by different points of the string ; and these will , in general , be different curves . But the following section shows that there is but one evolute . P 22. Let AB be any curve , PQ a portion of an ...
Page 6
... considering the space described in an interval so short , that during its lapse the velocity does not sensibly alter in value . 26. When the point does not move uniformly , the velocity is variable , or different at different successive ...
... considering the space described in an interval so short , that during its lapse the velocity does not sensibly alter in value . 26. When the point does not move uniformly , the velocity is variable , or different at different successive ...
Page 7
... considering ( § 25 ) the motion for so short a time , that during that time the actual variation of speed may be small enough to be neglected . 28. In fact , if v be the velocity at either beginning or end , or at any instant , of an ...
... considering ( § 25 ) the motion for so short a time , that during that time the actual variation of speed may be small enough to be neglected . 28. In fact , if v be the velocity at either beginning or end , or at any instant , of an ...
Page 8
... consider motion in one plane , this is still true , only we have but two rectangular components . 31. These propositions are virtually equivalent to the following obvious geometrical construction : - To compound any two velocities as OA ...
... consider motion in one plane , this is still true , only we have but two rectangular components . 31. These propositions are virtually equivalent to the following obvious geometrical construction : - To compound any two velocities as OA ...
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Common terms and phrases
acceleration action amount angular velocity anticlastic attraction axis called Cambridge centre of gravity centre of inertia circle circular co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance ellipsoid elongation equal equations equilibrium external finite fixed point flexure fluid forces acting friction geometrical given force Hence hodograph horizontal infinitely small instant inversely kinetic energy length magnitude mass matter measured moment of inertia momentum moving normal section Octavo P. G. TAIT P₁ P₂ parallel particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular resultant 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 theory tion torsion uniform unit vertical whole wire
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