Elements of Natural Philosophy |
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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 ...
... 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 ...
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 . 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 . 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 . ข = 28. In fact , if v be the velocity at either beginning or end , or at any instant , of ...
... 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 . ข = 28. In fact , if v be the velocity at either beginning or end , or at any instant , of ...
Page 8
... consider motion in one plane , this is still true , only we have but two rectangular com- ponents . B 31. These propositions are virtually equivalent to the following obvious geometrical construction : — To compound any two velocities ...
... consider motion in one plane , this is still true , only we have but two rectangular com- ponents . B 31. These propositions are virtually equivalent to the following obvious geometrical construction : — To compound any two velocities ...
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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 cord 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 weight whole wire