Elements of Natural Philosophy |
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Page 5
... portion of an involute , pP , qQ positions of the free part of the string . It will be seen at once that these must be tangents to the arc P AB at p and q . Also the string at any stage , as pP , ultimately revolves about . Hence pP is ...
... portion of an involute , pP , qQ positions of the free part of the string . It will be seen at once that these must be tangents to the arc P AB at p and q . Also the string at any stage , as pP , ultimately revolves about . Hence pP is ...
Page 15
... portion of a conic section and S one focus . Let P move so that SP describes equal areas in equal times , that is ( § 48 ) , let the velocity be inversely as the perpendicular SY from S to the tangent to the orbit . If ABP be an ellipse ...
... portion of a conic section and S one focus . Let P move so that SP describes equal areas in equal times , that is ( § 48 ) , let the velocity be inversely as the perpendicular SY from S to the tangent to the orbit . If ABP be an ellipse ...
Page 28
... portion of a parabola , and is gone over twice in opposite directions by the moving point in each complete period . If the periods be not exactly as 1 : 2 the form of the path pro- duced by the combination changes gradually from one to ...
... portion of a parabola , and is gone over twice in opposite directions by the moving point in each complete period . If the periods be not exactly as 1 : 2 the form of the path pro- duced by the combination changes gradually from one to ...
Page 35
... portions . If PQR be any subsequent position of the generating circle , Q and S the new positions of A and B , QPS is of course a right angle . If , therefore , QR be drawn parallel tó PS , PR is a diameter of the rolling circle , and R ...
... portions . If PQR be any subsequent position of the generating circle , Q and S the new positions of A and B , QPS is of course a right angle . If , therefore , QR be drawn parallel tó PS , PR is a diameter of the rolling circle , and R ...
Page 39
... portions . E of the surface of a vertical right cylinder , the motion of DF parallel to AC will become a rotation about the axis of the cylinder , and the necessary accompaniment of vertical motion will remain un- changed . As it is ...
... portions . E of the surface of a vertical right cylinder , the motion of DF parallel to AC will become a rotation about the axis of the cylinder , and the necessary accompaniment of vertical motion will remain un- changed . As it is ...
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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