Elements of Natural Philosophy, Volume 1 |
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Page 32
... parallel to the fixed line . 101. As an interesting example of this theorem , let us recur to the case of § 96 : —A circle may evidently be circumscribed about OBQA ; and it must be of invariable magnitude , since in it a chord of given ...
... parallel to the fixed line . 101. As an interesting example of this theorem , let us recur to the case of § 96 : —A circle may evidently be circumscribed about OBQA ; and it must be of invariable magnitude , since in it a chord of given ...
Page 33
... parallel to PS , PR is a diameter of the rolling circle , and R lies in a straight line AH drawn parallel to BC . Thus AR = BP . Produce QR to T , making RT = QR = PS . Evidently the curve AT , which is the locus of T , is similar and ...
... parallel to PS , PR is a diameter of the rolling circle , and R lies in a straight line AH drawn parallel to BC . Thus AR = BP . Produce QR to T , making RT = QR = PS . Evidently the curve AT , which is the locus of T , is similar and ...
Page 35
... parallel to OB , OA respectively . Then , expressing in two ways the area of the parallelogram IpOq , we have Hence Oq.IB = Op.Ia . Oq : Op :: w1 : w . In words , if on the axes OA , OB , we measure off from O lines Op , Oq ...
... parallel to OB , OA respectively . Then , expressing in two ways the area of the parallelogram IpOq , we have Hence Oq.IB = Op.Ia . Oq : Op :: w1 : w . In words , if on the axes OA , OB , we measure off from O lines Op , Oq ...
Page 36
... parallel planes in a rigid body which are parallel to each other in any two positions of the body . The parallel lines of the body perpendicular to these planes are of course parallel to each other in the two positions . Let C and C ...
... parallel planes in a rigid body which are parallel to each other in any two positions of the body . The parallel lines of the body perpendicular to these planes are of course parallel to each other in the two positions . Let C and C ...
Page 37
... 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 evident that all portions of AB will be equally inclined to the axis of the ...
... 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 evident that all portions of AB will be equally inclined to the axis of the ...
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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 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 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 P₁ P₂ parallel parallelogram of forces particle path pendulum perpendicular plane perpendicular portion position potential pressure principal axes principle produce projection proportional quantity radius radius of gyration reckoned rectangular 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