Elements of Natural Philosophy, Volume 1 |
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Page 13
... fixed point , and we thus prove the second theorem of § 45 , that in the case supposed the areas described by the radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area ...
... fixed point , and we thus prove the second theorem of § 45 , that in the case supposed the areas described by the radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area ...
Page 14
... fixed point , which has just been shown to be a constant quantity . Other examples of these principles will be met with in the chapters on Kinetics . 49. If , as in § 35 , from any fixed point , lines be drawn at every instant ...
... fixed point , which has just been shown to be a constant quantity . Other examples of these principles will be met with in the chapters on Kinetics . 49. If , as in § 35 , from any fixed point , lines be drawn at every instant ...
Page 15
... fixed point , and if the hodograph be a circle , the orbit must be a conic section of which the fixed point is a focus . But we may also prove this important proposition as follows : Let A be the centre of the circle , and O the ...
... fixed point , and if the hodograph be a circle , the orbit must be a conic section of which the fixed point is a focus . But we may also prove this important proposition as follows : Let A be the centre of the circle , and O the ...
Page 16
... fixed one , as the rate of increase of the angle contained by them ; but unless their line of intersection remain fixed , or at all events parallel to itself , a somewhat more laboured statement is required to give a complete ...
... fixed one , as the rate of increase of the angle contained by them ; but unless their line of intersection remain fixed , or at all events parallel to itself , a somewhat more laboured statement is required to give a complete ...
Page 17
... fixed point , the acceleration varies inversely as the square of the distance of the moving point from the fixed point . 62. From §§ 61 , 52 , it follows that when a particle moves with acceleration towards a fixed point , varying ...
... fixed point , the acceleration varies inversely as the square of the distance of the moving point from the fixed point . 62. From §§ 61 , 52 , it follows that when a particle moves with acceleration towards a fixed point , varying ...
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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