Elements of Natural Philosophy, Volume 1 |
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Page 13
... radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence in this case the velocity at any point is inversely as ...
... radius - vector are proportional to the times ; for , as we have seen , the moment of the velocity is double the area traced out by the radius - vector in unit of time . 48. Hence in this case the velocity at any point is inversely as ...
Page 15
... radius - vector is pro- portional to that perpendicular to a fixed line : and therefore the radius - vector of any point is proportional to the distance of that point from a fixed line - a property belonging exclusively to the conic ...
... radius - vector is pro- portional to that perpendicular to a fixed line : and therefore the radius - vector of any point is proportional to the distance of that point from a fixed line - a property belonging exclusively to the conic ...
Page 16
... radius ; being an angle of nearly . П = 57 ° 29578 ... = 57 ° 17′44 ′′ .8 56. The angular velocity of a point in a plane is evidently to be found by dividing the velocity perpendicular to the radius - vector by the length of the radius ...
... radius ; being an angle of nearly . П = 57 ° 29578 ... = 57 ° 17′44 ′′ .8 56. The angular velocity of a point in a plane is evidently to be found by dividing the velocity perpendicular to the radius - vector by the length of the radius ...
Page 17
... radius - vector ; and therefore ( § 59 ) directly as the angular velocity . Hence the arc of PQ , described in any time , is proportional to the corresponding angle - vector in the orbit , i.e. to the angle through which the tangent to ...
... radius - vector ; and therefore ( § 59 ) directly as the angular velocity . Hence the arc of PQ , described in any time , is proportional to the corresponding angle - vector in the orbit , i.e. to the angle through which the tangent to ...
Page 21
... radius is described . For in the fig . , the acceleration of Q ( by § 36 ) is V2 QQ along QO . Supposing , for a moment , QO to represent the magnitude of this ac- celeration , we may resolve it into QP , PO . The acceleration of P is ...
... radius is described . For in the fig . , the acceleration of Q ( by § 36 ) is V2 QQ along QO . Supposing , for a moment , QO to represent the magnitude of this ac- celeration , we may resolve it into QP , PO . The acceleration of P 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 cloth co-ordinates component configuration consider constant cosine couple curvature curve cylinder denote density described diagram displacement distance elements ellipse ellipsoid elongation equal equations equilibrium external point Extra fcap finite 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 Natural Philosophy normal section Oxford P₁ parallel particle path pendulum 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 theory tion torsion uniform unit vertical whole wire
Popular passages
Page 161 - that every particle of matter in the universe attracts every other particle, with a force whose direction is that of the line joining the two, and whose magnitude is directly as the product of their masses, and inversely as the square of their distances from each other.
Page 65 - Every body continues in its state of rest or of uniform motion in a straight line, except in so far as it is compelled by force to change that state.
Page 28 - Fourier's theorem is not only one of the most beautiful results of modern analysis, but may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.
Page 161 - Newton generalized the law of attraction into a statement that every particle of matter in the universe attracts every other particle with a force which varies directly as the product of their masses and inversely as the square of the distance between them; and he thence deduced the law of attraction for spherical shells of constant density.
Page 66 - Change of motion is proportional to the impressed force and takes place in the direction of the straight line in which the force acts.
Page 68 - To every action there is always an equal and contrary reaction; or, the mutual actions of any two bodies are always equal and oppositely directed in the same straight line.
Page 130 - UNTIL we know thoroughly the nature of matter and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question.