Elements of Natural Philosophy, Volume 1 |
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Page 2
... infinite force . It is useful to con- sider at the outset various theorems connected with the geometrical notion of ... smaller . The curvature at any point is the reciprocal of the radius of this circle for a small arc on each side of ...
... infinite force . It is useful to con- sider at the outset various theorems connected with the geometrical notion of ... smaller . The curvature at any point is the reciprocal of the radius of this circle for a small arc on each side of ...
Page 41
... infinite in number , and the angles of bending infinitely small , but such that their sum may be finite , we have our plane surface bent into a curved surface , which is of course ' developable ' ( § 125 ) . 129. Lift a square of paper ...
... infinite in number , and the angles of bending infinitely small , but such that their sum may be finite , we have our plane surface bent into a curved surface , which is of course ' developable ' ( § 125 ) . 129. Lift a square of paper ...
Page 49
... infinitely small portion bears to the volume of this portion at the same instant . 164. To find the differential equation of continuity , imagine a space fixed in the interior of a fluid , and consider the fluid which flows into this ...
... infinitely small portion bears to the volume of this portion at the same instant . 164. To find the differential equation of continuity , imagine a space fixed in the interior of a fluid , and consider the fluid which flows into this ...
Page 54
... infinitely small . Hence the above statement . It is often convenient to use Newton's Fluxional notation for the rate of change of any quantity per unit of 1 T time . In this notation ( § 28 ) v stands for ( v , -v ) ; so that the rate ...
... infinitely small . Hence the above statement . It is often convenient to use Newton's Fluxional notation for the rate of change of any quantity per unit of 1 T time . In this notation ( § 28 ) v stands for ( v , -v ) ; so that the rate ...
Page 65
... infinite space . But it is remarkable that the first law of motion enables us ( § 215 , below ) to explain what may ... small and trivial cases as well as to the grandest phenomena we can conceive . A curling - stone , projected along a ...
... infinite space . But it is remarkable that the first law of motion enables us ( § 215 , below ) to explain what may ... small and trivial cases as well as to the grandest phenomena we can conceive . A curling - stone , projected along a ...
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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.