Elements of Natural Philosophy, Volume 1 |
From inside the book
Results 1-5 of 47
Page 3
... passes from one position to the next by revolving about the tangent to the curve . 13. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the cur- vature lies is ...
... passes from one position to the next by revolving about the tangent to the curve . 13. Thus , as we proceed along such a curve , the curvature in general varies ; and , at the same time , the plane in which the cur- vature lies is ...
Page 4
... passing round the figure . This is true whether the polygon be closed or not . If closed , then , as long as it is not crossed , this sum is four right angles , —an extension of the result in Euclid , where all reëntrant polygons are ...
... passing round the figure . This is true whether the polygon be closed or not . If closed , then , as long as it is not crossed , this sum is four right angles , —an extension of the result in Euclid , where all reëntrant polygons are ...
Page 11
... passing through the origin . ( d ) When the velocity is uniform , but in a direction revolving uni- formly in a right circular cone , the motion of the point is in a circular helix whose axis is parallel to that of the cone . 42. When a ...
... passing through the origin . ( d ) When the velocity is uniform , but in a direction revolving uni- formly in a right circular cone , the motion of the point is in a circular helix whose axis is parallel to that of the cone . 42. When a ...
Page 12
... passing through that point ; and in this plane the areas traced out by the radius - vector are proportional to the times employed . This includes the case of a satellite or planet revolving about its primary , according to Kepler's ...
... passing through that point ; and in this plane the areas traced out by the radius - vector are proportional to the times employed . This includes the case of a satellite or planet revolving about its primary , according to Kepler's ...
Page 13
... passes through the point , its moment vanishes . This is the case of a motion in which the acceleration is directed to a fixed point , and we thus prove the second theorem of § 45 , that in the case supposed the areas described by the ...
... passes through the point , its moment vanishes . This is the case of a motion in which the acceleration is directed to a fixed point , and we thus prove the second theorem of § 45 , that in the case supposed the areas described by the ...
Other editions - View all
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.