A Treatise on Infinitesimal Calculus: Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics, Volume 4The University Press, 1862 - Calculus |
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Common terms and phrases
a₁ a²x² angle angular velocity axes fixed axial components axis passing b₁ blow body rotates central principal centre of gravity cone confocal constant coordinate axes couple D'Alembert's principle d2x dt2 determined direction-cosines displacement distance dt dt dt dt2 dt2 earth ellipse equal equations of motion expressed fixed point given horizontal infinitesimal instantaneous axis integration invariable plane let us suppose line of action mass moment of inertia momental ellipsoid moments of inertia momentum momentum-increments motion of translation nutation origin oscillation P₁ parallel pendulum perpendicular plate polhode position principal axes principal moments principal plane quantities radius of gyration radius vector relative rotation-axis shews sphere spontaneous axis string surface system of particles theorem tion values velocity-increment vertical vis viva viva w₁ w₂
Popular passages
Page 298 - Newton discovered, as a fundamental law of nature, that every particle attracts every other particle with a force which varies directly as the product of the masses and inversely as the square of the distance between them.
Page 13 - To prove that the locus of the middle points of a system of parallel chords of a parabola is a straight line parallel to the axis of the parabola.
Page 542 - This proves the first part of the theorem. To prove the second part : Take any two lines of the system, 34 and 56.
Page 89 - ... bottom of which are formed by planes perpendicular to its axis, contains elastic fluid, the weight of which may be neglected. If the vessel revolve uniformly about its axis, find the pressure at any point of the fluid mass. 6. The motion of rotation of a rigid system acted on by any forces, about its centre of gravity, is the same as if the centre of gravity were fixed, and the same forces acted. A heavy beam moves about a horizontal axis passing through one extremity ; apply the preceding principle...
Page 93 - Conservation of vis viva, the Principle of the Conservation of the Motion of the Centre of Gravity, and the like.
Page 188 - Ip = /« — /„, or the polar moment of inertia is equal to the sum of the moments of inertia about any two axes at right angles to each other in the plane of the area and intersecting at the pole.
Page 38 - ... and the greater the gain of the dial upon the hand. The wheels of both dial and hand are constantly revolving in the direction opposite to that of the' motion of the hands of a watch. The belt of the hand-wheel runs always upon the rod, where its diameter is constant, and as the rod moves laterally under the little belts, guides are necessary to keep the belts themselves from moving laterally also. The proportions of the cones on the rod, and of the two wheels which carry the dial...
Page 91 - Thus it is proved that, in the case of a body acted on by any forces, the motion of the centre of gravity is the same as if...
Page 300 - When we say that a force varies directly as the mass of the attracting body, and inversely as the square of...
Page 120 - Si corporum systemata duo similia ex aequali particularum numero constent, et particuli correspondentes similes suit et proportionales, singulae in *uno systemate singulis in altero, et similiter sitae inter se, ac...