## A treatise on infinitesimal calculus, containing differential and integral calculus, calculus of variations, applications to algebra and geometry, and analytical mechanics, Volume 4 |

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### Common terms and phrases

angle angular velocity axes fixed axial components axis passing becomes blow body rotates central ellipsoid centre of gravity centrifugal forces coefficients cone confocal constant coordinate axes corresponding couple cube curve D'Alembert's principle determined differential direction-cosines displacement distance earth elastic ellipse ellipsoid of gyration equa equal equations of motion equilibrium evident expressed fixed in space fixed point focal conic Hence horizontal infinitesimal initial instantaneous axis integration intersection invariable axis invariable plane isochronous length Let the rotation-axis let us suppose line of action machine mass momental ellipsoid moments of inertia momentum momentum-increments moving system nutation origin oscillation parallel pendulum perpendicular plate polhode position pressure principal moments principal plane quantities radii radius of gyration radius vector respectively second degree shews sphere string surface system of particles theorem tion values velocity-increment vertex vertical vibrations viva

### 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 536 - ... x = r sin 6 cos <f>, y — r sin 6 sin <f>, z = r cos 6.

Page 122 - Remembering that the resistance of the air varies as the square of the velocity, it might easily be shown that the strength should be at least eight times, instead of twice, as great. Passing to the question of power. The soaring of birds is a most important fact, of which no one who has taken the trouble to make observations has any doubt. Though it was lately the subject of a...

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...