## The mathematical principles of mechanical philosophy |

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### Common terms and phrases

accelerating force action angle angular velocity arch axes axis beam calculate catenary centre of gravity co-ordinates conditions of equilibrium conic section consequence constant cos2 curve density determine differential direction distance disturbing force dt dt dx dy dy dz Earth ellipse equal equations of motion equilibrium extrados fluid forces acting formula friction function given heavenly bodies Hence horizontal impulsive forces inclination instant integration invariable plane inversely law of attraction length line of nodes longitude magnitude mass mean motion measured molecules Moon moving nearly neglect observations oscillation parallel pendulum perigee perihelion perpendicular plane position pressure principal axes principle Prob Prop prove quantities radius ratio resolved respect resultant rigid body shew shewn sphere spheroid square suppose surface syzygy tion uniform varies vertical Virtual Velocities voussoirs weight

### Popular passages

Page 505 - A uniform ladder, 10 feet long, rests with one end against a smooth vertical wall and the other on the ground, the coefficient of friction between the ladder and the ground being J.

Page x - D'Alembert, was the Precession of the equinoxes and the Nutation of the earth's axis, according to the theory of gravitation.

Page 236 - Gravitation is, that every particle of matter attracts every other particle with a force which varies directly as the mass of the attracting particle, and inversely as the square of the distance.

Page 66 - ... is the length of the path described by the centre of gravity of the area.

Page 4 - ... method, and the forces are called kinetic forces. Weight is the name given to the pressure which the attraction of the earth causes a body to exert. Hence, since static forces produce pressure, we may take, as the unit of force, a pressure of one pound (Art. 11). Therefore, the magnitude of a force may be measured statically by the pressure it will produce upon some body, and expressed in pounds. This is called the Static...

Page 69 - The portions of the lever into which the fulcrum divides it are called the arms of the lever : when the arms are in the same straight line, it is called a straight lever, and in other cases a bent lever.

Page 83 - Mechanical Power is the Wedge. This is a triangular prism, and is used to separate obstacles by introducing its edge between them and then thrusting the wedge forward. This is effected by the blow of a hammer or other such means, which produces a violent pressure for a short time, sufficient to overcome the greatest forces. 168.

Page 6 - If two forces act on a body in opposite directions their resultant is equal to their difference and acts in the direction of the greater; thus two forces acting in opposite directions and equal to 9 and 4 Ibs.

Page 229 - Hence the orbit described about this centre of force will be an ellipse, parabola, or hyperbola according as the velocity is less than, equal to, or greater than that from infinity.

Page 71 - ... grate. Scissors, shears, nippers, pincers, and other similar instruments are composed of two levers of the first kind; the fulcrum being the joint or pivot, and the weight the resistance of the substance to be cut or seized ; the power being the fingers applied at the other end of the levers. The brake of a pump is a lever of the first kind; the pump-rods and piston being the weight to be raised.