## The Mathematical Principles of Mechanical Philosophy, and Their Application to the Theory of Universal Gravitation |

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### Common terms and phrases

action angle application arch attraction axes axis beam body calculation called cause centre of gravity co-ordinates consequently constant couple curve described determine direction distance disturbing dt dt Earth effect ellipse equal equations equilibrium extremity figure fixed forces acting function given gives greater Hence horizontal integration length limits magnitude manner mass mean measured moments Moon motion move nearly observed obtain orbit origin P₁ parallel particle passing perpendicular plane portions position pressure principle produced projection PROP prove quantities radius resolved respect rest resultant shew space sphere square suppose surface uniform unit values varies velocity vertical weight

### Popular passages

Page 525 - 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 70 - ... is the length of the path described by the centre of gravity of the area.

Page 235 - 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 4 - Weight is the name given to the pressure which the attraction of the Earth causes a body to exert on another with which it is in contact.

Page 198 - There are no perfectly hard inelastic bodies, as assumed by the early and some of the modern writers on mechanics. 3. The elasticity, as measured by the velocity of recoil divided by the velocity of impact, is a ratio which (though it decreases as the velocity increases) is nearly constant when the same rigid bodies are struck together with considerably different...

Page 73 - A Lever is an inflexible rod moveable only about a fixed axis, which is called the fulcrum. 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 ; in other cases a lent lever.

Page 542 - Let us express a in terms of the ratio of the centrifugal force at the equator to the equatorial gravity. Call this ratio m, which is small in the case of the earth, being of the same order as g.

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 22 - Now the weight of a body may be considered as the resultant of the weights of the different elementary portions of the body, acting in parallel and vertical lines. In this case, the point above described as the centre of parallel forces is called the centre of gravity of the body.

Page 228 - 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.