A Treatise on Infinitesimal Calculus: Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics, Volume 3University Press, 1868 - Calculus |
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Common terms and phrases
a₁ action-lines angle attracted particle balls beam catenary central axis centre of gravity components consequently constant coordinate axes curve determined direction-angles displacement distance dx dy dy dx dy dz ellipsoid equal equilibrium equilibrium-axis equilibrium-system force of translation forces acting geometrical given point Hence horizontal line impressed forces infinitesimal integration inversely law of attraction length line of action magnitude mass material particle matter moment-axis moment-centre momentum motion moving normal origin P₁ P₂ parallel forces parallelogram of forces perpendicular plate point of application position preceding pressure principal quantity radius resolved rest resultant couple rigid body rotation rotation-axis shell space sphere straight line string suppose surface system of forces tension theorem thickness and density three forces varies velocity-increment vertex vertical virtual velocities vis viva weight Y₁
Popular passages
Page 555 - When we contemplate the constituents of the planetary system from the point of view which this relation affords us, it is no longer mere analogy which strikes us — no longer a general resemblance among them, as individuals independent of each other, and circulating about the sun, each according to its own peculiar nature, and connected with it by its own peculiar tie. The resemblance is now perceived to be a true family likeness ; they are bound up in one chain — interwoven in one web of mutual...
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Page 5 - Admission to its sanctuary, and to the privileges and feelings of a- votary, is only to be gained by one means — sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any other of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range.
Page 69 - ... 7, 6, and 9 pounds respectively at the points A, B, D, E, F; AB = 3 feet, BD = 6 feet, DE = 5 feet, EF = 4 feet. Find the magnitude of the resultant, and the distance of its point of application, G, from A. Ans. R — 42 pounds. AG = 8| feet.
Page 473 - V (5) <7 which is the equation of a parabola with its axis vertical and the vertex the highest point of the curve. The distance, OB, between the point of projection and the point where the projectile strikes the horizontal plane is called the Range on the horizontal plane, and is the value of x when y = 0. Putting y = 0 in (3) of Art.
Page 554 - Of all the laws to which induction from pure observation has ever conducted man, this third law (as it is called) of Kepler may justly be regarded as the most remarkable, and the most pregnant with important consequences.
Page 252 - Every particle of matter in the universe attracts every other particle with a force that varies directly as the product of the masses of the particles and inversely as the square of the distance between them.
Page 557 - In this case, it is obvious that the plane of the circle of illumination would be perpendicular to a line drawn from the centre of the sun to the centre of the earth...
Page 490 - ... force between bodies as varying directly as their masses and inversely as the square of the distance between them; and would predict the elliptical planetary orbits that are in fact found in the solar system.
Page 264 - ... bodies is proportional to the product of their masses divided by the square of the distance between them.