The Elements of the Differential and Integral Calculus: With Numerous Examples |
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Common terms and phrases
abscissas acceleration algebraic function angle approaches zero area inclosed Ax=0 Ax ax² axis Ay Ax body CHAPTER circular sectors concave constant cos² curvature cycloid Definition Denote derivative differential direction displacement distance double integration dx dx dx dy dx x=x0 dy dx equation EXAMPLE EXERCISES feet Find the area Find the coördinates Find the length force formulas function given increases without limit infinite infinitesimal initial line mass moment of inertia motion negative ordinates corresponding P₁ P₂ parabola parallel particle perpendicular plane positive preceding article radius rectangles required area respectively revolution Rolle's Theorem sec² Simpson's Rule sin² single valued speed subtangent surface tangent line Taylor's Theorem Theorem unit valued and continuous variable velocity x-axis x=xo xy-plane y-axis Δα
Popular passages
Page 361 - 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 296 - ... form : — When any forces whatever act on a body, then, whether the body be originally at rest or moving with any velocity and in any direction, each force produces in the body the exact change of motion which it would have produced if it had acted singly on the body originally at rest.
Page 352 - ... attracts m at the distance r from m: m' J = K~^ . 246. It will be shown later (Art. 253) that the attraction of a homogeneous sphere at any external point is the same as if the mass of the sphere were concentrated at its center. Hence if m...
Page 75 - Assuming that the work of driving a steamer through the water varies as the cube of her speed, show that her most economical rate per hour against a current running с miles per hour is 3c/'2 miles per hour.