The Mathematician, Volum 2G. Bell, 1856 |
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Frases i termes més freqüents
a₁ angular points arbitrary axes b₁ bisect centre of gravity chord circle circumscribed coefficients collinear axis conic section conjugate coordinates corresponding points cos² denote diagonals diameters directrices divided draw ellipse ellipsoid equation fixed point G. W. Hearn generatrices geometrical given plane given points given surface Greatham hence hyperbola hyperboloid inertia inscribed integral locus logarithms Mathematician meet moment of inertia multiplied nth degree P₁ P₂ parabola parallel parallelogram parallelopiped perpendicular plane curve points of intersection polygon positive properties quadrilateral r₁ radii radius ratio respectively second degree second order SECOND SOLUTION Shalbourne Shooter's Hill sides similarly sin² sphere spherical square straight line tangent tetrahedron theorem Thomas Weddle three given u₁ values vertex vertical x₁ Y₁
Passatges populars
Pàgina 71 - B' sin B sin C' sin C sin A cos a = cos 6 cos c + sin b sin c cos A. with similar formulae for cos 6 and cos c. cos A = — cos B cos C + sin B sin C.
Pàgina 166 - Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians.
Pàgina 334 - The sum of the squares of the reciprocals of the areas of the sections of an ellipsoid made by any three diametral planes at right angles to each other is constant.
Pàgina 331 - V ; shew that if 0 be the limiting value of the angle of inclination of the beam to the horizon at which it will rest, W its weight, and R, R
Pàgina 212 - A merchant bought a cask of spirits for $48, and sold a quantity exceeding three-fourths of the whole by two gallons, at a profit of 25 per cent. He afterwards sold the remainder at such a price as to clear 60 per cent, by the whole transaction, but if he had sold the whole quantity at the latter price, he would have gained 176 per cent.
Pàgina 329 - ... join DB. Then AD is equal to the given straight line. And the angle ACB is equal to the sum of the angles CDB and CBD (I. 32), that is, to twice the angle CDB (I. 5). Therefore the angle ADB is half of the angle in the given segment. Hence we have the following synthetical solution. Describe on AB a segment of a circle containing an angle equal to half the angle in the given segment. With A as centre, and a radius equal to the given straight line, describe a circle. Join A with a point of intersection...
Pàgina 19 - F(z) given by (2) we obtain _^,1_=РтГ 1 1 о«, 04 " where the upper or lower sign is to be taken according as the...
Pàgina 276 - This point is called the centre of vibration, and it is obvious that the time of vibration of a compound pendulum is the same as that of a simple pendulum whose length is equal to the distance of the centre of vibration from the point of suspension.
Pàgina 95 - t' is the distance between the points (x¡, y,, z¡) and (x, y, z) if a, b, c, are dc's of the line. Vector equation of a lin« passing through the point A(o) and parallel to vector 6 is r '= a + К b for scalar X.
Pàgina 69 - ... 0. It is therefore evident that the Archimedean axiom is not satisfied by this system of lunar angles. As for the addition of such angles, we may define the sum of the angles formed by two tangent circles as the angle formed by that tangent circle the reciprocal of whose radius is equal to the sum of the reciprocals of the radii of the two given circles. If then we have any circle through...