A treatise on infinitesimal calculus, Volume 1University Press, 1852 - Calculus |
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Common terms and phrases
according affected algebraical angles applicable asymptote axis becomes branches calculated called changes sign Chapter circle coefficients consider constant continuous corresponding curve decreases derived derived-functions determine differential direction drawn dx dy dy dx dy dy eliminated equal equation equicrescent Evaluate examples expand expression f(xo factor finite fraction function geometrical give given greater Hence homogeneous function increases increments independent indicates infinite infinitesimal infinity involved less limits maximum means method multiplying negative observed origin partial particular passing plane positive powers quantity relation replaced represent respect result roots side similar Similarly straight line substituted successive suppose symbol tangent Theorem tion values vanish variables variation vary whence
Popular passages
Page 431 - When one medium is a vacuum, n is the ratio of the sine of the angle of incidence to the sine of the angle of refraction. retardation, & — optical path difference between two beams in an interferometer; also known as "optical path difference
Page 16 - It would, therefore, occupy 206265 times this interval or 3 years and 83 days to traverse the distance in question. Now as this is an inferior limit which it is already ascertained that even the brightest and therefore (in the absence of all other indications) the nearest stars exceed, what are we to allow for the distance of those innumerable stars of the smaller magnitudes which the telescope discloses to us ! What for the dimensions of the galaxy in whose remoter regions, as we have seen, the...
Page 281 - Find its equation. Show that the radius of curvature at each point of the curve is inversely proportional to the length of the normal intercepted between the point on the curve and the ?/-axis.
Page 14 - The powers, therefore, of our senses and mind place the limit to the finite ; but those magnitudes which severally transcend these limits, by reason of their being too great or too small, we call i...
Page 16 - It would, therefore, occupy 100000000 seconds, or upwards of three years, in such a journey, at the very lowest estimate. What, then, are we to allow for the distance of those innumerable stars of the smaller magnitudes which the telescope discloses to us ! If we admit the light of a star of each magnitude to be half that of the magnitude next above it, it will follow that a star of the first...
Page 281 - The Cycloid. The cycloid is traced out by a point in the circumference of a circle as the circle rolls along a straight line.
Page 244 - Find a point within a triangle such that the sum of the square of its distances from the three angular points is a minimum.
Page 356 - Conic, p = ed: which will denote an ellipse, a parabola, or an hyperbola, according as e is less than, equal to, or greater than unity.
Page 390 - MM'PP', we take the equation of this plane y = ax + ß (1), z indeterminate ; a being the tangent of the angle made with the axis of X by the trace PP', and equal to -~ = т...
Page 388 - As shown on p. 84 for the cycloid, the arc of the evolute is equal to the difference of the radii of curvature at its end-points.