A Treatise on Infinitesimal Calculus: Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics, Volumen 1
The University Press, 1852 - 540 páginas
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algebraical arbitrary functions asymptote axis becomes calculated change of sign changes sign Chapter circle consider constant coordinates corresponding cycloid decreases derived determine developable surface drawn dy _ eliminated equa equal equicrescent variable Evaluate explicit function expression factor finite and continuous finite quantity fraction geometrical given Hence homogeneous function hyperbola increases increments indeterminate indeterminate form infinite infinity intersection involving lines of curvature logarithm maxima and minima maximum or minimum means method minimum value negative normal sections numerator and denominator ordinate origin osculating plane parabola partial derived-functions particular values pass perpendicular plane curve plane of reference polar positive proper fraction radii radius of curvature result roots shewn Similarly straight line substituting suppose supposition symbols tangent plane Taylor's Series tesimal tion total differential vanish variation vary whence
Página 435 - 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
Página 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...
Página 289 - 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.
Página 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...
Página 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...
Página 289 - The Cycloid. The cycloid is traced out by a point in the circumference of a circle as the circle rolls along a straight line.
Página 252 - Find a point within a triangle such that the sum of the square of its distances from the three angular points is a minimum.
Página 423 - From a fixed point on the circumference of a circle chords are drawn, and on these as diameters circles are drawn.
Página 360 - Now the conic section is an ellipse, parabola, or hyperbola according as e is less than, equal to, or greater than unity.