A Treatise on Infinitesimal Calculus: Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics, Band 1The University Press, 1852 |
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Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
a₁ algebraical angle asymptote axis becomes calculated change of sign changes sign circle coefficients consider constant curve d2 F d²x d²y d2y dx2 d³u d³y denominator derived-functions determine dr dy dx dr dx dx dx dy dx dy dy dx² dy dx dy dz dy² dy³ dz dy equal equation equicrescent variable explicit function expression f(xo factor finite quantity fraction geometrical given Hence homogeneous function increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithm loge Maclaurin's maxima and minima maximum or minimum minimum value negative parabola plane plane of reference positive radius Similarly straight line substituting suppose supposition symbol tangent tesimal Theorem tion total differential vanish variation versin whence
Beliebte Passagen
Seite 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...
Seite 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.
Seite 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...
Seite 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...
Seite 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.
Seite 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.
Seite 419 - From a fixed point on the circumference of a circle chords are drawn, and on these as diameters circles are drawn.
Seite 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...
Seite 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.
Seite 51 - In words, the derivative of the product of two functions is the sum of the products obtained by multiplying the derivative of each function by the other function.