Parabolas sentence example

parabolas
  • were parabolas in most cases within the limits of error of his observations.
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  • This value of 0 is the same for all parabolas which pass through D and E and have their axes at right angles to KL.
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  • As the loads move over the girder, the points C, D, E describe the parabolas M1, M2, M3 i the middle ordinates of which are 4W 1 1, 4W 2 1, and 4W3l.
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  • The three lightly W2 dotted parabolas are the curves of maximum moment for each of the loads taken separately.
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  • In the geometry of plane curves, the term parabola is often used to denote the curves given by the general equation a' n x n = ym+n, thus ax= y 2 is the quadratic or Apollonian parabola; a 2 x = y 3 is the cubic parabola, a 3 x = y4 is the biquadratic parabola; semi parabolas have the general equation ax n-1 = yn, thus ax e = y 3 is the semicubical parabola and ax 3 = y 4 the semibiquadratic parabola.
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  • Diverging parabolas are cubic curves given by the equation y 2 = 3 -f-bx 2 -cx+d.
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  • The same holds for the four points B, C, D, E and so on; but since a parabola is uniquely determined by the direction of its axis and by three points on the curve, the successive parabolas ABCD, BCDE, CDEF ...
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  • The sun is a small target for a meteorite coming from infinity to hit, and if this considerable quantity reaches its mark, a much greater amount will circulate round the sun in parabolas, and there is no evidence of it where it would certainly make itself felt, in perturbations of the planets.
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  • The genera may be arranged as follows: 1,2,3,4 redundant hyperbolas 5,6 defective hyperbolas 7,8 parabolic hyperbolas 9 hyperbolisms of hyperbola To „ II „ „ parabola 12 trident curve 13 divergent parabolas 14 cubic parabola; and thus arranged they correspond to the different relations of the line infinity to the curve.
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  • Thirdly, the three intersections by the line infinity may be coincident and real; or say we have a threefold point: this may be an inflection, a crunode or a cusp, that is, the line infinity may be a tangent at an inflection, and we have the divergent parabolas; a tangent at a crunode to one branch, and we have the trident curve; or lastly, a tangent at a cusp, and we have the cubical parabola.
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  • It is to be remarked that the classification mixes together non-singular and singular curves, in fact, the five kinds presently referred to: thus the hyperbolas and the divergent parabolas include curves of every kind, the separation being made in the species; the hyperbolisms of the hyperbola and ellipse, and the trident curve, are nodal; the hyperbolisms of the parabola, and the cubical parabola, are cuspidal.
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  • The five divergent parabolas are curves each of them symmetrical with regard to an axis.
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  • It should also be remarked that even if the curves were not parabolas, it would always be possible to draw parabolas to agree closely with the observations over a restricted range of temperature.
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  • Akad., 1899) have gone back to Tait's method at high temperatures, employing arcs of parabolas for limited ranges.
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  • If one of the foci be at infinity, the conics are confocal parabolas, which may also be regarded as parabolas having a common focus and axis.
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  • He discovered a simpler method of quadrating parabolas than that of Archimedes, and a method of finding the greatest and the smallest ordinates of curved lines analogous to that of the then unknown differential calculus.
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  • The second includes a "Method for the Quadrature of Parabolas," and a treatise "on Maxima and Minima, on Tangents, and on Centres of Gravity," containing the same solutions of a variety of problems as were afterwards incorporated into the more extensive method of fluxions by Newton and Leibnitz.
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  • parabolas of joy, and their authors.
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  • In tangential q, r) co-ordinates the inscribed and circumscribed conics take the forms Xqr+µrp+vpq=o and 1/ X p+ 1 /µ q + V y r = o; these are parabolas when X++'=° and V X = 1 / µ 1 / v= o respectively.
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  • The divergent parabolas are of five species which respectively belong to and determine the five kinds of cubic curves; Newton gives (in two short paragraphs without any development) the remarkable theorem that the five divergent parabolas by their shadows generate and exhibit all the cubic curves.
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  • He also discovered the remarkable fact that the parabolas described (in a vacuum) by indefinitely numerous projectiles discharged from the same point with equal velocities, but in all directions have a paraboloid of revolution for their envelope.
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