A treatise on infinitesimal calculus, Volume 1University Press, 1852 - Calculus |
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Page xviii
... Asymptotes to Plane Curves referred to Rectangular Coordinates . 191. On rectilinear asymptotes .. 299 192. Method of determining asymptotes by means of expansion in descending powers of a 300 193. Examples of the method 301 194 ...
... Asymptotes to Plane Curves referred to Rectangular Coordinates . 191. On rectilinear asymptotes .. 299 192. Method of determining asymptotes by means of expansion in descending powers of a 300 193. Examples of the method 301 194 ...
Page xix
... asymptotes out of the plane of reference . 197. Curvilinear asymptotes SECTION 3. - On Direction of Curvature and Points of Inflexion . 198. Direct proof that a curve is convex or concave downwards d2y dx2 according as is positive or ...
... asymptotes out of the plane of reference . 197. Curvilinear asymptotes SECTION 3. - On Direction of Curvature and Points of Inflexion . 198. Direct proof that a curve is convex or concave downwards d2y dx2 according as is positive or ...
Page xx
... Asymptotes to Polar Curves . 224. Means of determining rectilinear asymptotes 225. Examples in illustration ... 226. Asymptotic circles .. SECTION 4. — On Direction of Curvature and Points of Inflexion . 227. A curve is concave or ...
... Asymptotes to Polar Curves . 224. Means of determining rectilinear asymptotes 225. Examples in illustration ... 226. Asymptotic circles .. SECTION 4. — On Direction of Curvature and Points of Inflexion . 227. A curve is concave or ...
Page 224
... 1 . Required to find the maxima and minima values of y , having given y3 + x3 - 3axy = 0 . dy x2 - ay = - dx y2 — ax ' the equation which = 0 , if a2 = ay 224 [ 133 . MAXIMA AND MINIMA OF Means of determining rectilinear asymptotes.
... 1 . Required to find the maxima and minima values of y , having given y3 + x3 - 3axy = 0 . dy x2 - ay = - dx y2 — ax ' the equation which = 0 , if a2 = ay 224 [ 133 . MAXIMA AND MINIMA OF Means of determining rectilinear asymptotes.
Page 266
... asymptote at the pole of the circle of infinite radius opposite to a , and has re- turned in the direction EF , the branch in the direction of E being a continuation of that in the direction of D. Similarly the branch in the direction F ...
... asymptote at the pole of the circle of infinite radius opposite to a , and has re- turned in the direction EF , the branch in the direction of E being a continuation of that in the direction of D. Similarly the branch in the direction F ...
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Common terms and phrases
a₁ algebraical angle asymptote axis becomes calculated change of sign changes sign circle coefficients consider curve d2 F d2F d2F d²x d²y d2y dx2 d³y decreases denominator derived-functions determine dr dy dx dr dx dx dx dy dx dy dx dx² dy dx dy dy dy dz dy² dy³ equal equation equicrescent Evaluate explicit function expression f(xo factor finite quantity fraction geometrical given Hence homogeneous function hyperbola increases increments indeterminate form infinite infinitesimal Infinitesimal Calculus infinity involved logarithm maxima and minima maximum or minimum minimum value negative origin particular value plane of reference positive proper fraction radius real roots roots of f(x Similarly straight line substituting suppose supposition symbol tangent Taylor's Series tion vanish versin 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...
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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...
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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.