# A Treatise on Infinitesimal Calculus, Containing Differential and Integral Calculus, Calculus of Variations, Applications to Algebra and Geometry, and Analytical Mechanics, Volumen 2

University Press, 1865

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Página 233 - Find the curves in which the perpendicular from the origin on the tangent is equal to the abscissa of the point of contact. [The circles r - 2a cos в.] 13.
Página 484 - A point moves on an ellipsoid so that its direction of motion always passes through the perpendicular from the centre of the ellipsoid on the tangent plane at any point ; shew that the curve traced out by the point is given by the intersection of the ellipsoid with the surface xm~" yn~l zl~m = constant, I, m, n being inversely proportional to the squares of the semiaxes of the ellipsoid.
Página 562 - Jujdy, du\ctz, are proportional to the direction cosines of the normal to the surface u — c, and therefore P, Q, R are proportional to the direction cosines of a tangent line to
Página vii - The short time which has elapsed since the publication of the first edition of this work, is sufficient evidence of the estimation in which it is held.
Página 323 - ... is equal to the product of the length of the curve and the length of the path described by the centroid of the curve.
Página 269 - Y will be identical, and all points will lie on a line passing through the origin and making an angle of 45° with the two axes.
Página 513 - F' (x) is the trigonometrical tangent of the angle between the axis of x and the tangent to the curve at the point (x, y). Art. 38. Let OM=x1, MN=h, Ffa+k)-Ffa) h then is the tangent of the inclination of the chord PQ to the axis of x. Hence Art. 101 amounts to asserting that at some point R between P and Q the tangent RT to the curve is parallel to PQ. We call this an illustration. When, however, the student has sufficiently...
Página 323 - Ü where e2= — . a2 (2) Find the area of the surface generated by the revolution of the catenary about the axis of X ; about the axis of Y.
Página 611 - By making *' = 0, we find the co-ordinates of the point where the normal meets the plane of xy, also, the length of the normal, intercepted between the surface and the plane of wy, is РнoB.
Página 448 - A common method of denoting the algebraic sum of a series of terms, all of which are of the same form, is to write only a single term preceded by the Greek letter 2.