The Messenger of Mathematics, Volume 3

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Macmillan and Company, 1866 - Mathematics
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Page 133 - Newton's rule in its complete form may be stated as follows : — On writing the complete series of quadratic under the complete series of simple elements of fx in their natural order, the number of double permanences in the associated series, or...
Page 195 - The fundamental principle states that if one thing can be done in m different ways and, when it is done in any one of these ways, a second thing can be done in n different ways, and if a third thing can then be done in p ways, ... then the successive things can be done in mnp...
Page 86 - Let p denote the radius of curvature at any point of the curve, s the length of the arc of the curve measured from any fixed origin up to this point; /"*' then we require that I p ds should be a minimum.
Page 218 - ... is proportional to the product of the sines of the angles which...
Page 241 - It is a recognised principle, and one of great importance in these investigations, that when a problem is determinate any solution which satisfies all the requisite conditions, no matter how obtained, is the solution of the problem. In the case of fluid motion, when the initial circumstances and the conditions with respect to the boundaries of the fluid are given, the problem is determinate.
Page 34 - But the director of a conic is the locus of intersection of tangents at right angles to each other.
Page 6 - The tangents at the extremities of a focal chord intersect on the directrix, at E, as in the case of the parabola, but they are not at right angles.
Page 7 - Let (xv yj be the point of intersection of the tangents at the extremities of the chord (2).
Page 227 - Let z = f(x, y) be a function of two independent variables x and y. Relative maximum: f(x, y) is said to have a relative maximum at a point (a, b) if f(a,b)> f(a+hb + k) for small positive or negative values of h and k...
Page 33 - PROPOSITION XI. 123. The pairs of tangents from any point to a system of conies inscribed in the same quadrilateral form a pencil in involution, and conversely. Let four tangents to a conic intersect in the three pairs of points <', bb\ cc...

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