The Mathematician, Volum 3

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G. Bell, 1850
 

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Pàgina 98 - The sum of the squares of the reciprocals of the areas of the sections of an ellipsoid made by any three diametral planes at right angles to each other is constant.
Pàgina 317 - ... of invention and variety of resource, they are in many cases decidedly inferior to those furnished by the latter. In these respects both his published and his manuscript writings fully confirm the accuracy of the opinion expressed by the late Professor Davies, that " a familiar acquaintance with the works on geometry -which have been published in this country during the past and present century has led to the conviction, that Mr. Swale was undoubtedly the most independent and original geometer...
Pàgina 168 - ABCD is a quadrilateral inscribed in a circle whose centre is O, and E, F are the middle points of BC, CD.
Pàgina 317 - Swale was undoubtedly the most independent and original geometer of his time. Everything he wrote was more free from the impress of the writings of others, even where the subjects are the same ; and so elementary too, that we should hardly suppose it possible for two different methods to be purposed, than I find to be the case with any other geometer except Dr. Matthew ^Stewart. Swale's geometry, in fact, was his own invention, for he was singularly unacquainted with the writings of other geometers,...
Pàgina 317 - Everything he wrote was more free from the impress of the writings of others, even where the subjects are the same ; and so elementary, too, that we should hardly suppose it possible for two different methods to be proposed, than I find to be the case with any other geometer, except Dr. Matthew Stewart. Swale's geometry, in fact, was his own invention ; and I have been informed, by a mutual friend of his and mine, that he was singularly unacquainted with the writings of other geometers, even of the...
Pàgina 209 - A diameter of a curve is the locus of the middle points of a series of parallel chords.
Pàgina 131 - ... being therefore at right angles to every line it meets with in the plane of the circle ABC, is at right angles to that plane (4. 2. Sup.). Therefore the straight line drawn from the pole of any great circle to the centre of the sphere is at right angles to the plane of that circle ; and, conversely, a straight line drawn from the centre of the sphere perpendicular to the plane of any greater circle, meets the superficies of the sphere in the pole of that circle.
Pàgina 297 - is an arbitrary constant, и z' denotes any number; hence (5) holds true for all values of у, т being a constant. The constant m is called the Modulus of the system of logarithms whose base is a.
Pàgina 75 - 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...
Pàgina 291 - When two quantities are so related that a change in one causes a change in the other, the one is said to be a function of the other. The...

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