The Mathematician, Volume 3G. Bell, 1856 |
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Termos e frases comuns
A. R. Clarke a₁ angular points axes axis bisects centre chord coefficients cone conic section conjugate coordinates cosec cubic equation denote diameter diametral plane directing cosines director draw drawn Elliott ellipse equal equation evidently expression geometry given circle given curve given points given surface Greatham hence hyperbola imaginary inscribed circle intersection James Cockle Lamesley locus m₁ Mathematician Messrs method middle point obtain P₁ P₂ parabola parallel pass perpendicular Peter Elliott plane of yz polar plane polar reciprocal pole polygon porism positive principal vertex problem PROP r₁ radii radius reciprocal curve reciprocal surfaces respect right angles roots second degree SECOND SOLUTION Seedley Shalbourne Shooter's Hill sides Simson sphere straight line substituting tangent plane tetrahedron theorem Thomas Weddle values vertex
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Página 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.
Página 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...
Página 168 - ABCD is a quadrilateral inscribed in a circle whose centre is O, and E, F are the middle points of BC, CD.
Página 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,...
Página 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...
Página 112 - A diameter of a curve is the locus of the middle points of a series of parallel chords.
Página 219 - The area of any triangle is equal to the product of the radius of...
Página 122 - If </> be the angle between the two rays, we have cos <£ = cos a' cos a" + cos /3' cos /3" + cos 7
Página 259 - Solution of Numerical Equations : in which by one uniform process, the imaginary as well as the real roots are easily determined.
Página 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.