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angular points axes axis becomes bisects Castillon centre chord coefficients cone conic section conjugate construction coordinates corresponding cosec cubic equation denote determine diameter diametral plane directing cosines director draw drawn Elliott ellipse equal evidently expression fraction function geometers geometry given circle given curve given points given surface hence hyperbola imaginary inscribed circle join Lamesley locus Mathematician Messrs method middle point Multiply Nicholas Smyth obtain origin parabola paraboloid parallel pass perpendicular Peter Elliott Pi Pi Pi plane of yz polar plane polar reciprocal pole polygon porism positive principal vertex problem projection Prop radii radius reciprocal curve reciprocal surfaces relation respect result right angles roots second degree Second Solution Seedley segment Shalbourne Shooter's Hill sides similarly Simson's sphere straight line substituting tangent plane tangent plane applied tetrahedron theorem touches values vertex Wimbledon
Pàgina 319 - ... 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 319 - 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 319 - 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 219 - The area of any triangle is equal to the product of the radius of...
Pàgina 259 - Solution of Numerical Equations : in which by one uniform process, the imaginary as well as the real roots are easily determined.
Pàgina 299 - 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...