Introduction to Quaternions, with Numerous Examples |
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Common terms and phrases
axis bisects centre chord circle cone conjugate diameters constant diagonals drawn ellipse ellipsoid equal find the equation find the locus given lines given point given straight lines gives Hence hyperbola intersection line which joins m₁ mean point middle points multiplication notation parabola parallelepiped parallelogram quadrilateral Quaternions right angles Saß scalar second order semi-diameters shews sides Similarly simple shear squares strain Tait tangent plane tensor tetrahedron three vectors triangle unit vectors values Vaß vector parallel vector perpendicular whence α² αα αβ αβγ αγ αδ αδαρ β² βα βγ βγδ βδ γ² Γαβ γβ γδ δαβ δρ ηβ ναβ ρ² Σαρ Σαφα Σρφρ φα φπ φρ
Popular passages
Page 9 - Any two sides of a triangle are together greater than the third side.
Page 90 - A point moves so that the sum of the squares of its distances from the points (0, 0), (1, 0) is constant.
Page 10 - FG [Hypothesit. and joined towards the same parts by the straight lines BE, CH. But straight lines which join the extremities of equal and parallel straight lines towards the same parts are themselves equal and parallel.
Page 91 - Thus a parabola is the locus of a point which moves so that its distance from a fixed point is equal to its distance from a fixed straight line (see fig.
Page 71 - Find the locus of a point whose distances from two given straight lines are in a given ratio.
Page 67 - Find the locus of a point such that the ratio of its distances from two fixed points is constant.
Page 6 - Hamilton extended algebra to space : ' ' He had done a considerable amount of good work, obstructed as he was, when about the year 1843, he perceived clearly the obstruction to his progress in the shape of an old law, which prior to that time, had appeared like a law of common sense. The law in question is known as the commutative law of multiplication. Presented in its simplest form it is nothing more than this : ' five times three is the same as three times five' ; more generally, it appears under...
Page 91 - IF we define a conic section as "the locus of a point which moves so that its distance from a fixed point bears a constant ratio to its distance from a fixed straight line
Page 153 - a where p is the perpendicular from the centre on the tangent plane, r the distance from the focus, and A, B the constants of integration.
Page 7 - A vector is the representative of transference through a given distance, in a given direction.