Introduction to QuaternionsMacmillan and Company, 1882 - 232 |
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Strona 99
... conjugate . 3. The equation of the chord of contact is Sσ = 1 . For Spp1 ( 45. Cor . 2 ) is satisfied by the values of p at Q and at R , and since Spp1 or Sσp = 1 is the equation N R T of a straight line , π being a constant vector ( 32 ...
... conjugate . 3. The equation of the chord of contact is Sσ = 1 . For Spp1 ( 45. Cor . 2 ) is satisfied by the values of p at Q and at R , and since Spp1 or Sσp = 1 is the equation N R T of a straight line , π being a constant vector ( 32 ...
Strona 100
... conjugate diameters . 7 . a = 4 ̄1 ¥ a = − ( aiSiya + bjSj ↓ a ) - B = 4 ̄14ẞ = — ( aiSi ¥ ß + bjSj ¥ ß ) ; - .. Vaß ab Vij ( SiyaSjyß - SiyẞSjya ) . If now we call k the unit vector perpendicular to the plane of the ellipse , we get ...
... conjugate diameters . 7 . a = 4 ̄1 ¥ a = − ( aiSiya + bjSj ↓ a ) - B = 4 ̄14ẞ = — ( aiSi ¥ ß + bjSj ¥ ß ) ; - .. Vaß ab Vij ( SiyaSjyß - SiyẞSjya ) . If now we call k the unit vector perpendicular to the plane of the ellipse , we get ...
Strona 104
... conjugate diameters . Let PQRS be the parallelogram . PQ = a , PS = ß , then wherefore Similarly CP = p , CS = p ' ; CQ = p + a , CR = p ' + a ; .. Spop = 1 , S ( p + a ) $ ( p + a ) = 1 ; 2.Sppa + Sapa = 0 . 2Sp'pa + Sapa = 0 ; - :: S ...
... conjugate diameters . Let PQRS be the parallelogram . PQ = a , PS = ß , then wherefore Similarly CP = p , CS = p ' ; CQ = p + a , CR = p ' + a ; .. Spop = 1 , S ( p + a ) $ ( p + a ) = 1 ; 2.Sppa + Sapa = 0 . 2Sp'pa + Sapa = 0 ; - :: S ...
Strona 105
... conjugate . 7. Also diameters which coincide with the diagonals of any parallelogram formed by tangents at the extremities of conjugate diameters are conjugate . 8. The angular points of these parallelograms lie on an ellipse similar to ...
... conjugate . 7. Also diameters which coincide with the diagonals of any parallelogram formed by tangents at the extremities of conjugate diameters are conjugate . 8. The angular points of these parallelograms lie on an ellipse similar to ...
Strona 120
... conjugate semi - diameters . EXAMPLES . ( 3 ) . Ex . 1. One diagonal of a parallelogram whose sides are the co - ordinates being the radius vector , the other diagonal is parallel to the tangent . We have CN = ta , NQ = B , and the ...
... conjugate semi - diameters . EXAMPLES . ( 3 ) . Ex . 1. One diagonal of a parallelogram whose sides are the co - ordinates being the radius vector , the other diagonal is parallel to the tangent . We have CN = ta , NQ = B , and the ...
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A. S. WALPOLE A. W. VERRALL ALGEBRA ARITHMETIC Assistant Master aßy axis BEGINNERS bisects Cambridge centre chord circle cone CONIC SECTIONS conjugate diameters constant drawn Edited ELEMENTARY TREATISE ellipse ellipsoid ENGLISH equal EXAMPLES Exercises Fcap find the locus G. E. FASNACHT GEOMETRY given lines given point gives GRAMMAR GREEK Hence HISTORY hyperbola Illustrated intersection Introduction and Notes ISAAC TODHUNTER J. P. MAHAFFY LATIN Litt Litt.D LL.D M.A. BOOK M.A. Cr MACMILLAN'S Mathematics middle points parabola parallelepiped parallelogram PRIMER Prof Professor quaternion revised right angles rotation Sapa Saß scalar School shews Spop squares strain tangent plane tetrahedron Translated triangle Trinity College unit vectors values Vaß vector parallel vector perpendicular Vẞy whence yẞ αβγ φρ
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