Introduction to Quaternions |
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Page xii
... PARABOLA AND HYPERBOLA Equation of the parabola in terms of øp , with examples , 52-54 ; equations of the parabola , ellipse and hyperbola in a form corre- sponding to those with Cartesian co - ordinates , with examples , 55 ...
... PARABOLA AND HYPERBOLA Equation of the parabola in terms of øp , with examples , 52-54 ; equations of the parabola , ellipse and hyperbola in a form corre- sponding to those with Cartesian co - ordinates , with examples , 55 ...
Page 105
... is bisected by the smaller ellipse at Q. 13. If TP , TQ be tangents to an ellipse , and PCP ' be the diameter through P , then PQ is parallel to CT . CHAPTER VII . THE PARABOLA AND HYPERBOLA . 51. As EX . 6. ] 105 THE ELLIPSE .
... is bisected by the smaller ellipse at Q. 13. If TP , TQ be tangents to an ellipse , and PCP ' be the diameter through P , then PQ is parallel to CT . CHAPTER VII . THE PARABOLA AND HYPERBOLA . 51. As EX . 6. ] 105 THE ELLIPSE .
Page 106
... parabola which may be conveniently developed by a process more analogous to that of the Cartesian geometry . This process we shall develope presently . In the meantime we proceed to give a brief outline of the application to the parabola ...
... parabola which may be conveniently developed by a process more analogous to that of the Cartesian geometry . This process we shall develope presently . In the meantime we proceed to give a brief outline of the application to the parabola ...
Page 107
... ) , and there results by ( 6 ) whence x + Sa ̄1p = 1 , 1 α = a - aSa ̄1p ; ( x - 1 ) = 2 i.e. vector AT = -vector AN ( by 11 ) ; .. line AT AN ; = and ST = xa gives ST2 = ( a — ART . 52. ] THE PARABOLA AND HYPERBOLA . 107.
... ) , and there results by ( 6 ) whence x + Sa ̄1p = 1 , 1 α = a - aSa ̄1p ; ( x - 1 ) = 2 i.e. vector AT = -vector AN ( by 11 ) ; .. line AT AN ; = and ST = xa gives ST2 = ( a — ART . 52. ] THE PARABOLA AND HYPERBOLA . 107.
Page 109
... parabola , the ratio of the rectangles of their segments is always ART . 54. ] THE PARABOLA AND HYPERBOLA . 109.
... parabola , the ratio of the rectangles of their segments is always ART . 54. ] THE PARABOLA AND HYPERBOLA . 109.
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Common terms and phrases
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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