Introduction to Quaternions |
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Page xii
... CIRCLE AND SPHERE Equations of the circle , with examples , 36 , 37 ; tangent to circle and chord of contact , 38 , 39 ; examples , 40 ; equations of the sphere , with examples , 41 , 42 . ADDITIONAL EXAMPLES TO CHAPTER V. THE ELLIPSE ...
... CIRCLE AND SPHERE Equations of the circle , with examples , 36 , 37 ; tangent to circle and chord of contact , 38 , 39 ; examples , 40 ; equations of the sphere , with examples , 41 , 42 . ADDITIONAL EXAMPLES TO CHAPTER V. THE ELLIPSE ...
Page 52
... circle ; AB = a , BC = ß , CD = y , DA = 8 ; TaTẞTY 8 . αβγ = TS Let unit vectors along AB , BC , CD , DA be a ' , B ' , y ' , & ; and let the exterior angles at B and D be and respectively ; then a'ß'y ' = ( − cos 0 + e sin 0 ) y ...
... circle ; AB = a , BC = ß , CD = y , DA = 8 ; TaTẞTY 8 . αβγ = TS Let unit vectors along AB , BC , CD , DA be a ' , B ' , y ' , & ; and let the exterior angles at B and D be and respectively ; then a'ß'y ' = ( − cos 0 + e sin 0 ) y ...
Page 71
... circle . 4. Prove that the locus of a point whose distances from two given straight lines have a constant ratio is a surface of the second order . 5. A straight line moves parallel to a fixed plane and is ter- minated by two given ...
... circle . 4. Prove that the locus of a point whose distances from two given straight lines have a constant ratio is a surface of the second order . 5. A straight line moves parallel to a fixed plane and is ter- minated by two given ...
Page 72
... between the triangles ABC , ABD . 12. Vap Vẞp + ( Vaẞ ) = 0 is the equation of a hyperbola in p , the asymptotes being parallel to a , ß . CHAPTER V. THE CIRCLE AND SPHERE . 36. Equations of 72 [ CHAP . IV . QUATERNIONS .
... between the triangles ABC , ABD . 12. Vap Vẞp + ( Vaẞ ) = 0 is the equation of a hyperbola in p , the asymptotes being parallel to a , ß . CHAPTER V. THE CIRCLE AND SPHERE . 36. Equations of 72 [ CHAP . IV . QUATERNIONS .
Page 73
Philip Kelland, Peter Guthrie Tait. CHAPTER V. THE CIRCLE AND SPHERE . 36. Equations of the circle . Let AD be the diameter of the circle , centre C , radius = a , P any point . If vector CD = a , CP = p , we have p3 = — a3 ...
Philip Kelland, Peter Guthrie Tait. CHAPTER V. THE CIRCLE AND SPHERE . 36. Equations of the circle . Let AD be the diameter of the circle , centre C , radius = a , P any point . If vector CD = a , CP = p , we have p3 = — a3 ...
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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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