Introduction to Quaternions |
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Page xiii
... diameters and diame- tral planes , with examples , 60-64 ; the cone , 65 , 66 ; examples on central surfaces , 67 ; Pascal's hexagram , 68 ADDITIONAL EXAMPLES TO CHAPTER VIII . CHAPTER IX . FORMULE AND THEIR APPLICATION Formulæ , 69 ...
... diameters and diame- tral planes , with examples , 60-64 ; the cone , 65 , 66 ; examples on central surfaces , 67 ; Pascal's hexagram , 68 ADDITIONAL EXAMPLES TO CHAPTER VIII . CHAPTER IX . FORMULE AND THEIR APPLICATION Formulæ , 69 ...
Page 73
... diameter of the circle , centre C , radius = a , P any point . If vector CD = a , CP = p , we have p3 = — a3 ............... ... ... ... ... ... .. ( 1 ) . A D If however AP = P CP = p - a , we have ( p − a ) 3 = - a3 .... ... ( 2 ) ...
... diameter of the circle , centre C , radius = a , P any point . If vector CD = a , CP = p , we have p3 = — a3 ............... ... ... ... ... ... .. ( 1 ) . A D If however AP = P CP = p - a , we have ( p − a ) 3 = - a3 .... ... ( 2 ) ...
Page 75
... diameter is 04 . Ex . 6. A chord QR is drawn parallel to the diameter AB of a circle : P is any point in AB ; to prove that Let then But PQ + PRPA ' + PB2 . CQ = P , CR = p ' , PC = a ; PQ ' = - ( vector PQ ) 3 == - ( a + p ) 3 ...
... diameter is 04 . Ex . 6. A chord QR is drawn parallel to the diameter AB of a circle : P is any point in AB ; to prove that Let then But PQ + PRPA ' + PB2 . CQ = P , CR = p ' , PC = a ; PQ ' = - ( vector PQ ) 3 == - ( a + p ) 3 ...
Page 77
... diameter is AB , QN perpen- dicular to AB . AM is taken equal to BN , and MP is drawn perpendicular to AB to meet AQ in P ; the locus of P is the cissoid . then Let vector APT , AC = a , AM = yα , AQ = xπ ; y : 12 - y : x , by the ...
... diameter is AB , QN perpen- dicular to AB . AM is taken equal to BN , and MP is drawn perpendicular to AB to meet AQ in P ; the locus of P is the cissoid . then Let vector APT , AC = a , AM = yα , AQ = xπ ; y : 12 - y : x , by the ...
Page 78
... diameter is a unit parallel to a and the origin a point in the circumference ; and ẞ a tangent vector at the origin . Otherwise , 1 1 + x2 Sap = SPP = 1 + x3 x . : ( Sap ) + ( SBP ) = Sap , or - p2 = Sap . Or , again , whence = a + xß ...
... diameter is a unit parallel to a and the origin a point in the circumference ; and ẞ a tangent vector at the origin . Otherwise , 1 1 + x2 Sap = SPP = 1 + x3 x . : ( Sap ) + ( SBP ) = Sap , or - p2 = Sap . Or , again , whence = a + xß ...
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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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