Introduction to Quaternions |
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Page xii
... chord of contact , 38 , 39 ; examples , 40 ; equations of the sphere , with examples , 41 , 42 . ADDITIONAL EXAMPLES TO CHAPTER V. THE ELLIPSE · CHAPTER VI . 73-90 . 91-105 Equations of the ellipse , 43 ; properties of pp , 44 ...
... chord of contact , 38 , 39 ; examples , 40 ; equations of the sphere , with examples , 41 , 42 . ADDITIONAL EXAMPLES TO CHAPTER V. THE ELLIPSE · CHAPTER VI . 73-90 . 91-105 Equations of the ellipse , 43 ; properties of pp , 44 ...
Page 75
... 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 = − ( a3 + 2Sap + p2 ) , PR ...
... 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 = − ( a3 + 2Sap + p2 ) , PR ...
Page 76
... chords of section will form a triangle , the loci of the angular points of which are three straight lines respectively perpendicular to the lines which join the centres of the given circles ; and these three lines meet in a point . Let ...
... chords of section will form a triangle , the loci of the angular points of which are three straight lines respectively perpendicular to the lines which join the centres of the given circles ; and these three lines meet in a point . Let ...
Page 77
... chord in a circle whose 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 ...
... chord in a circle whose 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 ...
Page 79
... chord ( p ) and the tangent ( B ) . 38. To draw a tangent to a circle . 1. If we assume the first form of the equation , the centre being the origin , and assume also that the tangent is at right angles to the radius drawn to the point ...
... chord ( p ) and the tangent ( B ) . 38. To draw a tangent to a circle . 1. If we assume the first form of the equation , the centre being the origin , and assume also that the tangent is at right angles to the radius drawn to the point ...
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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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