Introduction to Quaternions: With Numerous Examples |
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Page xii
... hyperbola in a form corre- sponding to those with Cartesian co - ordinates , with examples , 55 . ADDITIONAL EXAMPLES TO CHAPTER VII . PAGES . 59-72 73-90 91-105 106-127 CHAPTER VIII . CENTRAL SURFACES OF THE SECOND ORDER . xii CONTENTS .
... hyperbola in a form corre- sponding to those with Cartesian co - ordinates , with examples , 55 . ADDITIONAL EXAMPLES TO CHAPTER VII . PAGES . 59-72 73-90 91-105 106-127 CHAPTER VIII . CENTRAL SURFACES OF THE SECOND ORDER . xii CONTENTS .
Page xiii
... surfaces , 67 ; Pascal's hexagram , 68 ADDITIONAL EXAMPLES TO CHAPTER VIII . CHAPTER IX . FORMULE AND THEIR APPLICATION Formulæ , 69 , 70 ; examples , 71 . ADDITIONAL EXAMPLES TO CHAPTER IX . PAGES 128-153 154-181 CHAPTER X. VECTOR ...
... surfaces , 67 ; Pascal's hexagram , 68 ADDITIONAL EXAMPLES TO CHAPTER VIII . CHAPTER IX . FORMULE AND THEIR APPLICATION Formulæ , 69 , 70 ; examples , 71 . ADDITIONAL EXAMPLES TO CHAPTER IX . PAGES 128-153 154-181 CHAPTER X. VECTOR ...
Page 68
... surface of the second order . - COR . Ife = 1 , and the surface be cut by a plane perpendicular to DQ whose equation is Syp = c , the equation of the section is a2 + c2 - 2 , Sap = 0 , another plane , so that the section is a straight ...
... surface of the second order . - COR . Ife = 1 , and the surface be cut by a plane perpendicular to DQ whose equation is Syp = c , the equation of the section is a2 + c2 - 2 , Sap = 0 , another plane , so that the section is a straight ...
Page 71
... surface of the second order . 3. Prove that the section of this surface by a plane perpen- dicular to the line to which the generating lines are drawn perpen- dicular is a circle . 4. Prove that the locus of a point whose distances from ...
... surface of the second order . 3. Prove that the section of this surface by a plane perpen- dicular to the line to which the generating lines are drawn perpen- dicular is a circle . 4. Prove that the locus of a point whose distances from ...
Page 86
... surface required . Hence it is a sphere whose diameter is the line joining the origin with the given point . Ex . 4. Perpendiculars are drawn from a point on the surface of a sphere to all tangent planes , to find the locus of their ...
... surface required . Hence it is a sphere whose diameter is the line joining the origin with the given point . Ex . 4. Perpendiculars are drawn from a point on the surface of a sphere to all tangent planes , to find the locus of their ...
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Common terms and phrases
ALGEBRA ARITHMETIC Assistant Master aßy axis BEGINNERS bisects Cambridge centre chord circle Clifton College cone CONIC SECTIONS conjugate diameters constant drawn Edited ELEMENTARY TREATISE ellipse ellipsoid ENGLISH equal EXAMPLES FASNACHT Fcap find the locus G. E. FASNACHT GEOMETRY given lines given point gives GRAMMAR GREEK Hence hyperbola Illustrated intersection Introduction and Notes ISAAC TODHUNTER J. P. MAHAFFY LATIN Lecturer LL.D M.A. Cr m₁ MACMILLAN'S Mathematics middle points Owens College p₁ parabola parallelepiped parallelogram PRIMER Prof Professor quaternion revised right angles rotation Sapa Saß scalar School shews squares strain tangent plane tetrahedron Translated triangle Trinity College unit vectors Vaß vector parallel vector perpendicular Vẞy whence yẞ αβγ φρ
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