Introduction to Quaternions: With Numerous ExamplesMacmillan, 1882 - 232 σελίδες |
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Σελίδα 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 ...
Σελίδα 73
... diameter of the circle , centre C , radius = a , P any point . If vector CD = a , CP = p , we have If however we have p2 = — a3 .... . ( 1 ) . A AP = P , CP = p - a , ( pa ) = = - ( 2 ) . If O be any point , we have OP = p , OC = y , CP ...
... diameter of the circle , centre C , radius = a , P any point . If vector CD = a , CP = p , we have If however we have p2 = — a3 .... . ( 1 ) . A AP = P , CP = p - a , ( pa ) = = - ( 2 ) . If O be any point , we have OP = p , OC = y , CP ...
Σελίδα 75
... diameter is OA . 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 PQ2 + PR2 = PA2 + PB3 . CQ = p , CR = p ' , PC = a ; PQ- ( vector PQ ) 3 == ( a + p ) : = − ( a2 + ...
... diameter is OA . 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 PQ2 + PR2 = PA2 + PB3 . CQ = p , CR = p ' , PC = a ; PQ- ( vector PQ ) 3 == ( a + p ) : = − ( a2 + ...
Σελίδα 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 . Let vector AP = π , AC = a , then AM ya , AQ = : = = Xπ ; y : 12 - y : x , by ...
... 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 . Let vector AP = π , AC = a , then AM ya , AQ = : = = Xπ ; y : 12 - y : x , by ...
Σελίδα 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 = х SBp = ; 1 + x2 . : ( Sap ) 2 + ( Sẞp ) 3 = Sap , or - p2 = Sap . Or , again , whence -1 ...
... 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 = х SBp = ; 1 + x2 . : ( Sap ) 2 + ( Sẞp ) 3 = Sap , or - p2 = Sap . Or , again , whence -1 ...
Άλλες εκδόσεις - Προβολή όλων
Introduction to Quaternions, with Numerous Examples Philip Kelland,Peter Guthrie Tait Πλήρης προβολή - 1873 |
Introduction to Quaternions, with Numerous Examples. Philip Kelland Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2010 |
Introduction to Quaternions, with Numerous Examples P. Kelland,P. G. Tait Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2017 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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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