Introduction to QuaternionsMacmillan and Company, 1882 - 232 |
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Strona 51
... = - Say , Say ac cos B Sa ( a + iẞ ) a2 + ab sin C = a2 + bc xSaẞ = ysiaß ; .. y b x = с bc v LE um cist a2 + bc ' + which being symmetrical in b and c shews that CF 4-2 ART . 29. ] VECTOR MULTIPLICATION AND DIVISION . 51.
... = - Say , Say ac cos B Sa ( a + iẞ ) a2 + ab sin C = a2 + bc xSaẞ = ysiaß ; .. y b x = с bc v LE um cist a2 + bc ' + which being symmetrical in b and c shews that CF 4-2 ART . 29. ] VECTOR MULTIPLICATION AND DIVISION . 51.
Strona 52
Philip Kelland, Peter Guthrie Tait. which being symmetrical in b and c shews that CF , AL intersect in the same point in which BK , AL intersect . BO c2 COR . Since = BK a2 + bc ' со b2 we have = CF a2 + bc ; AO bc also = BD a2 + bc AO ...
Philip Kelland, Peter Guthrie Tait. which being symmetrical in b and c shews that CF , AL intersect in the same point in which BK , AL intersect . BO c2 COR . Since = BK a2 + bc ' со b2 we have = CF a2 + bc ; AO bc also = BD a2 + bc AO ...
Strona 69
... shews that p lies in a plane through O perpendicular to AB ( 33. Cor . 2 ) . The second and third equations give x = y = 2 ( SBp + SBy Syp ) ( SBY ) -1 2 ( Syp + SBY SBP ) ( Spy ) -1 Now ( 2 ) gives , by squaring , " - 4c2 = 4a2 + x2ß2 ...
... shews that p lies in a plane through O perpendicular to AB ( 33. Cor . 2 ) . The second and third equations give x = y = 2 ( SBp + SBy Syp ) ( SBY ) -1 2 ( Syp + SBY SBP ) ( Spy ) -1 Now ( 2 ) gives , by squaring , " - 4c2 = 4a2 + x2ß2 ...
Strona 74
... shews that Tp has two values corresponding to each value of Up , the product of which is c2 - a2 . Therefore , & c . Ex . 3. If two circles cut one another , the straight line which joins the points of section is perpendicular to the ...
... shews that Tp has two values corresponding to each value of Up , the product of which is c2 - a2 . Therefore , & c . Ex . 3. If two circles cut one another , the straight line which joins the points of section is perpendicular to the ...
Strona 79
... shews that the angles in the same segment of a circle are equal to one another . Further , the form of the right - hand side of the equation , viz . -SBUp , shews that the angle in the segment is equal to the sup- plement of the angle ...
... shews that the angles in the same segment of a circle are equal to one another . Further , the form of the right - hand side of the equation , viz . -SBUp , shews that the angle in the segment is equal to the sup- plement of the angle ...
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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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