Introduction to QuaternionsMacmillan and Company, 1882 - 232 |
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Strona 52
... expression - cos + esin 0 , we have seen that it may be regarded as a versor through an angle in a certain direction . Now if we write in place of 0 in this expression it assumes the form cos 0 - esin 0 , which must on the same ...
... expression - cos + esin 0 , we have seen that it may be regarded as a versor through an angle in a certain direction . Now if we write in place of 0 in this expression it assumes the form cos 0 - esin 0 , which must on the same ...
Strona 129
... expressions approaches in value to the first alone : that is , for the tangent plane , Sẞop = 0 , where ẞ is a vector along that plane . If be the vector to a point in the tangent plane , π = = p + xß ; and - .. § ( π − p ) & p = xSB ...
... expressions approaches in value to the first alone : that is , for the tangent plane , Sẞop = 0 , where ẞ is a vector along that plane . If be the vector to a point in the tangent plane , π = = p + xß ; and - .. § ( π − p ) & p = xSB ...
Strona 155
... expression at pleasure . By bearing this in mind the reader will readily apprehend the demonstrations which follow , even in cases where we have studied brevity . Again , S. aßy S. ( Saß + Vaß ) y = = S. yVaß , ( by 1. a ) , = S.y ( Saß ...
... expression at pleasure . By bearing this in mind the reader will readily apprehend the demonstrations which follow , even in cases where we have studied brevity . Again , S. aßy S. ( Saß + Vaß ) y = = S. yVaß , ( by 1. a ) , = S.y ( Saß ...
Strona 159
... expressions being equated , and the common terms deleted , there results 15 . 16 . 17 . SS . aßy = VaßSyd + VßySad + VyaSßd ........................ . ( 14 ) . S.aßys = S. ( S. aßy + V. aßy ) 8 = S . ( V. aẞy ) d = S . ( aSBy - ẞSay + ...
... expressions being equated , and the common terms deleted , there results 15 . 16 . 17 . SS . aßy = VaßSyd + VßySad + VyaSßd ........................ . ( 14 ) . S.aßys = S. ( S. aßy + V. aßy ) 8 = S . ( V. aẞy ) d = S . ( aSBy - ẞSay + ...
Strona 160
... expressions . § . αβγδε = - 5. εδγβα , Γ . αβγδε = Γ . εδγβα ...... .. ( 18 ) . 70. Many of these formulæ might have been proved differ- ently , and some of them more directly , by assuming for instance that a , ß , y are not in the ...
... expressions . § . αβγδε = - 5. εδγβα , Γ . αβγδε = Γ . εδγβα ...... .. ( 18 ) . 70. Many of these formulæ might have been proved differ- ently , and some of them more directly , by assuming for instance that a , ß , y are not in the ...
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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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