Introduction to Quaternions |
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Page 32
... operator on that which follows : in other words that aß shall read a into ẞ ' , and denote a operating on ß . 6 16. As in the Cartesian Geometry , so here we indicate the position of a point in space by its relation to three axes ...
... operator on that which follows : in other words that aß shall read a into ẞ ' , and denote a operating on ß . 6 16. As in the Cartesian Geometry , so here we indicate the position of a point in space by its relation to three axes ...
Page 34
... operator on j the duty of turning j through a right angle as if by a left - handed turn with a cork - screw handle , thus throwing jup from the plane xy ; when , on the other hand , j is the operator and i the vector operated on , a ...
... operator on j the duty of turning j through a right angle as if by a left - handed turn with a cork - screw handle , thus throwing jup from the plane xy ; when , on the other hand , j is the operator and i the vector operated on , a ...
Page 45
... operator of the same β α character ask ore ( as we have now called the corresponding unit vector ) ; with this difference only , that whereas - k or e as an operator would turn a through a right angle , cos 0 + € sin ✪ turns it , in ...
... operator of the same β α character ask ore ( as we have now called the corresponding unit vector ) ; with this difference only , that whereas - k or e as an operator would turn a through a right angle , cos 0 + € sin ✪ turns it , in ...
Page 46
... operator Y β about the same axis in the same direction acting on ẞ , it will bring it into the position y . E B 0 But it is evident that acting on a would at once have brought it into the position γ . γ α This is equivalent to the fact ...
... operator Y β about the same axis in the same direction acting on ẞ , it will bring it into the position y . E B 0 But it is evident that acting on a would at once have brought it into the position γ . γ α This is equivalent to the fact ...
Page 47
... operator . ( 3 ) Now we have already seen ( 19. 1 ) that e3 = -1 ; = +1 . Conversely , if e " , n must be an odd number ; if e " = - 1 , n must be an odd multiple of 2 ; and if e " = + 1 , n must be an even multiple of 2 . ( 4 ) When a ...
... operator . ( 3 ) Now we have already seen ( 19. 1 ) that e3 = -1 ; = +1 . Conversely , if e " , n must be an odd number ; if e " = - 1 , n must be an odd multiple of 2 ; and if e " = + 1 , n must be an even multiple of 2 . ( 4 ) When a ...
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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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