Introduction to Quaternions: With Numerous Examples |
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Page 32
... right angles , which we designate the axes of x , y , and z respectively . For graphic representation the axes of x and y are drawn in the plane of the paper whilst that of z being perpendicular to that plane is drawn in perspective ...
... right angles , which we designate the axes of x , y , and z respectively . For graphic representation the axes of x and y are drawn in the plane of the paper whilst that of z being perpendicular to that plane is drawn in perspective ...
Page 33
... right angles to each other . 17. DEFINITION . If i , j , k be unit vectors along Ox , Oy , Oz respectively , the result of the multiplication of i into j or ij is defined to be the turning of j through a right angle in the plane ...
... right angles to each other . 17. DEFINITION . If i , j , k be unit vectors along Ox , Oy , Oz respectively , the result of the multiplication of i into j or ij is defined to be the turning of j through a right angle in the plane ...
Page 35
... right angle reverses a vector . 2. Again , ijki.jki . ii = -1 . Similarly it may be proved that jki = kij = -1 , or ... angles to each other . 20. We have already ( Art . 8 ) laid down the principle of separation of the vector into the ...
... right angle reverses a vector . 2. Again , ijki.jki . ii = -1 . Similarly it may be proved that jki = kij = -1 , or ... angles to each other . 20. We have already ( Art . 8 ) laid down the principle of separation of the vector into the ...
Page 36
... right angles to one another . 1. Let a , ẞ be unit vectors . Let OA = a , OB = B . = لا Take OC a unit vector perpen ... angle BOA = 0 ; then D A N vector OA = OM + MA = OM + ON ( Art . 1 ) = part of OB + part of OC ( Art . 3 ) . M B Now ...
... right angles to one another . 1. Let a , ẞ be unit vectors . Let OA = a , OB = B . = لا Take OC a unit vector perpen ... angle BOA = 0 ; then D A N vector OA = OM + MA = OM + ON ( Art . 1 ) = part of OB + part of OC ( Art . 3 ) . M B Now ...
Page 37
... right angles to each other consists of two distinct parts , a numerical quantity and a vector perpendicular to the plane of a , B. The former of these Sir William Hamilton terms the SCALAR part , the latter the VECTOR part . We may now ...
... right angles to each other consists of two distinct parts , a numerical quantity and a vector perpendicular to the plane of a , B. The former of these Sir William Hamilton terms the SCALAR part , the latter the VECTOR part . We may now ...
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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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