Introduction to Quaternions: With Numerous Examples |
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Page 28
... axes OX , OY , and designate by a , ẞ unit vectors parallel to these axes ; and by p1 , P1 , & c . the vectors to the different points ; and if we write x1 , y1 ; X , Y ,, & c . for the Cartesian co - ordinates of the different points ...
... axes OX , OY , and designate by a , ẞ unit vectors parallel to these axes ; and by p1 , P1 , & c . the vectors to the different points ; and if we write x1 , y1 ; X , Y ,, & c . for the Cartesian co - ordinates of the different points ...
Page 32
... axes , mutually at 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 ...
... axes , mutually at 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 ...
Page 45
... axis were along OD ( Fig . Art . 21 ) . By comparing the result of that article with the definitions of Art . β 17 , it is clear that or cos + sin is an operator of the same α character as - k or € ( as we have now called the ...
... axis were along OD ( Fig . Art . 21 ) . By comparing the result of that article with the definitions of Art . β 17 , it is clear that or cos + sin is an operator of the same α character as - k or € ( as we have now called the ...
Page 46
... axis to bring it into the γ position B. If now be a second operator β about the same axis in the same direction acting on ß , it will bring it into the position y . γ β 0 But it is evident that acting on a would at once have brought it ...
... axis to bring it into the γ position B. If now be a second operator β about the same axis in the same direction acting on ß , it will bring it into the position y . γ β 0 But it is evident that acting on a would at once have brought it ...
Page 56
... axes . Let A , B , C be the three given points ; then and line OA = a , OB = b , OC = c ; x , y , z the co - ordinates of the given point P , - - vector OA ai , OB bj , OC = ck ; OP = xi + yj + zk ;. .. PA = 0A - OP = − { ( x − a ) i ...
... axes . Let A , B , C be the three given points ; then and line OA = a , OB = b , OC = c ; x , y , z the co - ordinates of the given point P , - - vector OA ai , OB bj , OC = ck ; OP = xi + yj + zk ;. .. PA = 0A - OP = − { ( x − a ) i ...
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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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