An Elementary Treatise on Quaternions |
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Page xv
... considered as a quadrantal versor whose plane is perpendicular to the vector . Hence the equations just written are true of any set of rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two vectors at ...
... considered as a quadrantal versor whose plane is perpendicular to the vector . Hence the equations just written are true of any set of rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two vectors at ...
Page 2
... considered as a single quan- tity , denoting the point whose cöordinates are a and b . Or , it may be used as an expression for the line joining that point with the origin . In the latter sense , the expression a + b√√ — 1 implicitly ...
... considered as a single quan- tity , denoting the point whose cöordinates are a and b . Or , it may be used as an expression for the line joining that point with the origin . In the latter sense , the expression a + b√√ — 1 implicitly ...
Page 5
... considered with reference to direction as well as length , contains implicitly three numbers , and all lines parallel and equal to AB depend in the same way upon the same three . Hence , all lines which are equal and parallel may be ...
... considered with reference to direction as well as length , contains implicitly three numbers , and all lines parallel and equal to AB depend in the same way upon the same three . Hence , all lines which are equal and parallel may be ...
Page 8
... considered positive . - Let A , B , C , D be , in order , the corners of a parallelogram ; we have , obviously , AB = DC , AD = BC . And AB + BC = AC = AD + DC = BC + AB . Hence the commutative law is true for the addition of any two ...
... considered positive . - Let A , B , C , D be , in order , the corners of a parallelogram ; we have , obviously , AB = DC , AD = BC . And AB + BC = AC = AD + DC = BC + AB . Hence the commutative law is true for the addition of any two ...
Page 26
... considered as the factor or agent which changes one definite vector into another , may itself be decomposed into two factors of which the order is immaterial . The stretching factor , or that which performs the first operation in § 47 ...
... considered as the factor or agent which changes one definite vector into another , may itself be decomposed into two factors of which the order is immaterial . The stretching factor , or that which performs the first operation in § 47 ...
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Common terms and phrases
a₁ axes axis Cartesian centre Chapter circle condition cone conjugate cöordinates coplanar curvature curve cylinder developable surface direction drawn easily Eliminating ellipsoid equal equation becomes evidently expression extremity Find the equation Find the locus formula given equation given lines given point gives Hamilton Hence integral intersection LAOB last section length linear and vector normal obviously once operating origin osculating plane parallel perpendicular properties prove quaternion radius rectangular system represents result right angles rotation S.aßp S.aßy Sapa Saß scalar scalar equations second order shew sin sin sin solution sphere spherical conic Spopp ẞ² suppose surface of revolution tangent plane tensor tetrahedron theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor write written Τρ φρ