An Elementary Treatise on Quaternions |
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Page xv
... rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two vectors at right angles to each other is a third perpendicular to both . Hence Ka = -α , and ( Ta ) 2 = aKa = -a2 . § 73 . Every versor may be ...
... rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two vectors at right angles to each other is a third perpendicular to both . Hence Ka = -α , and ( Ta ) 2 = aKa = -a2 . § 73 . Every versor may be ...
Page xviii
... rectangular unit - vectors whatever , we have Sq = -m2 , Vq = € . This quaternion can be expressed in the important form q = op . §§ 170-174 . Degrees of indeterminateness of the solution of a quaternion equation— Examples . §§ 175-179 ...
... rectangular unit - vectors whatever , we have Sq = -m2 , Vq = € . This quaternion can be expressed in the important form q = op . §§ 170-174 . Degrees of indeterminateness of the solution of a quaternion equation— Examples . §§ 175-179 ...
Page 1
... rectangular axes are employed , this amounts to reckoning each unit of length along Oy as +1 , and on Oy as -1 ; while on Ox each unit is +1 , and on Ox it is 10 B -1 . If we look at these four lines in -VECTORS AND THEIR COMPOSITION 1 ...
... rectangular axes are employed , this amounts to reckoning each unit of length along Oy as +1 , and on Oy as -1 ; while on Ox each unit is +1 , and on Ox it is 10 B -1 . If we look at these four lines in -VECTORS AND THEIR COMPOSITION 1 ...
Page 4
... in space , and suppose A given , on how many numbers does B's relative position depend ? If we refer to Cartesian cöordinates ( rectangular or not ) we find that the data required are the excesses of B's three 4 [ 13 . QUATERNIONS .
... in space , and suppose A given , on how many numbers does B's relative position depend ? If we refer to Cartesian cöordinates ( rectangular or not ) we find that the data required are the excesses of B's three 4 [ 13 . QUATERNIONS .
Page 7
... rectangular parallelepiped of which p is the vector - diagonal ; so that the length of p is , in this case , Let √x2 + y2 + z2 . § i + nj + Šk @ = be any other vector , then ( by the proposition of § 23 ) the vector equation p = w ...
... rectangular parallelepiped of which p is the vector - diagonal ; so that the length of p is , in this case , Let √x2 + y2 + z2 . § i + nj + Šk @ = be any other vector , then ( by the proposition of § 23 ) the vector equation p = w ...
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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