An Elementary Treatise on Quaternions |
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Page xi
... effect the application of Quaternions to line , surface , and volume integrals , such as occur in Hydrokinetics , Electricity , and Potentials generally . I was first attracted to the study of Quaternions by their promise of usefulness ...
... effect the application of Quaternions to line , surface , and volume integrals , such as occur in Hydrokinetics , Electricity , and Potentials generally . I was first attracted to the study of Quaternions by their promise of usefulness ...
Page xx
... Effect of V on various functions of Vp = -3 , VTp = Up , ¬Up = Applications of the theorem 8.8p Tap Tp3 = 1 P = ix + jy + kz . 2 · ▽ Sapa , Vap = 2a . Τρ SS.av §§ 449-457 . • Τρ Farther examination of the use of ▽ as applied to ...
... Effect of V on various functions of Vp = -3 , VTp = Up , ¬Up = Applications of the theorem 8.8p Tap Tp3 = 1 P = ix + jy + kz . 2 · ▽ Sapa , Vap = 2a . Τρ SS.av §§ 449-457 . • Τρ Farther examination of the use of ▽ as applied to ...
Page 2
... effect on any line is to make it rotate ( positively ) about the origin through an angle of 90 ° . - 5. ] In such a system , a point is defined by a single imaginary expression . Thus a + b√1 may be considered as a single quan- tity ...
... effect on any line is to make it rotate ( positively ) about the origin through an angle of 90 ° . - 5. ] In such a system , a point is defined by a single imaginary expression . Thus a + b√1 may be considered as a single quan- tity ...
Page 25
... , and ( remembering the effect of the first operation ) we see that the two vectors now coincide or become The equation @ = between two vectors, is equivalent to three distinct equations among numbers § -PRODUCTS AND QUOTIENTS OF VECTORS.
... , and ( remembering the effect of the first operation ) we see that the two vectors now coincide or become The equation @ = between two vectors, is equivalent to three distinct equations among numbers § -PRODUCTS AND QUOTIENTS OF VECTORS.
Page 28
... effect of the other . The joint effect of these factors is therefore merely to multiply twice over by the common tensor . 53. ] It is evident from the results of § 50 that , if a and ß be of equal length , their quaternion quotient ...
... effect of the other . The joint effect of these factors is therefore merely to multiply twice over by the common tensor . 53. ] It is evident from the results of § 50 that , if a and ß be of equal length , their quaternion quotient ...
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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