An Elementary Treatise on Quaternions |
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Page xx
... circles of contact . Lines of vibration , & c . §§ 407-427 . Electrodynamics . The vector action of a closed circuit on an element of current a , is proportional to Va1ẞ where Vada B = = = fara , Ta3 the integration extending round the ...
... circles of contact . Lines of vibration , & c . §§ 407-427 . Electrodynamics . The vector action of a closed circuit on an element of current a , is proportional to Va1ẞ where Vada B = = = fara , Ta3 the integration extending round the ...
Page 23
... circle through an angle in the and positive direction of rotation , without altering its length , deduce the ordinary formulæ for cos ( A + B ) , cos ( 4— B ) , sin ( A + B ) , sin ( 4 - B ) , in terms of sines and cosines of A and B ...
... circle through an angle in the and positive direction of rotation , without altering its length , deduce the ordinary formulæ for cos ( A + B ) , cos ( 4— B ) , sin ( A + B ) , sin ( 4 - B ) , in terms of sines and cosines of A and B ...
Page 28
... circle , of which the two vectors are radii . This is of considerable importance in the proofs which follow . B A1 A Thus the versor may be represented OB OA in magnitude , plane , and direction ( § 50 ) by the arc AB , which may in ...
... circle , of which the two vectors are radii . This is of considerable importance in the proofs which follow . B A1 A Thus the versor may be represented OB OA in magnitude , plane , and direction ( § 50 ) by the arc AB , which may in ...
Page 29
... circle on the unit - sphere , we can easily prove that quaternion multiplication is not generally commutative . or OB 04 Thus let ૧ be the versor AB Make BC = AB , ( which , it must be remembered , makes the points A , B , C lie in one ...
... circle on the unit - sphere , we can easily prove that quaternion multiplication is not generally commutative . or OB 04 Thus let ૧ be the versor AB Make BC = AB , ( which , it must be remembered , makes the points A , B , C lie in one ...
Page 30
... circles , for their tensors may obviously ( § 48 ) be divided out from both sides , being commutative with the versors . = = q , and FE = r . Let AB = p , ED – CA Join BC and produce the great circle till it meets EF in H , and make KH ...
... circles , for their tensors may obviously ( § 48 ) be divided out from both sides , being commutative with the versors . = = q , and FE = r . Let AB = p , ED – CA Join BC and produce the great circle till it meets EF in H , and make KH ...
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Common terms and phrases
a₁ axes axis Cartesian centre of inertia Chapter circle cloth cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression Extra fcap extremity fcap Find the equation Find the locus given equation given line given vectors gives Hamilton Hence hodograph integral intersection last section length linear and vector locus normal obviously once operator origin osculating osculating plane P₁ parabola parallel perpendicular properties quaternion radius rectangular represents result right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate shew solution sphere spherical straight line suppose surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vectors Vaß vector function versor w₁ write written Τρ φρ