An Elementary Treatise on Quaternions |
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Page xiv
... TENSOR , and the turning factor or VERSOR . These are denoted by Tq , and Uq . § 48 . The equation B = qa gives β - or βασι = α q , but not in general a 1B = q . § 49 . q or Ba - 1 depends only on the relative lengths , and directions ...
... TENSOR , and the turning factor or VERSOR . These are denoted by Tq , and Uq . § 48 . The equation B = qa gives β - or βασι = α q , but not in general a 1B = q . § 49 . q or Ba - 1 depends only on the relative lengths , and directions ...
Page 26
... TENSOR , and is denoted by prefixing T to the quaternion considered . The turning factor , or that corresponding to the second operation in § 47 , is called the VERSOR , and is denoted by the letter U prefixed to the quaternion . 49 ...
... TENSOR , and is denoted by prefixing T to the quaternion considered . The turning factor , or that corresponding to the second operation in § 47 , is called the VERSOR , and is denoted by the letter U prefixed to the quaternion . 49 ...
Page 28
... tensor of the reciprocal of a quaternion is therefore the reciprocal of the tensor ; and the versor differs merely by the reversal of its representative angle . The versor , it must be remembered , gives the plane and angle of the ...
... tensor of the reciprocal of a quaternion is therefore the reciprocal of the tensor ; and the versor differs merely by the reversal of its representative angle . The versor , it must be remembered , gives the plane and angle of the ...
Page 30
... tensors may obviously ( § 48 ) be divided out from both sides , being commutative with the versors . Let AB = p , ED = CA = q , and FE = r . Join BC and produce the great circle till it meets EF in H , and make KH = FE = r , and HG = CB ...
... tensors may obviously ( § 48 ) be divided out from both sides , being commutative with the versors . Let AB = p , ED = CA = q , and FE = r . Join BC and produce the great circle till it meets EF in H , and make KH = FE = r , and HG = CB ...
Page 32
... tensors of q and r . This will be useful to us in the proof of the distributive law , to which we proceed . L K pvq Uq pur H E F p ß d бер р พ 62. ] Quaternion multi- plication , and therefore di- vision , is distributive . One simple ...
... tensors of q and r . This will be useful to us in the proof of the distributive law , to which we proceed . L K pvq Uq pur H E F p ß d бер р พ 62. ] Quaternion multi- plication , and therefore di- vision , is distributive . One simple ...
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Common terms and phrases
a₁ axes axis Cartesian centre of inertia Chapter circle condition cone conjugate cöordinates coplanar curvature curve developable surface differential direction drawn easily Eliminating ellipsoid envelop equal evidently expression extremity Find the equation Find the locus formula given equation given lines given point gives Hamilton Hence hodograph integral intersection LAOB last section length linear and vector magnetism normal obviously once operator origin osculating plane P₁ parabola parallel pass perpendicular properties prove quaternion radius represents result right angles rotation S.aßy Saß scalar scalar equations second order shew solution sphere spherical conic straight line suppose surface surface of revolution tangent plane tensor tetrahedron theorem three vectors triangle unit-vectors Vaß vector function vector perpendicular versor write written Τρ φρ
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Page 299 - SCRIPTURES, &c. The Cambridge Paragraph Bible of the Authorized English Version, with the Text revised by a Collation of its Early and other Principal Editions...
Page 298 - VILLEMAIN, with a Biographical Sketch of the Author, a Selection of Poems on Greece, and Notes Historical and Philological. By the same Editor, is.
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Page 138 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Page 11 - The perpendicular bisectors of the sides of a triangle meet in a point which is equidistant from the vertices of the triangle. Let the -l. bisectors EE' and DD
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