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 Vaß where В = -fVada - fata , 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 Vaß where В = -fVada - fata , Ta3 the integration extending round the ...
Page 23
... circle through an angle in the positive direction of rotation , without altering its length , deduce the ordinary formulæ for cos ( A + B ) , cos ( A − B ) , sin ( A + B ) , and sin ( A – B ) , in terms of sines and cosines of A and B ...
... circle through an angle in the positive direction of rotation , without altering its length , deduce the ordinary formulæ for cos ( A + B ) , cos ( A − B ) , sin ( A + B ) , and sin ( A – 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 A OB Thus the versor may be represented OA in magnitude , plane , and direction ( § 50 ) by the arc AB , which may in this ...
... circle , of which the two vectors are radii . This is of considerable importance in the proofs which follow . B A OB Thus the versor may be represented OA in magnitude , plane , and direction ( § 50 ) by the arc AB , which may in this ...
Page 29
... circle on the unit - sphere , we can easily prove that quaternion multiplication is not generally commutative . OB Thus let q be the versor AB or Չ ОА Make BC = ÁB , ( which , it must be remembered , makes the points A , B , C lie in ...
... circle on the unit - sphere , we can easily prove that quaternion multiplication is not generally commutative . OB Thus let q be the versor AB or Չ ОА Make BC = ÁB , ( which , it must be remembered , makes the points A , B , C lie in ...
Page 30
... circles , for their 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 ...
... circles , for their 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 ...
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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.
Page 299 - Students of the Bible should be particularly grateful to (the Cambridge University Press) for having produced, with the able assistance of Dr Scrivener, a complete critical edition of the Authorized Version of the English Bible, an edition such as, to use the words of the Editor, 'would have been executed long ago had this version been nothing more than the greatest and best known of English classics.
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
Page 299 - Mr. Scrivener has carefully collated the text of our modern Bibles with that of the first edition of 1611, restoring the original reading in most places, and marking every place where an obvious correction has been made ; he has made the spelling as uniform as possible ; revised the punctuation (punctuation, as those who cry out for the Bible without note or comment should remember, is a continuous commentary on the text); carried out consistently the plan of marking' with italics all words not found...