An Elementary Treatise on Quaternions |
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Page 5
... definite translation in space . : 17. ] We may here remark , once for all , that in establishing a new Calculus , we are at liberty to give any definitions whatever of our symbols , provided that no two of these interfere with , or ...
... definite translation in space . : 17. ] We may here remark , once for all , that in establishing a new Calculus , we are at liberty to give any definitions whatever of our symbols , provided that no two of these interfere with , or ...
Page 7
... definite point Q , else PQ , and therefore CO , would be parallel to BOA , a case specially excepted . ] From Q draw QR parallel to BO , meeting OA in R. Then we have OP = OR + RQ + QP ( § 21 ) , P R A -B and these components are ...
... definite point Q , else PQ , and therefore CO , would be parallel to BOA , a case specially excepted . ] From Q draw QR parallel to BO , meeting OA in R. Then we have OP = OR + RQ + QP ( § 21 ) , P R A -B and these components are ...
Page 8
... definite vector , and x an indefinite number , represents the straight line drawn from the origin parallel to ẞ ( § 22 ) . The straight line drawn from 4 , where OA = 8 [ 26 . QUATERNIONS . De Moivre's Theorem interpreted in plane ...
... definite vector , and x an indefinite number , represents the straight line drawn from the origin parallel to ẞ ( § 22 ) . The straight line drawn from 4 , where OA = 8 [ 26 . QUATERNIONS . De Moivre's Theorem interpreted in plane ...
Page 26
... definite vector into another , may itself be decomposed into two factors of which the order is immaterial . The stretching factor , or that which performs the first operation in § 47 , is called the TENSOR , and is denoted by prefixing ...
... definite vector into another , may itself be decomposed into two factors of which the order is immaterial . The stretching factor , or that which performs the first operation in § 47 , is called the TENSOR , and is denoted by prefixing ...
Page 29
... definite , and is given by the inter- section of the planes of the two versors ; O being the centre of the unit - sphere . Now Hence ос or qr = OD a great circle . rOD = OB , and qOB = OC , qr OD = = OC , , and may therefore be ...
... definite , and is given by the inter- section of the planes of the two versors ; O being the centre of the unit - sphere . Now Hence ос or qr = OD a great circle . rOD = OB , and qOB = OC , qr OD = = OC , , and may therefore be ...
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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...