An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina xiv
... factors , whose order is indifferent , the stretching factor or 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 ...
... factors , whose order is indifferent , the stretching factor or 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 ...
Pagina xv
... factor , may be considered as a quadrantal versor whose plane is perpendicular to the vector . Hence the equations just written are true of any set of rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two ...
... factor , may be considered as a quadrantal versor whose plane is perpendicular to the vector . Hence the equations just written are true of any set of rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two ...
Pagina 2
... factor 1. Hence we may consider 1 as an operator , analogous to a handle perpendicular to the plane of xy , whose effect on any line is to make it rotate ( positively ) about the origin through an angle of 90 ° . 5. ] In such a system ...
... factor 1. Hence we may consider 1 as an operator , analogous to a handle perpendicular to the plane of xy , whose effect on any line is to make it rotate ( positively ) about the origin through an angle of 90 ° . 5. ] In such a system ...
Pagina 26
... factor or agent which changes one 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 ...
... factor or agent which changes one 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 ...
Pagina 28
... 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 becomes a versor ( the tensor being unity ) and may ...
... 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 becomes a versor ( the tensor being unity ) and may ...
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Veelvoorkomende woorden en zinsdelen
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
Populaire passages
Pagina 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...
Pagina 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.
Pagina 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.
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Pagina 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
Pagina 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...