An Elementary Treatise on Quaternions |
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Page vii
... operators and functions : and therefore the student is not wholly unprepared to meet it . No one is puzzled by the fact that log.cos.c * This has been done by Hamilton himself , as one among many methods he has employed ; and it is also ...
... operators and functions : and therefore the student is not wholly unprepared to meet it . No one is puzzled by the fact that log.cos.c * This has been done by Hamilton himself , as one among many methods he has employed ; and it is also ...
Page viii
... operators and functions in other methods , that they are not generally commutative , is in Quaternions true in the multipli- cation of ( vector ) cöordinates . ' It will be observed by those who are acquainted with the Cal- culus that I ...
... operators and functions in other methods , that they are not generally commutative , is in Quaternions true in the multipli- cation of ( vector ) cöordinates . ' It will be observed by those who are acquainted with the Cal- culus that I ...
Page xiv
... operator which turns one vector into another . It is thus decomposable into two 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 ...
... operator which turns one vector into another . It is thus decomposable into two 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 ...
Page xix
... operator qs ( _ ) q - 8 turns the system it is applied to through 28 times the angle of q , about the axis of q . If the position of a system at time t is derived from the initial position by q ( ) - 1 , the instantaneous axis is ...
... operator qs ( _ ) q - 8 turns the system it is applied to through 28 times the angle of q , about the axis of q . If the position of a system at time t is derived from the initial position by q ( ) - 1 , the instantaneous axis is ...
Page 2
... 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 , a point is defined by a single ...
... 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 , a point is defined by a single ...
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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
Popular passages
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...