An Elementary Treatise on Quaternions |
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Page vii
... fact that log.cos.c * This has been done by Hamilton himself , as one among many methods he has employed ; and it is also the foundation of a memoir by M. Allégret , entitled Essai sur le Calcul des Quaternions ( Paris , 1862 ) . dy is ...
... fact that log.cos.c * This has been done by Hamilton himself , as one among many methods he has employed ; and it is also the foundation of a memoir by M. Allégret , entitled Essai sur le Calcul des Quaternions ( Paris , 1862 ) . dy is ...
Page viii
... fact , even when Quaternions degrade to scalars , they give the solution of the most general statement of the problem they are applied to , quite inde- pendent of any limitations as to choice of particular cöordinate axes . ' There is ...
... fact , even when Quaternions degrade to scalars , they give the solution of the most general statement of the problem they are applied to , quite inde- pendent of any limitations as to choice of particular cöordinate axes . ' There is ...
Page 2
... fact , it is easy to see that if we use , instead of √1 , the more general factor cos a + √1 sin a , its effect on any line is to turn it through the ( positive ) angle a in the plane of x , y . [ Of course the former factor , -1 , is ...
... fact , it is easy to see that if we use , instead of √1 , the more general factor cos a + √1 sin a , its effect on any line is to turn it through the ( positive ) angle a in the plane of x , y . [ Of course the former factor , -1 , is ...
Page 3
... fact , the first operator produces m successive rotations in the same direction , each through the angle a ; the second , a single rotation through the angle ma . 9. ] It may be interesting , at this stage , to anticipate so far as to ...
... fact , the first operator produces m successive rotations in the same direction , each through the angle a ; the second , a single rotation through the angle ma . 9. ] It may be interesting , at this stage , to anticipate so far as to ...
Page 4
... fact , as we shall see , the Quaternion method is independent of axes or any supposed directions in space , and takes its reference lines solely from the problem it is applied to . 14. ] But , for the purpose of elementary exposition ...
... fact , as we shall see , the Quaternion method is independent of axes or any supposed directions in space , and takes its reference lines solely from the problem it is applied to . 14. ] But , for the purpose of elementary exposition ...
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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...