An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina xiv
... length is ds . §§ 38 , 39 . Examples with solutions . §§ 40-44 . EXAMPLES TO CHAPTER I. • 22-24 CHAPTER II ... lengths , and directions , of ẞ and a . § 50 . Reciprocal of a quaternion defined , β 1 q = gives or q1 = q - 1 α Չ β ' 1 T.q ...
... length is ds . §§ 38 , 39 . Examples with solutions . §§ 40-44 . EXAMPLES TO CHAPTER I. • 22-24 CHAPTER II ... lengths , and directions , of ẞ and a . § 50 . Reciprocal of a quaternion defined , β 1 q = gives or q1 = q - 1 α Չ β ' 1 T.q ...
Pagina 1
... length , of lines . 2. ] Thus it was long ago seen that if positive quantities were measured off in one direction along a fixed line , a useful and lawful convention enabled us to express negative quantities of the same kind by simply ...
... length , of lines . 2. ] Thus it was long ago seen that if positive quantities were measured off in one direction along a fixed line , a useful and lawful convention enabled us to express negative quantities of the same kind by simply ...
Pagina 2
... length , of this line ; since , as - b -1 we see at once , the direction is inclined at an angle tan- to the axis of a , and the length is √a2 + b2 . a 6. ] Operating on this symbol by the factor -1 , it becomes -b + a√1 ; and now ...
... length , of this line ; since , as - b -1 we see at once , the direction is inclined at an angle tan- to the axis of a , and the length is √a2 + b2 . a 6. ] Operating on this symbol by the factor -1 , it becomes -b + a√1 ; and now ...
Pagina 5
... length to AB and if these lines be parallel , we have evidently CD AB = a , where it will be seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended ...
... length to AB and if these lines be parallel , we have evidently CD AB = a , where it will be seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended ...
Pagina 6
... between A and C , other- wise negative but such that its numerical value , independent of sign , is the ratio of the length of BC to that of AB . This is at once evident if AB and BC be commensurable ; 6 [ 20 . QUATERNIONS .
... between A and C , other- wise negative but such that its numerical value , independent of sign , is the ratio of the length of BC to that of AB . This is at once evident if AB and BC be commensurable ; 6 [ 20 . QUATERNIONS .
Overige edities - Alles bekijken
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 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...