An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina xiii
... formula p = xa + yẞ + 27 , which exhibits the three numbers on which the vector depends . § 23 . Any vector in the same plane with a and ẞ may be written p = xa + yẞ . § 24 . The equation @ = P2 between two vectors , is equivalent to ...
... formula p = xa + yẞ + 27 , which exhibits the three numbers on which the vector depends . § 23 . Any vector in the same plane with a and ẞ may be written p = xa + yẞ . § 24 . The equation @ = P2 between two vectors , is equivalent to ...
Pagina 13
... formula , ma + m1 a 1 ) + m2 A z ( m + m1 ) ( m + m1 ( m + m1 ) + m2 ma + m1 a1 + m2 a2 . m + m1 + m2 For any number of masses , expressed generally by m at the extre- mity of the vector a , we have the vector of the centre of inertia B ...
... formula , ma + m1 a 1 ) + m2 A z ( m + m1 ) ( m + m1 ( m + m1 ) + m2 ma + m1 a1 + m2 a2 . m + m1 + m2 For any number of masses , expressed generally by m at the extre- mity of the vector a , we have the vector of the centre of inertia B ...
Pagina 43
... formula ( Ta ) 2 = -a2 , and also , to a certain extent , in § 25 .. 88. ] Now let q and r be any quaternions , then S.gr = S. ( Sq + Vq ) ( Sr + Vr ) , = = S. ( Sq Sr + Sr.Vq + Sq .Vr + VqVr ) , Sq Sr + SVqVr , since the two middle ...
... formula ( Ta ) 2 = -a2 , and also , to a certain extent , in § 25 .. 88. ] Now let q and r be any quaternions , then S.gr = S. ( Sq + Vq ) ( Sr + Vr ) , = = S. ( Sq Sr + Sr.Vq + Sq .Vr + VqVr ) , Sq Sr + SVqVr , since the two middle ...
Pagina 44
... formula of constant occurrence . ( 1 ) Adding aSẞy to both sides we get another most valuable formula V.aẞy aSẞy - BSya + ySaß ; Γ . αβγ = ( 2 ) and the form of this shews that we may interchange y and a without altering the right ...
... formula of constant occurrence . ( 1 ) Adding aSẞy to both sides we get another most valuable formula V.aẞy aSẞy - BSya + ySaß ; Γ . αβγ = ( 2 ) and the form of this shews that we may interchange y and a without altering the right ...
Pagina 45
Peter Guthrie Tait. a very useful formula , expressing any vector whatever in terms of three given vectors . 92. ] That such an expression is possible we knew already by § 23. For variety we may seek another expression of a similar ...
Peter Guthrie Tait. a very useful formula , expressing any vector whatever in terms of three given vectors . 92. ] That such an expression is possible we knew already by § 23. For variety we may seek another expression of a similar ...
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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.
Pagina 138 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
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...