An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina 118
... radius are given . 17. ( Hamilton , Bishop Law's Premium Ex . , 1858 ) . ( a . ) Assign some of the transformations of the expression Vaß B - " α where a and ẞ are the vectors of two given points A and B. ( 6. ) The expression ...
... radius are given . 17. ( Hamilton , Bishop Law's Premium Ex . , 1858 ) . ( a . ) Assign some of the transformations of the expression Vaß B - " α where a and ẞ are the vectors of two given points A and B. ( 6. ) The expression ...
Pagina 120
... radius Ta whose centre is the origin . In § 107 several transformations of this equation were ob- tained , some of which we will repeat here with their interpretations . Thus S ( pa ) ( pa ) = 0 shews that the chords drawn from any ...
... radius Ta whose centre is the origin . In § 107 several transformations of this equation were ob- tained , some of which we will repeat here with their interpretations . Thus S ( pa ) ( pa ) = 0 shews that the chords drawn from any ...
Pagina 122
... radius is T ( 2 ) , and whose centre is at B , where OB = 1 - α n2 1 , a definite point in the line OA . 222. ] If in any line , OP , drawn from the origin to a given plane , OQ be taken such that OQ.OP is constant , find the locus of Q ...
... radius is T ( 2 ) , and whose centre is at B , where OB = 1 - α n2 1 , a definite point in the line OA . 222. ] If in any line , OP , drawn from the origin to a given plane , OQ be taken such that OQ.OP is constant , find the locus of Q ...
Pagina 125
... radius of the sphere , ẞ the vector of the given point , and Syp = a the equation of the given plane . The vector - perpendicular from the point ra on the given plane is ( § 208 ) ( a − xSya ) y ̄1 . Hence , to determine x we have the ...
... radius of the sphere , ẞ the vector of the given point , and Syp = a the equation of the given plane . The vector - perpendicular from the point ra on the given plane is ( § 208 ) ( a − xSya ) y ̄1 . Hence , to determine x we have the ...
Pagina 126
... radius ; its equation is T ( p - σ ) = r . Since the two given lines are tangents , the following equations in x and 1 must have pairs of equal roots , T ( a + xẞ - o ) = " " , T ( −a + x1ß1 − σ ) = r . The equality of the roots in ...
... radius ; its equation is T ( p - σ ) = r . Since the two given lines are tangents , the following equations in x and 1 must have pairs of equal roots , T ( a + xẞ - o ) = " " , T ( −a + x1ß1 − σ ) = r . The equality of the roots in ...
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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...