An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina 3
... referred ) that is not the algebraic √1 , but may be any directed unit - line what- ever in space . 10. ] In the present century Argand , Warren , and others , extended the results of Wallis and De Moivre . They attempted to express as ...
... referred ) that is not the algebraic √1 , but may be any directed unit - line what- ever in space . 10. ] In the present century Argand , Warren , and others , extended the results of Wallis and De Moivre . They attempted to express as ...
Pagina 15
... referred the parabola . Then the pole is Q , where P = bB ; and the polar is the line TU , for which p = bB + pa . Hence the polar of any point is parallel to the 31. ] 15 VECTORS , AND THEIR COMPOSITION . Elementary geometrical ideas ...
... referred the parabola . Then the pole is Q , where P = bB ; and the polar is the line TU , for which p = bB + pa . Hence the polar of any point is parallel to the 31. ] 15 VECTORS , AND THEIR COMPOSITION . Elementary geometrical ideas ...
Pagina 16
... referred to its asymptotes . But , so far as we have yet gone with the explanation of the calculus , as we are not prepared to determine the lengths or in- clinations of vectors , we can investigate only a very small class of the ...
... referred to its asymptotes . But , so far as we have yet gone with the explanation of the calculus , as we are not prepared to determine the lengths or in- clinations of vectors , we can investigate only a very small class of the ...
Pagina 37
... referred to in § 64. We have treated i , j , k simply as quadrantal versors ; and I , J , K as unit - vectors at right angles to each other , and coinciding with the axes of rotation of these versors . But if we collate and compare the ...
... referred to in § 64. We have treated i , j , k simply as quadrantal versors ; and I , J , K as unit - vectors at right angles to each other , and coinciding with the axes of rotation of these versors . But if we collate and compare the ...
Pagina 56
... referred to Hamilton's works for the treatment of this subject by quaternion exponentials . 111. ] Let a , ß , y be unit - vectors drawn from the centre to the corners A , B , C of a triangle on the unit - sphere . Then it is evident ...
... referred to Hamilton's works for the treatment of this subject by quaternion exponentials . 111. ] Let a , ß , y be unit - vectors drawn from the centre to the corners A , B , C of a triangle on the unit - sphere . Then it is evident ...
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.
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...