An Elementary Treatise on Quaternions |
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Page 7
... respectively to any three given vectors , no two of which are parallel , and which are not parallel to one plane . Let OA , OB , OC be the three fixed vectors , C OP any other vector . From P draw PQ parallel to CO , meeting the plane ...
... respectively to any three given vectors , no two of which are parallel , and which are not parallel to one plane . Let OA , OB , OC be the three fixed vectors , C OP any other vector . From P draw PQ parallel to CO , meeting the plane ...
Page 8
... respectively , in these three expressions , AB + BC + CD = AB + ( BC + CD ) = ( AB + BC ) + CD . And thus the truth of the associative law is evident . 28. ] The equation p = χβ , where p is the vector connecting a variable point with ...
... respectively , in these three expressions , AB + BC + CD = AB + ( BC + CD ) = ( AB + BC ) + CD . And thus the truth of the associative law is evident . 28. ] The equation p = χβ , where p is the vector connecting a variable point with ...
Page 12
... respectively ; the locus of Q is a straight line parallel A M to OA . P ช Let OM = ea . Then AP e - 1a + xß . Hence the equation of OQ is p = y ( e − 1a + xß ) ; and that of BQ is p = B + z ( ea + xẞ ) . 04 B At Q we have , therefore ...
... respectively ; the locus of Q is a straight line parallel A M to OA . P ช Let OM = ea . Then AP e - 1a + xß . Hence the equation of OQ is p = y ( e − 1a + xß ) ; and that of BQ is p = B + z ( ea + xẞ ) . 04 B At Q we have , therefore ...
Page 14
... respectively the coefficients of a and B. Hence t = p ± √ p2 -2q . Thus , in general , two tangents can be drawn from a given point . These coincide if p2 = 2q ; that is , if the vector of the point from which they are to be drawn is p ...
... respectively the coefficients of a and B. Hence t = p ± √ p2 -2q . Thus , in general , two tangents can be drawn from a given point . These coincide if p2 = 2q ; that is , if the vector of the point from which they are to be drawn is p ...
Page 15
... respectively , it is obvious that the vector join- ing the points of contact is at2 + Bl2 Bt 2 at2- 2 2 which is parallel to t1 + t2 a + ß ; 2 or , by the values of t , and to in ( g ) , a + pß . Its direction , therefore , does not ...
... respectively , it is obvious that the vector join- ing the points of contact is at2 + Bl2 Bt 2 at2- 2 2 which is parallel to t1 + t2 a + ß ; 2 or , by the values of t , and to in ( g ) , a + pß . Its direction , therefore , does not ...
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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...