An Elementary Treatise on Quaternions |
From inside the book
Results 1-5 of 49
Page xvi
... Loci represented by different equations - points , lines , surfaces , and solids . 116-119 . Proof that -1 ( r2q2 ) q1 = U ( rq + Kr Kq ) . § 120 . Proof of the transformation ( Sap ) 2 + ( SBp ) 2 + ( Svp ) 2 = ( T ( ip + pk ) 3 ...
... Loci represented by different equations - points , lines , surfaces , and solids . 116-119 . Proof that -1 ( r2q2 ) q1 = U ( rq + Kr Kq ) . § 120 . Proof of the transformation ( Sap ) 2 + ( SBp ) 2 + ( Svp ) 2 = ( T ( ip + pk ) 3 ...
Page 12
... 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 , xy = 1 + zx , y ...
... 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 , xy = 1 + zx , y ...
Page 17
... locus of the extremity of p is a surface ; whose equation is sometimes written P = $ ( t , u ) . ( m . ) Thus the equation belongs to a helix . Again , p = a cost + ẞ sin t + yt p = pa + qB + ry with a condition of the form ap2 + bg2 + ...
... locus of the extremity of p is a surface ; whose equation is sometimes written P = $ ( t , u ) . ( m . ) Thus the equation belongs to a helix . Again , p = a cost + ẞ sin t + yt p = pa + qB + ry with a condition of the form ap2 + bg2 + ...
Page 22
... locus of a point which divides in a given ratio a line cutting off a given area from two fixed axes , is a hyperbola of which these axes are the asymptotes . COR . ( 3 ) . If we take tt1 ( t + t1 ) = constant the locus is a parabola ...
... locus of a point which divides in a given ratio a line cutting off a given area from two fixed axes , is a hyperbola of which these axes are the asymptotes . COR . ( 3 ) . If we take tt1 ( t + t1 ) = constant the locus is a parabola ...
Page 31
... locus , c , of p is a circle , being the intersection of the two spheres A and a . Let OqQ be any other side of the cone , q and Q being points in c , C respectively . Then the quadrilateral qQ Pp is inscribed in a circle ( that in ...
... locus , c , of p is a circle , being the intersection of the two spheres A and a . Let OqQ be any other side of the cone , q and Q being points in c , C respectively . Then the quadrilateral qQ Pp is inscribed in a circle ( that in ...
Other editions - View all
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
Popular passages
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...