An Elementary Treatise on Quaternions |
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Page xiv
... involves four distinct numbers - and is thus a QUATERNION . § 47 . A quaternion regarded as the operator which turns one vector into another . It is thus decomposable into two factors , whose order is indifferent , the stretching factor ...
... involves four distinct numbers - and is thus a QUATERNION . § 47 . A quaternion regarded as the operator which turns one vector into another . It is thus decomposable into two factors , whose order is indifferent , the stretching factor ...
Page xviii
... involves a scalar equation of degree m1 . § 184 . Solution of the equation q2 EXAMPLES TO CHAPTER V. = qa + b . § 185 . 101-103 CHAPTER VI . - GEOMETRY OF THE STRAIGHT LINE AND PLANE · EXAMPLES TO CHAPTER VI . CHAPTER VII . - THE SPHERE ...
... involves a scalar equation of degree m1 . § 184 . Solution of the equation q2 EXAMPLES TO CHAPTER V. = qa + b . § 185 . 101-103 CHAPTER VI . - GEOMETRY OF THE STRAIGHT LINE AND PLANE · EXAMPLES TO CHAPTER VI . CHAPTER VII . - THE SPHERE ...
Page 7
... ( by the proposition of § 23 ) the vector equation p = w obviously involves the following three equations among numbers , X = = ε , y = n , z = 5 . Suppose i to be drawn eastwards , j northwards , 25. ] 7 VECTORS , AND THEIR COMPOSITION .
... ( by the proposition of § 23 ) the vector equation p = w obviously involves the following three equations among numbers , X = = ε , y = n , z = 5 . Suppose i to be drawn eastwards , j northwards , 25. ] 7 VECTORS , AND THEIR COMPOSITION .
Page 9
... involve the indefinite quantity x , they are virtually equivalent to but two , as in ordinary Geometry of Three Dimensions . 29. ] A good illustration of this remark is furnished by the fact that the equation p = ya + xß , which ...
... involve the indefinite quantity x , they are virtually equivalent to but two , as in ordinary Geometry of Three Dimensions . 29. ] A good illustration of this remark is furnished by the fact that the equation p = ya + xß , which ...
Page 29
... proved are , of course , true of quater- nions as well as of versors ; for the former involve only an additional numerical factor which has reference to the length merely , 56. ] 29 PRODUCTS AND QUOTIENTS OF VECTORS .
... proved are , of course , true of quater- nions as well as of versors ; for the former involve only an additional numerical factor which has reference to the length merely , 56. ] 29 PRODUCTS AND QUOTIENTS OF VECTORS .
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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...