An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina xi
... tion of motion of the hands of a watch . In Sir W. Hamilton's great works the opposite is employed . The student will find no difficulty in passing from the one to the other ; but , without pre- vious warning , he is liable to be much ...
... tion of motion of the hands of a watch . In Sir W. Hamilton's great works the opposite is employed . The student will find no difficulty in passing from the one to the other ; but , without pre- vious warning , he is liable to be much ...
Pagina 26
... tion in the case of a planet's orbit ) to fix the plane in which the rotation takes place , and one angle for the amount of this rotation . Thus it appears that the ratio of two vectors , or the multiplier required to change one vector ...
... tion in the case of a planet's orbit ) to fix the plane in which the rotation takes place , and one angle for the amount of this rotation . Thus it appears that the ratio of two vectors , or the multiplier required to change one vector ...
Pagina 65
... tion with all other factors . Thus it appears , by the same proof as in algebra , that any quaternion expression which contains this imaginary can always be broken up into the sum of two parts , one real , the other multiplied by the ...
... tion with all other factors . Thus it appears , by the same proof as in algebra , that any quaternion expression which contains this imaginary can always be broken up into the sum of two parts , one real , the other multiplied by the ...
Pagina 68
... tion about a line equally inclined to the three . ( c . ) Rectangular turned to oblique , one of the new axes lying in each of the former cöordinate planes . = 2. If Tp mations that Ta = TB = 1 , and S.aßp = 0 , shew by direct transfor ...
... tion about a line equally inclined to the three . ( c . ) Rectangular turned to oblique , one of the new axes lying in each of the former cöordinate planes . = 2. If Tp mations that Ta = TB = 1 , and S.aßp = 0 , shew by direct transfor ...
Pagina 71
... tion of a quaternion function of any number of scalar independent variables . In fact , this process is identical with ordinary differ- entiation . 129. ] But when we come to differentiate a function of a vector , or of a quaternion ...
... tion of a quaternion function of any number of scalar independent variables . In fact , this process is identical with ordinary differ- entiation . 129. ] But when we come to differentiate a function of a vector , or of a quaternion ...
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...