An Elementary Treatise on Quaternions |
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Page 2
... evidently 90 ° greater than before the operation . 7. ] De Moivre's Theorem tends to lead us still farther in the same direction . In fact , it is easy to see that if we use , instead of √1 , the more general factor cos a + √1 sin a ...
... evidently 90 ° greater than before the operation . 7. ] De Moivre's Theorem tends to lead us still farther in the same direction . In fact , it is easy to see that if we use , instead of √1 , the more general factor cos a + √1 sin a ...
Page 5
... evidently CD AB = a , where it will be seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended the meaning of an algebraical symbol . And it is to be ...
... evidently CD AB = a , where it will be seen that the sign of equality between vectors contains implicitly equality in length and parallelism in direction . So far we have extended the meaning of an algebraical symbol . And it is to be ...
Page 6
... evidently but different expressions of the same truth . 21. ] In any triangle , ABC , we have , of course , AB + BC + CA = 0 ; and , in any closed polygon , whether plane or gauche , AB + BC + ...... + YZ + ZA In the case of the polygon ...
... evidently but different expressions of the same truth . 21. ] In any triangle , ABC , we have , of course , AB + BC + CA = 0 ; and , in any closed polygon , whether plane or gauche , AB + BC + ...... + YZ + ZA In the case of the polygon ...
Page 14
... > p2 , i . e . if the point be p2 p = pa + 2 + r ) B , r being positive . Such a point is evidently within the curve , as at R , where OQ = 22 ß , QP = pa , PR = rß . 2 ( h . ) Calling the values of t for 14 [ 31 . QUATERNIONS .
... > p2 , i . e . if the point be p2 p = pa + 2 + r ) B , r being positive . Such a point is evidently within the curve , as at R , where OQ = 22 ß , QP = pa , PR = rß . 2 ( h . ) Calling the values of t for 14 [ 31 . QUATERNIONS .
Page 16
... evidently represents a hyperbola 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 ...
... evidently represents a hyperbola 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 ...
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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...