An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina 5
... distance or radius - vector . Three again . 16. ] Here it is to be carefully noticed that nothing has been said of the actual coordinates of either A or B , or of the earth and moon , in space ; it is only the relative cöordinates that ...
... distance or radius - vector . Three again . 16. ] Here it is to be carefully noticed that nothing has been said of the actual coordinates of either A or B , or of the earth and moon , in space ; it is only the relative cöordinates that ...
Pagina 59
... distance of a quadrant from its middle point . All spherical tri- angles , with a common side , and having their other sides bisected by the same great circle ( i . e . having their vertices in a small circle parallel to this great ...
... distance of a quadrant from its middle point . All spherical tri- angles , with a common side , and having their other sides bisected by the same great circle ( i . e . having their vertices in a small circle parallel to this great ...
Pagina 76
... distance of the tangent - plane from the origin . And we will shew , later , that if p = ix + jy + kz , then ע d d d v = ( i // + j & + k ) P ( p ) . + dy dz 1. Shew that EXAMPLES TO CHAPTER IV . ( a . ) d.SUq = S.UqV dq q ( b . ) d.VUq ...
... distance of the tangent - plane from the origin . And we will shew , later , that if p = ix + jy + kz , then ע d d d v = ( i // + j & + k ) P ( p ) . + dy dz 1. Shew that EXAMPLES TO CHAPTER IV . ( a . ) d.SUq = S.UqV dq q ( b . ) d.VUq ...
Pagina 110
... ( y - ẞ ) = —a ̄1Va ( ẞ — y ) , agrees with the result of last section . 203. ] To find the shortest vector distance between two lines p = B + xa , and 01 = 31 + a1 ; we must put or or dT ( p— p1 ) 110 [ 201 . QUATERNIONS .
... ( y - ẞ ) = —a ̄1Va ( ẞ — y ) , agrees with the result of last section . 203. ] To find the shortest vector distance between two lines p = B + xa , and 01 = 31 + a1 ; we must put or or dT ( p— p1 ) 110 [ 201 . QUATERNIONS .
Pagina 111
... distance required is ( 1 ) TS.aa1 ( B - B1 ) T ( p — P1 ) = T ( yVaa1 ) = = TS . ( UVaa1 ) ( ẞ — ß1 ) . TVaa [ Note . In the two last expressions T before S is inserted simply to ensure that the length be positive . If then ( § 89 ) S ...
... distance required is ( 1 ) TS.aa1 ( B - B1 ) T ( p — P1 ) = T ( yVaa1 ) = = TS . ( UVaa1 ) ( ẞ — ß1 ) . TVaa [ Note . In the two last expressions T before S is inserted simply to ensure that the length be positive . If then ( § 89 ) S ...
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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...