An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina xvii
... Elimination of Sq , and reduction to the vector equation фр = = Σ . aSBp Y. §§ 138 , 139 . General proof that p3p is expressible as a linear function of p , pp , and p2p . § 140 . Value of for an ellipsoid , employed to illustrate the ...
... Elimination of Sq , and reduction to the vector equation фр = = Σ . aSBp Y. §§ 138 , 139 . General proof that p3p is expressible as a linear function of p , pp , and p2p . § 140 . Value of for an ellipsoid , employed to illustrate the ...
Pagina 21
... eliminating 1 , = X1 tı 1 ( 1-10 ) , t ( 1 − x ) = t1 ( 1– or x = t1 + t Hence the vector of the point of intersection is P = att1 + ß t1 + t , and thus , for the ultimate intersections , where = 43. ] 21 VECTORS , AND THEIR COMPOSITION .
... eliminating 1 , = X1 tı 1 ( 1-10 ) , t ( 1 − x ) = t1 ( 1– or x = t1 + t Hence the vector of the point of intersection is P = att1 + ß t1 + t , and thus , for the ultimate intersections , where = 43. ] 21 VECTORS , AND THEIR COMPOSITION .
Pagina 66
... Eliminating we have qq - qr = — qʻr , which gives i . e . ( g ' - 1q ) 2 = −1 , q = qa where a is some unit - vector . And the two equations now agree in giving —r = ar ' , so that we have the biquaternion factors in the form g ' ( a + ...
... Eliminating we have qq - qr = — qʻr , which gives i . e . ( g ' - 1q ) 2 = −1 , q = qa where a is some unit - vector . And the two equations now agree in giving —r = ar ' , so that we have the biquaternion factors in the form g ' ( a + ...
Pagina 77
... Eliminating Sdq between the equations for Sdr and Vdr it is obvious that a linear and vector expression in Vdq will remain . Such an expression , so far as it contains Vdq , may always be reduced to the form of a sum of terms of the ...
... Eliminating Sdq between the equations for Sdr and Vdr it is obvious that a linear and vector expression in Vdq will remain . Such an expression , so far as it contains Vdq , may always be reduced to the form of a sum of terms of the ...
Pagina 82
... Eliminating x from these equations we find m1 = $ ( m2 - 4 ) + mp ̄1 , or mp1 = m1 — m2 $ + p2 , - which contains the complete solution of linear and vector equations . 149. ] More to satisfy the student of the validity of the above ...
... Eliminating x from these equations we find m1 = $ ( m2 - 4 ) + mp ̄1 , or mp1 = m1 — m2 $ + p2 , - which contains the complete solution of linear and vector equations . 149. ] More to satisfy the student of the validity of the above ...
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...