An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina 14
... determine t and x , t + x = p , t2 + xt = q ; 2 by equating respectively the coefficients of a and B. Hence t = p ± √ p2 -2q . Thus , in general , two tangents can be drawn from a given point . These coincide if p2 = 2q ; that is , if ...
... determine t and x , t + x = p , t2 + xt = q ; 2 by equating respectively the coefficients of a and B. Hence t = p ± √ p2 -2q . Thus , in general , two tangents can be drawn from a given point . These coincide if p2 = 2q ; that is , if ...
Pagina 16
... determine the others . Then , if 1 , 2 , 3 represent the vectors of the points of intersection of the tangents with the sides , we easily find These values give 2t - t t1 Also @ 1 @ 2 = = t t12 + 1/2 3 ) , 2 t1 - t ( a + t2 2t - t tt1 ...
... determine the others . Then , if 1 , 2 , 3 represent the vectors of the points of intersection of the tangents with the sides , we easily find These values give 2t - t t1 Also @ 1 @ 2 = = t t12 + 1/2 3 ) , 2 t1 - t ( a + t2 2t - t tt1 ...
Pagina 42
... determines w . Also we have , from the same three , by the help of the first , ¿ x ′ + ny ′ + 5 % = 0 ; which , combined with the first , gives § yz - zy η Š zx - xz = xy ' — yx ' ' and the common value of these three fractions is then ...
... determines w . Also we have , from the same three , by the help of the first , ¿ x ′ + ny ′ + 5 % = 0 ; which , combined with the first , gives § yz - zy η Š zx - xz = xy ' — yx ' ' and the common value of these three fractions is then ...
Pagina 45
... determine the direction in which it must lie . It cannot be a vector parallel to them ; for by changing the sign of both factors the product is unchanged , whereas , as the whole system has been reversed , the product vector ought to ...
... determine the direction in which it must lie . It cannot be a vector parallel to them ; for by changing the sign of both factors the product is unchanged , whereas , as the whole system has been reversed , the product vector ought to ...
Pagina 46
... determine the rule which connects the directions in which these angles are to be measured . 2. Hence derive another proof that we have not generally pq = qp . 3. Hence shew that the proof of the associative principle , § 57 , may be ...
... determine the rule which connects the directions in which these angles are to be measured . 2. Hence derive another proof that we have not generally pq = qp . 3. Hence shew that the proof of the associative principle , § 57 , may be ...
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...