An Elementary Treatise on Quaternions |
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Page xv
... rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two vectors at right angles to each other is a third perpendicular to both . Hence Ka = -a , and ( Ta ) 2 = aKa = -a2 . § 73 . Every versor may be ...
... rectangular unit - vectors i , j , k . § 72 . The product , and the quotient , of two vectors at right angles to each other is a third perpendicular to both . Hence Ka = -a , and ( Ta ) 2 = aKa = -a2 . § 73 . Every versor may be ...
Page xviii
... rectangular unit - vectors whatever , we have Sq = -m2 , Vq = € . This quaternion can be expressed in the important form q = Vop . §§ 170-174 . Degrees of indeterminateness of the solution of a quaternion equation— Examples . §§ 175-179 ...
... rectangular unit - vectors whatever , we have Sq = -m2 , Vq = € . This quaternion can be expressed in the important form q = Vop . §§ 170-174 . Degrees of indeterminateness of the solution of a quaternion equation— Examples . §§ 175-179 ...
Page 1
... of two dimensions , when rectangular axes are employed , this amounts to reckoning each unit of length along Oy as + √ — 1 , and on Oy as √1 ; while on Ox each unit is +1 , and on Ox it is - ~ lo B - -1 . If we look at these four lines ...
... of two dimensions , when rectangular axes are employed , this amounts to reckoning each unit of length along Oy as + √ — 1 , and on Oy as √1 ; while on Ox each unit is +1 , and on Ox it is - ~ lo B - -1 . If we look at these four lines ...
Page 4
... in space , and suppose A given , on how many numbers does B's relative position depend ? If we refer to Cartesian cöordinates ( rectangular or not ) we find that the data required are the excesses of B's three 4 [ 13 . QUATERNIONS .
... in space , and suppose A given , on how many numbers does B's relative position depend ? If we refer to Cartesian cöordinates ( rectangular or not ) we find that the data required are the excesses of B's three 4 [ 13 . QUATERNIONS .
Page 7
... rectangular parallelepiped of which ρ is the vector - diagonal ; so that the length of p is , in this case , Let √ x2 + y2 + x2 . @ = §i + nj + Šk be any other vector , then ( by the proposition of § 23 ) the vector equation p = w ...
... rectangular parallelepiped of which ρ is the vector - diagonal ; so that the length of p is , in this case , Let √ x2 + y2 + x2 . @ = §i + nj + Šk be any other vector , then ( by the proposition of § 23 ) the vector equation p = w ...
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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...
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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.
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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...