An Elementary Treatise on Quaternions |
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Page vii
... properties of i , j , k merely , it is possible to construct from them the whole system * ; just as we deal with the imaginary of Algebra , or , to take a closer analogy , just as Hamilton himself dealt with Couples , Triads , and Sets ...
... properties of i , j , k merely , it is possible to construct from them the whole system * ; just as we deal with the imaginary of Algebra , or , to take a closer analogy , just as Hamilton himself dealt with Couples , Triads , and Sets ...
Page xi
... properties of the linear and vector function , based directly upon the Kinematics of Homogeneous Strain , and therefore so different in method from that employed in this work that it may prove of interest to even the advanced student ...
... properties of the linear and vector function , based directly upon the Kinematics of Homogeneous Strain , and therefore so different in method from that employed in this work that it may prove of interest to even the advanced student ...
Page xviii
... properties of p . Proof that Sp ( p + g ) 1p = 0 , and Sp ( p + h ) −1p = 0 represent the same surface if mSpp - 1p = ghp2 . φρ = φ'ρ + Περ . Proof that when 4 is not self - conjugate Proof that , if 4 = αφα + βφβ + γΦΥ , where a , B ...
... properties of p . Proof that Sp ( p + g ) 1p = 0 , and Sp ( p + h ) −1p = 0 represent the same surface if mSpp - 1p = ghp2 . φρ = φ'ρ + Περ . Proof that when 4 is not self - conjugate Proof that , if 4 = αφα + βφβ + γΦΥ , where a , B ...
Page 15
... properties of the pole and polar in the parabola ; but , for the sake of the beginner , we adopt a simpler , though equally general , process . Suppose a = 0. This merely restricts the pole to the particular diameter to which we have ...
... properties of the pole and polar in the parabola ; but , for the sake of the beginner , we adopt a simpler , though equally general , process . Suppose a = 0. This merely restricts the pole to the particular diameter to which we have ...
Page 16
... very small class of the properties of curves , represented by such equations as those above written . ( 7. ) We may now , in extension of 16 [ 31 . QUATERNIONS . Definition of a VECTOR It may be employed to denote translation §
... very small class of the properties of curves , represented by such equations as those above written . ( 7. ) We may now , in extension of 16 [ 31 . QUATERNIONS . Definition of a VECTOR It may be employed to denote translation §
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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...