An Elementary Treatise on Quaternions |
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Page xi
... prove of interest to even the advanced student . Since the appearance of the first edition I have managed ( at least partially ) to effect the application of Quaternions to line , surface , and volume integrals , such as occur in ...
... prove of interest to even the advanced student . Since the appearance of the first edition I have managed ( at least partially ) to effect the application of Quaternions to line , surface , and volume integrals , such as occur in ...
Page 3
... proves . 11. ] A very curious speculation , due to Servois and published in 1813 in Gergonne's Annales , is the only one , so far as has been discovered , in which the slightest trace of an anticipation of Quaternions is contained ...
... proves . 11. ] A very curious speculation , due to Servois and published in 1813 in Gergonne's Annales , is the only one , so far as has been discovered , in which the slightest trace of an anticipation of Quaternions is contained ...
Page 4
... prove , it can be established , ab initio , in various ways , without even an allusion to Cartesian Geometry . As this work is written for students acquainted with at least the elements of the Cartesian method , we keep to the first ...
... prove , it can be established , ab initio , in various ways , without even an allusion to Cartesian Geometry . As this work is written for students acquainted with at least the elements of the Cartesian method , we keep to the first ...
Page 8
... prove this for the sign + , it will be equally proved for - , because - before a vector ( § 20 ) merely indicates that it is to be reversed before being considered positive . Let A , B , C , D be , in order , the corners of a ...
... prove this for the sign + , it will be equally proved for - , because - before a vector ( § 20 ) merely indicates that it is to be reversed before being considered positive . Let A , B , C , D be , in order , the corners of a ...
Page 10
... proving , in a very simple manner , numerous classes of propositions in plane and solid geo- metry . A very few examples , however , must suffice at this stage ; since we have hardly , as yet , crossed the threshold of the subject , and ...
... proving , in a very simple manner , numerous classes of propositions in plane and solid geo- metry . A very few examples , however , must suffice at this stage ; since we have hardly , as yet , crossed the threshold of the subject , and ...
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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
Popular passages
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...