An Elementary Treatise on Quaternions |
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Page xi
... 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 . Since 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 . Since the ...
Page xvi
... vectors , a and 5 , we have TV 3 73 = Dus f . 8a3 = -7a73 coef , IT3 = Ta73f . 48-67 ... vector reflected ray , when 8 is the incident ray and a normal to the ... linear and homogeneous in dq ; but we cannot generally write dFqf ( q ) dq ...
... vectors , a and 5 , we have TV 3 73 = Dus f . 8a3 = -7a73 coef , IT3 = Ta73f . 48-67 ... vector reflected ray , when 8 is the incident ray and a normal to the ... linear and homogeneous in dq ; but we cannot generally write dFqf ( q ) dq ...
Page xvii
... 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 general theory . §§ 141-143 . Hamilton's ...
... 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 general theory . §§ 141-143 . Hamilton's ...
Page 9
... vector OP or p ; or we may pass first to A , by means of OA or a , and then to P along a vector parallel to ß ( § 16 ) ... linear functions of one indeterminate number ; and a plane , if they be linear expres- sions containing two ...
... vector OP or p ; or we may pass first to A , by means of OA or a , and then to P along a vector parallel to ß ( § 16 ) ... linear functions of one indeterminate number ; and a plane , if they be linear expres- sions containing two ...
Page 32
... vector OA in that line , and at once find two others , OB and OC , such that OB = qOA , and OB + OC = OC + OB = OC ... linear function of three given rect- angular unit - vectors . And when the proposition is thus established , the ...
... vector OA in that line , and at once find two others , OB and OC , such that OB = qOA , and OB + OC = OC + OB = OC ... linear function of three given rect- angular unit - vectors . And when the proposition is thus established , the ...
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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...