An Elementary Treatise on Quaternions |
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Page 156
... curvature at the point s . 283. ] Thus , if OP os be the vector of any point P of the curve , and if C be the centre of curvature at P , we have and thus 1 PC = φς 1 ОС = фѕ- p's is the equation of the locus of the centre of curvature ...
... curvature at the point s . 283. ] Thus , if OP os be the vector of any point P of the curve , and if C be the centre of curvature at P , we have and thus 1 PC = φς 1 ОС = фѕ- p's is the equation of the locus of the centre of curvature ...
Page 159
... curvature of the tortuous 288. ] Let us recur for a moment to the equation of the parabola ( § 31 ( f . ) ) Bt2 p = at + 2 dt Here p = ( a + ẞt ) ds ' whence , if we assume Saß = 0 , ds = √ ― a2- B2 12 , dt from which the length of the ...
... curvature of the tortuous 288. ] Let us recur for a moment to the equation of the parabola ( § 31 ( f . ) ) Bt2 p = at + 2 dt Here p = ( a + ẞt ) ds ' whence , if we assume Saß = 0 , ds = √ ― a2- B2 12 , dt from which the length of the ...
Page 182
... curvature of a normal section of a central surface of the second order . In this , and the few similar investigations which follow , it will be simpler to employ infinitesimals than differentials ; though for a thorough treatment of the ...
... curvature of a normal section of a central surface of the second order . In this , and the few similar investigations which follow , it will be simpler to employ infinitesimals than differentials ; though for a thorough treatment of the ...
Page 183
... curvature , their being at right angles to each other , the curvature in any normal section in terms of the chief curvatures and the inclination to their planes , & c . , & c . , without farther analysis . And when , in a future section ...
... curvature , their being at right angles to each other , the curvature in any normal section in terms of the chief curvatures and the inclination to their planes , & c . , & c . , without farther analysis . And when , in a future section ...
Page 184
... curvature of the other . The student may form a notion of the nature of this proposition by con- sidering a small square plate , with normals drawn at every point , to be slightly bent , but by different amounts , in planes ...
... curvature of the other . The student may form a notion of the nature of this proposition by con- sidering a small square plate , with normals drawn at every point , to be slightly bent , but by different amounts , in planes ...
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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...