An Elementary Treatise on Quaternions |
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Page 141
... envelop , ( see next Chapter , ) Sw ' & w = 0,1 where ' dw , = or i.e. Hence and So'p = 0 , p = xp , { Vx = 0 } , -1 ... envelop of the plane of contact . If Sapa 1 be the outer , and Spyp 1 be the inner , and = = being any two self ...
... envelop , ( see next Chapter , ) Sw ' & w = 0,1 where ' dw , = or i.e. Hence and So'p = 0 , p = xp , { Vx = 0 } , -1 ... envelop of the plane of contact . If Sapa 1 be the outer , and Spyp 1 be the inner , and = = being any two self ...
Page 152
... envelop of all non - central plane sections of an ellip- soid whose area is constant . 8. Find the locus of the ... envelop of the planes of contact of tangent planes drawn to an ellipsoid from points of a concentric sphere . Find the ...
... envelop of all non - central plane sections of an ellip- soid whose area is constant . 8. Find the locus of the ... envelop of the planes of contact of tangent planes drawn to an ellipsoid from points of a concentric sphere . Find the ...
Page 154
... envelop of their planes of contact is Spp3p 1 . = 32. Tangent cones are drawn from every point of S ( p - a ) ( p - a ) = n2 , to the similar and similarly situated surface Spop = 1 , shew that their planes of contact envelop the ...
... envelop of their planes of contact is Spp3p 1 . = 32. Tangent cones are drawn from every point of S ( p - a ) ( p - a ) = n2 , to the similar and similarly situated surface Spop = 1 , shew that their planes of contact envelop the ...
Page 164
... = p + up = $ + up ' , 300. ] This leads us to the consideration of envelops generally , and the process just employed may easily be extended to the problem of finding the envelop of a series of surfaces whose 164 [ 298 . QUATERNIONS .
... = p + up = $ + up ' , 300. ] This leads us to the consideration of envelops generally , and the process just employed may easily be extended to the problem of finding the envelop of a series of surfaces whose 164 [ 298 . QUATERNIONS .
Page 165
... envelop is precisely the same as that employed in ordinary Cartesian geometry , though the work is often shorter and ... envelop . 301. ] As an example , let us find the envelop of the osculating plane of a tortuous curve . Here the ...
... envelop is precisely the same as that employed in ordinary Cartesian geometry , though the work is often shorter and ... envelop . 301. ] As an example , let us find the envelop of the osculating plane of a tortuous curve . Here 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...