An Elementary Treatise on QuaternionsClarendon Press, 1873 - 296 pagina's |
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Pagina xiv
... plane . § 30 . Examples with solutions . § 31 . Differentiation of a vector , when given as a function of one number . §§ 32-38 . If the equation of a curve be p = $ ( 8 ) where s is the length of the arc , dp is a vector tangent to the ...
... plane . § 30 . Examples with solutions . § 31 . Differentiation of a vector , when given as a function of one number . §§ 32-38 . If the equation of a curve be p = $ ( 8 ) where s is the length of the arc , dp is a vector tangent to the ...
Pagina 23
Peter Guthrie Tait. the middle points of the diagonals of any quadrilateral , plane ... tangent at the point where it meets the curves bisects the intercepts of the ... plane pa + q B + ry P = p + q + r is an ellipse which touches , at their ...
Peter Guthrie Tait. the middle points of the diagonals of any quadrilateral , plane ... tangent at the point where it meets the curves bisects the intercepts of the ... plane pa + q B + ry P = p + q + r is an ellipse which touches , at their ...
Pagina 54
... tangent at the vertex is parallel to the base . Here we have or αβ = αβγ , x ( a + y ) = a ( a + y ) y ; whence x ... plane . Again , may be written 2 Тр = Ta T = 1 , 2 α ( 82 ) - ( vf ) 2 = 1 , a ( p + a ) 2 - 28a ( p + a ) = 0 , p ...
... tangent at the vertex is parallel to the base . Here we have or αβ = αβγ , x ( a + y ) = a ( a + y ) y ; whence x ... plane . Again , may be written 2 Тр = Ta T = 1 , 2 α ( 82 ) - ( vf ) 2 = 1 , a ( p + a ) 2 - 28a ( p + a ) = 0 , p ...
Pagina 76
... tangent line dp , §§ 36 , 98. Its length , when Fis a surface of the second degree , is as the reciprocal of the distance of the tangent - plane from the origin . And we will shew , later , that if p = ix + jy + kz , then ע d d d v ...
... tangent line dp , §§ 36 , 98. Its length , when Fis a surface of the second degree , is as the reciprocal of the distance of the tangent - plane from the origin . And we will shew , later , that if p = ix + jy + kz , then ע d d d v ...
Pagina 123
... plane which touches the sphere at the extremity of p , -p is a line in the tangent plane , and therefore perpendicular to p . So that or Sp ( w - p ) = 0 , 2 Sap = Tp2 = a2 is the equation of the tangent plane . 225. ] If this plane ...
... plane which touches the sphere at the extremity of p , -p is a line in the tangent plane , and therefore perpendicular to p . So that or Sp ( w - p ) = 0 , 2 Sap = Tp2 = a2 is the equation of the tangent plane . 225. ] If this plane ...
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Veelvoorkomende woorden en zinsdelen
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
Populaire passages
Pagina 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...
Pagina 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.
Pagina 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.
Pagina 138 - The locus of the middle points of a system of parallel chords in a parabola is called a diameter.
Pagina 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
Pagina 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...