An Elementary Treatise on Quaternions |
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Page 16
... triangle be inscribed in a parabola , the three points in which the sides are met by tangents at the angles lie in a straight line . Since O is any point of the curve , we may take it as one corner of the triangle . Let t and t1 ...
... triangle be inscribed in a parabola , the three points in which the sides are met by tangents at the angles lie in a straight line . Since O is any point of the curve , we may take it as one corner of the triangle . Let t and t1 ...
Page 20
... triangle of constant area . If the axes be in the directions of a and ß , the intercepts may evidently be written at and 2. Hence the equation of the line is ( § 30 ) t p = at + x ( —at ) . The condition of envelopment is , obviously ...
... triangle of constant area . If the axes be in the directions of a and ß , the intercepts may evidently be written at and 2. Hence the equation of the line is ( § 30 ) t p = at + x ( —at ) . The condition of envelopment is , obviously ...
Page 23
... triangles ABC , abc , be so situated in space that Aa , Bb , Ce meet in a point , the intersections of AB , ab , of BC , bc , and of CA , ca , lie in a straight line . 5. Prove the converse of 4 , i . e . if lines be drawn , one in each ...
... triangles ABC , abc , be so situated in space that Aa , Bb , Ce meet in a point , the intersections of AB , ab , of BC , bc , and of CA , ca , lie in a straight line . 5. Prove the converse of 4 , i . e . if lines be drawn , one in each ...
Page 24
... triangle of whose corners a , ẞ , y are the vectors . ( Hamilton , Elements , p . 96. ) 12. The lines which divide , proportionally , the pairs of opposite sides of a gauche quadrilateral , are the generating lines of a hyper- bolic ...
... triangle of whose corners a , ẞ , y are the vectors . ( Hamilton , Elements , p . 96. ) 12. The lines which divide , proportionally , the pairs of opposite sides of a gauche quadrilateral , are the generating lines of a hyper- bolic ...
Page 46
... triangle must have an equivalent statement in which they are represented by angles in the polar triangle . Shew directly that the product of two versors represented by two angles of a spherical triangle is a third versor represented by ...
... triangle must have an equivalent statement in which they are represented by angles in the polar triangle . Shew directly that the product of two versors represented by two angles of a spherical triangle is a third versor represented by ...
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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...