An Elementary Treatise on Quaternions |
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Page xiii
... equation @ = P2 between two vectors , is equivalent to three distinct equations among numbers . § 25 . The Commutative and Associative Laws hold in the combination of vectors by the signs and The equation - $ 27 . ρ = αβ , where p is a ...
... equation @ = P2 between two vectors , is equivalent to three distinct equations among numbers . § 25 . The Commutative and Associative Laws hold in the combination of vectors by the signs and The equation - $ 27 . ρ = αβ , where p is a ...
Page xviii
... equation— Examples . §§ 175-179 . The linear function of a quaternion is given by a symbolical biquadratic . § 180 . Particular forms of linear equations . §§ 181-183 . A quaternion equation of the mth degree in general involves a ...
... equation— Examples . §§ 175-179 . The linear function of a quaternion is given by a symbolical biquadratic . § 180 . Particular forms of linear equations . §§ 181-183 . A quaternion equation of the mth degree in general involves a ...
Page xix
... equation of the Hodograph . p = vp ' + v2p " gives the normal and tangential accelerations . = Vpp 0 if acceleration directed to a point , whence Vpp = y . Examples . - Planetary acceleration . Here the equation is P = μυρ Тра given ...
... equation of the Hodograph . p = vp ' + v2p " gives the normal and tangential accelerations . = Vpp 0 if acceleration directed to a point , whence Vpp = y . Examples . - Planetary acceleration . Here the equation is P = μυρ Тра given ...
Page 8
... equation such as or p = w , xa + yẞ + zy = & a + nB + $ y , necessitates the three numerical equations x = ૐ y = n , ζγ , 2 = ૐ . For , if a , ß , y be coplanar ( § 24 ) , a condition of the following form must hold Hence and the equation ...
... equation such as or p = w , xa + yẞ + zy = & a + nB + $ y , necessitates the three numerical equations x = ૐ y = n , ζγ , 2 = ૐ . For , if a , ß , y be coplanar ( § 24 ) , a condition of the following form must hold Hence and the equation ...
Page 9
... Equation ( 1 ) is one of the many useful forms into which Quater- nions enable us to throw the general equation of a straight line in space . As we have seen ( § 25 ) it is equivalent to three numerical equations ; but , as these ...
... Equation ( 1 ) is one of the many useful forms into which Quater- nions enable us to throw the general equation of a straight line in space . As we have seen ( § 25 ) it is equivalent to three numerical equations ; but , as these ...
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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...