An Elementary Treatise on Quaternions, |
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Page xii
... vectors lie in one 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 = 4 ( 8 ) where s is the length of the arc , dp is a vector ...
... vectors lie in one 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 = 4 ( 8 ) where s is the length of the arc , dp is a vector ...
Page xv
Peter Guthrie Tait. Interpretation of aßy when it is a vector , § 106 . Examples ... function of more quaternions than one . d ( gr ) = qdr + dq.r , but not ... vector normal to the surface , § 137 . EXAMPLES TO CHAPTER IV . . 96 CHAPTER ...
Peter Guthrie Tait. Interpretation of aßy when it is a vector , § 106 . Examples ... function of more quaternions than one . d ( gr ) = qdr + dq.r , but not ... vector normal to the surface , § 137 . EXAMPLES TO CHAPTER IV . . 96 CHAPTER ...
Page xvi
... vector equation Pp = Z.aSBp = Y , §§ 138 , 139 . General proof that o3p is expressible as a linear function of p ... functions and p ' are said to be conjugate , and αφιλμ = φ'λφ ' μ . Proof that m , whose value may be written as Σ ...
... vector equation Pp = Z.aSBp = Y , §§ 138 , 139 . General proof that o3p is expressible as a linear function of p ... functions and p ' are said to be conjugate , and αφιλμ = φ'λφ ' μ . Proof that m , whose value may be written as Σ ...
Page 22
... functions of one indeterminate . In such a case the equation is sometimes written p = $ ( t ) . But , if P1 , P2 ... vector with reference to a single numerical variable of which it was given as an explicit function . As this process ...
... functions of one indeterminate . In such a case the equation is sometimes written p = $ ( t ) . But , if P1 , P2 ... vector with reference to a single numerical variable of which it was given as an explicit function . As this process ...
Page 23
... vector of a curve in space . Then , generally , p may be expressed as the sum of a number of terms , each of which is a multiple of a given vector by a function of some one indeterminate ; or , as in § 31 ( 1 ) , if P be a point on the ...
... vector of a curve in space . Then , generally , p may be expressed as the sum of a number of terms , each of which is a multiple of a given vector by a function of some one indeterminate ; or , as in § 31 ( 1 ) , if P be a point on the ...
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Common terms and phrases
a₁ axis B₁ Cartesian centre Chapter circle commutative law cone conjugate constant cöordinates coplanar curve diameters differential direction drawn easily ellipsoid envelop equal evidently expression extremity Find the equation Find the locus formula geometry given equation given lines given vectors gives Hamilton Hence hyperbola indeterminate intersection inverse function LAOB last section length linear and vector m₁ multiply obviously origin osculating plane P₁ parabola parallel perpendicular properties prove quaternion radius rectangular represented right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate sides solution Spdp sphere spherical conic Spopp straight line student surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vector Vaß vector function vector perpendicular versor written Γλμ φρ
Popular passages
Page 153 - Find the locus of a point the ratio of whose distances from two given points is constant. Let the given points be 0 and A, the extremities of the vector a.
Page 149 - Find the equation of the locus of a point the sum of the squares of whose distances from a number of given planes is constant. 11. Substitute " lines" for "planes
Page 217 - Differentiation of the equations gives us 3p + q+l equations, linear and homogeneous in the 3m + n differentials of the scalar parameters, so that by the elimination of these we have one final scalar equation in the first case, two in the second ; and thus in each case we have just equations enough to eliminate all the arbitrary parameters.
Page 14 - The bisectors of the sides of a triangle meet in a point, which trisects each of them.
Page 195 - Find the equation of the locus of a point the square of whose distance from a given line is proportional to its distance from a given plane.
Page 50 - It is curious to compare the properties of these quaternion symbols with those of the Elective Symbols of Logic, as given in BOOLE'S wonderful treatise on the Laws of Thought ; and to think that the same grand science of mathematical analysis, by processes remarkably similar to each other, reveals to us truths in the science of position far beyond the powers of the geometer, and truths of deductive reasoning to which unaided thought could never have led the logician.