Elements of Quaternions |
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Page v
... COMPLANAR QUATERNIONS , OR QUOTIENTS OF VECTORS IN ONE PLANE ; AND ON POWERS , ROOTS , and logarithms OF QUATERNIONS , The first six Sections of this Chapter ( II . ii . ) may be passed over in a first perusal . SECTION 1. - On Complanar ...
... COMPLANAR QUATERNIONS , OR QUOTIENTS OF VECTORS IN ONE PLANE ; AND ON POWERS , ROOTS , and logarithms OF QUATERNIONS , The first six Sections of this Chapter ( II . ii . ) may be passed over in a first perusal . SECTION 1. - On Complanar ...
Page vi
... Complanar Quaternions ; and on the Existence of n Real Quaternion Roots , of any such Equation of the nth Degree , • SECTION 6. On the n2n Imaginary ( or Symbolical ) Roots of a Quaternion Equation of the nth Degree , with Coefficients ...
... Complanar Quaternions ; and on the Existence of n Real Quaternion Roots , of any such Equation of the nth Degree , • SECTION 6. On the n2n Imaginary ( or Symbolical ) Roots of a Quaternion Equation of the nth Degree , with Coefficients ...
Page viii
... complanar . Constructions are given also for pro- ducts of successive sides of triangles , and other closed polygons , inscribed in circles , or in spheres ; for example , a characteristic property of the circle is contained in the ...
... complanar . Constructions are given also for pro- ducts of successive sides of triangles , and other closed polygons , inscribed in circles , or in spheres ; for example , a characteristic property of the circle is contained in the ...
Page x
... complanar ) . And here , perhaps , a student might consider his first perusal of this work as closed . * = CHAPTER II . ON DIFFERENTIALS AND DEVELOPMENTS OF FUNCTIONS OF QUA- TERNIONS ; AND ON SOME APPLICATIONS OF QUATERNIONS TO ...
... complanar ) . And here , perhaps , a student might consider his first perusal of this work as closed . * = CHAPTER II . ON DIFFERENTIALS AND DEVELOPMENTS OF FUNCTIONS OF QUA- TERNIONS ; AND ON SOME APPLICATIONS OF QUATERNIONS TO ...
Page xi
... complanar ; and therefore that we have not generally , dlp = dp Ρ if p be a variable vector ; although we have , in this Calculus , the scarcely less simple equation , which is useful in questions respecting orbital motion , p_dp dl = a ...
... complanar ; and therefore that we have not generally , dlp = dp Ρ if p be a variable vector ; although we have , in this Calculus , the scarcely less simple equation , which is useful in questions respecting orbital motion , p_dp dl = a ...
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Common terms and phrases
ABCD algebra angle anharmonic axis centre CHAP circle coefficients collinear comp Compare the Note complanar cone conic conjugate considered construction curvature curve cyclic deduced denote derived differential diplanar direction ellipsoid equal equation expression formula four fourth proportional function geometrical given plane given points harmonic conjugate imaginary interpreted intersection length line oa linear locus multiplication negative notation osculating osculating circle osculating plane P₁ parallelogram perpendicular positive quadratic quadrilateral quinary radius reciprocal relative direction represented right line right quaternions right quotient right versors roots rotation round scalar SECTION sides sphere spherical spherical angle sub-articles supposed surface symbol tangent tensor ternion theorem tion triangle ABC twisted cubic variable vector VIII whence whereof write