An Elementary Treatise on Quaternions |
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Page xiii
... Triangles and polygons of vectors , analogous to those of forces and of simul- taneous velocities . § 21 . When two vectors are parallel we have a = xB . § 22 . Any vector whatever may be expressed in terms of three distinct vectors ...
... Triangles and polygons of vectors , analogous to those of forces and of simul- taneous velocities . § 21 . When two vectors are parallel we have a = xB . § 22 . Any vector whatever may be expressed in terms of three distinct vectors ...
Page 6
... triangle , ABC , we have , of course , AB + BC + CA = 0 ; and , in any closed polygon , whether plane or gauche , AB + BC + .. ...... + YZ + ZA = 0 . In the case of the polygon we have also AB + BC + ...... + YZ = AZ . These are the ...
... triangle , ABC , we have , of course , AB + BC + CA = 0 ; and , in any closed polygon , whether plane or gauche , AB + BC + .. ...... + YZ + ZA = 0 . In the case of the polygon we have also AB + BC + ...... + YZ = AZ . These are the ...
Page 10
... triangle can be constructed , whose sides are parallel , and equal , to the bisectors of the sides of any triangle . Let ABC be any triangle , Aa , Bb , Ce the bisectors of the sides . Then Aa = AB + Ba = AB + 1⁄2 10 [ 31 . QUATERNIONS .
... triangle can be constructed , whose sides are parallel , and equal , to the bisectors of the sides of any triangle . Let ABC be any triangle , Aa , Bb , Ce the bisectors of the sides . Then Aa = AB + Ba = AB + 1⁄2 10 [ 31 . QUATERNIONS .
Page 11
... triangle meet in a point , which trisects each of them . Taking A as origin , and putting a , ß , y for vectors parallel , and equal , to the sides taken in order BC , CA , AB ; the equation of Bb is ( § 28 ( 1 ) ) x 1/2 p = y + x ( y + ...
... triangle meet in a point , which trisects each of them . Taking A as origin , and putting a , ß , y for vectors parallel , and equal , to the sides taken in order BC , CA , AB ; the equation of Bb is ( § 28 ( 1 ) ) x 1/2 p = y + x ( y + ...
Page 12
... . = ( e . ) To find the centre of inertia of any system . If OA = a , OB a1 , be the vector sides of any triangle , the vector from the vertex dividing the base AB in C so that BC : CA :: m : m1 is ma + 12 [ 31 . QUATERNIONS .
... . = ( e . ) To find the centre of inertia of any system . If OA = a , OB a1 , be the vector sides of any triangle , the vector from the vertex dividing the base AB in C so that BC : CA :: m : m1 is ma + 12 [ 31 . QUATERNIONS .
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Common terms and phrases
a₁ axes axis Cartesian centre of inertia Chapter circle cloth cone conjugate constant cöordinates coplanar curvature curve developable surface diameters differential direction drawn easily ellipsoid envelop equal evidently expression Extra fcap extremity fcap Find the equation Find the locus given equation given line given vectors gives Hamilton Hence hodograph integral intersection last section length linear and vector locus normal obviously once operator origin osculating osculating plane P₁ parabola parallel perpendicular properties quaternion radius rectangular represents result right angles rotation S.aßy Saß scalar scalar equations second order self-conjugate shew solution sphere spherical straight line suppose surface surface of revolution tangent plane Taylor's Theorem tensor theorem three vectors triangle unit-vectors Vaß vector function versor w₁ write written Τρ φρ