The Outlines of QuaternionsLongmans, Green, 1894 - 190 páginas |
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Página 8
... according to the ordinary laws of algebra . 23o . In equation ( 1 ) of 18 ° , AZ = mAB , where m is a positive ... according as x is positive or negative . Hence , T ( xp ) χρ = = + Up according as xo . P ± x = ± xTp , . х Up ρ • ( 2 ) ...
... according to the ordinary laws of algebra . 23o . In equation ( 1 ) of 18 ° , AZ = mAB , where m is a positive ... according as x is positive or negative . Hence , T ( xp ) χρ = = + Up according as xo . P ± x = ± xTp , . х Up ρ • ( 2 ) ...
Página 9
Henry William Lovett Hime. In general , TS = + S , according as So ; or , the tensor of scalar is that scalar taken positively . The tensor of a tensor is the tensor itself ; or , TT = T. If x and y be any scalars , S ( xp + y ) = y ...
Henry William Lovett Hime. In general , TS = + S , according as So ; or , the tensor of scalar is that scalar taken positively . The tensor of a tensor is the tensor itself ; or , TT = T. If x and y be any scalars , S ( xp + y ) = y ...
Página 15
... according as the rotation of a particle round its periphery , as seen from a given aspect of the plane , is right - handed or left - handed . Thus , for any triangle ABC , we have ABC = BCA CAB = and as for a line we have - BAC = ACB ...
... according as the rotation of a particle round its periphery , as seen from a given aspect of the plane , is right - handed or left - handed . Thus , for any triangle ABC , we have ABC = BCA CAB = and as for a line we have - BAC = ACB ...
Página 16
... according as the rotation of a particle round one of its faces is right - handed or left - handed , as seen from the opposite apex . Thus , — — à ̧ ̧à ̧ In this case we have = - AA2A3A4 : = —  ̧ ̧à ̧ = ¿à ̧À¡Ä ̧ AAA3A4 ...
... according as the rotation of a particle round one of its faces is right - handed or left - handed , as seen from the opposite apex . Thus , — — à ̧ ̧à ̧ In this case we have = - AA2A3A4 : = —  ̧ ̧à ̧ = ¿à ̧À¡Ä ̧ AAA3A4 ...
Página 37
... according as the rotation is positive or negative . ( c ) . The function , or effect , as versors , of all unit - vectors designated by symbols whose index is unity , is to turn vectors perpendicular to themselves through a quadrant ...
... according as the rotation is positive or negative . ( c ) . The function , or effect , as versors , of all unit - vectors designated by symbols whose index is unity , is to turn vectors perpendicular to themselves through a quadrant ...
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Términos y frases comunes
arcs axis bisects centre chord circle coinitial vectors collinear commutative law conic conjugate consequently coplanar coplanar quaternions Crown 8vo diameter differential diplanar direction equal equation geometric given Hence hyperbola Illustrations intersection latus rectum Let OA locus mean point mẞ Multiplying OABC operation opposite P₁ parabola parallel parallelopiped perpendicular plane AOB positive or negative reciprocal right angles right quaternion right versors rotation Saß Saßy scalar Scientific Works published Similarly sphere SrVq ẞa symbols tangent TaTẞ tensor three vectors triangle Tẞ TẞTa unit-vector variable Vaß vector versor vertex VqVr VrVq Vẞy Woodcuts α α αβ β α βα φρ ОА ов ос тв وو ᎢᏰ
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