The Outlines of QuaternionsLongmans, Green, 1894 - 190 páginas |
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Página 14
... respectively parallel vectors , they are connected together by equations of the form , - a = x1a ' , ẞ = y ~ ' B ' , y = z ̄1y ' ( 1 ) Substituting these values of a , ß , y , successively , in the given equation , we get lx - 1a ' + mẞ ...
... respectively parallel vectors , they are connected together by equations of the form , - a = x1a ' , ẞ = y ~ ' B ' , y = z ̄1y ' ( 1 ) Substituting these values of a , ß , y , successively , in the given equation , we get lx - 1a ' + mẞ ...
Página 15
... respective triangles . ( c ) . In such equations as those of ( 8 ) , attention must be paid to the signs of figures , plane and solid . Any plane figure is positive or negative according as the rotation of a particle round its periphery ...
... respective triangles . ( c ) . In such equations as those of ( 8 ) , attention must be paid to the signs of figures , plane and solid . Any plane figure is positive or negative according as the rotation of a particle round its periphery ...
Página 16
... respectively in given ratios ; and through their cross D ( instead of O , fig . 5 ) draw a line from C cutting AB in C ' . It is required to determine the ratios AD : DA ' ; BD : DB ' ; CD : DC ' ; and AC C'B . Let the given ratios be ...
... respectively in given ratios ; and through their cross D ( instead of O , fig . 5 ) draw a line from C cutting AB in C ' . It is required to determine the ratios AD : DA ' ; BD : DB ' ; CD : DC ' ; and AC C'B . Let the given ratios be ...
Página 19
... respectively , so that a + B + y = 0 . The tensors of these vectors , or the lengths of the sides of the triangle , will be represented by a , b , c . Let A ' and B ' be the middle points of BC and CA , and let AA ' and BB ' cross in M ...
... respectively , so that a + B + y = 0 . The tensors of these vectors , or the lengths of the sides of the triangle , will be represented by a , b , c . Let A ' and B ' be the middle points of BC and CA , and let AA ' and BB ' cross in M ...
Página 20
... respectively . Let CE produced meet AB ' in C " ; AE meet BC in A " ; and let the external angle - bisector at B meet CA in B " . Then , by + cB AA " = - ; BB " = с Hence , C'A = Therefore , 29 ° , by α b - ( BC'AC " ) ca + ay ; CC " С ...
... respectively . Let CE produced meet AB ' in C " ; AE meet BC in A " ; and let the external angle - bisector at B meet CA in B " . Then , by + cB AA " = - ; BB " = с Hence , C'A = Therefore , 29 ° , by α b - ( BC'AC " ) ca + ay ; CC " С ...
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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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