The Outlines of QuaternionsLongmans, Green, 1894 - 190 páginas |
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Página vi
... GIVEN PLANE SECTION 1 Linear Equations connecting Two Vectors 25 ° . If pa + qB = 0 , and Ρ and q have real and actual values , then a B 26 ° . If pa + qß 10 • = 0 , and a and B are oblique ; then p = 0 , q = o 10 SECTION 2 Linear ...
... GIVEN PLANE SECTION 1 Linear Equations connecting Two Vectors 25 ° . If pa + qB = 0 , and Ρ and q have real and actual values , then a B 26 ° . If pa + qß 10 • = 0 , and a and B are oblique ; then p = 0 , q = o 10 SECTION 2 Linear ...
Página 2
... given vectors are equal to each other when ( and only when ) the origin and term of the one can be brought to coincide simultaneously with the corresponding points of the other , by motion of translation , without rotation . As a ...
... given vectors are equal to each other when ( and only when ) the origin and term of the one can be brought to coincide simultaneously with the corresponding points of the other , by motion of translation , without rotation . As a ...
Página 9
... tensor of a vector 8 , or OD ; m for the tensor of for the tensor of a = OA , & c . , & c . μ • ( 3 ) d for the = OM , a CHAPTER II ON POINTS AND VECTORS IN A GIVEN PLANE SCALARS , UNIT - VECTORS , AND TENSORS 9 22° Definition of a scalar.
... tensor of a vector 8 , or OD ; m for the tensor of for the tensor of a = OA , & c . , & c . μ • ( 3 ) d for the = OM , a CHAPTER II ON POINTS AND VECTORS IN A GIVEN PLANE SCALARS , UNIT - VECTORS , AND TENSORS 9 22° Definition of a scalar.
Página 10
... given parallel vectors . connected together by an equation of ß = = ma • · ( 1 ) which expresses the collinearity of the three points , O , A , and B. If ẞ be a variable vector , p , and m a variable scalar , x , this equation may be ...
... given parallel vectors . connected together by an equation of ß = = ma • · ( 1 ) which expresses the collinearity of the three points , O , A , and B. If ẞ be a variable vector , p , and m a variable scalar , x , this equation may be ...
Página 11
... given vectors . Then , since لا Take OA ' = - la + mß + ny γ - α , n α n - and OB ' = and draw B'C and A'C . We have now , m = O , B. n m B ; let OC represent n OC = OA ' + OB ' ; but , 11 ° , therefore , OC = OA ' + A'C ; OB ' A'C ...
... given vectors . Then , since لا Take OA ' = - la + mß + ny γ - α , n α n - and OB ' = and draw B'C and A'C . We have now , m = O , B. n m B ; let OC represent n OC = OA ' + OB ' ; but , 11 ° , therefore , OC = OA ' + A'C ; OB ' A'C ...
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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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