The Outlines of QuaternionsLongmans, Green, 1894 - 190 páginas |
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Página xiii
... variable 111 ° . Differential of the square of a scalar 111 113 112 ° . " " an area 114 SECTION 2 Differential of a Vector 113 ° . General formula for the differential of a vector 114 ° . Differential of p = t2a 2 SECTION 3 115 116 = q2 ...
... variable 111 ° . Differential of the square of a scalar 111 113 112 ° . " " an area 114 SECTION 2 Differential of a Vector 113 ° . General formula for the differential of a vector 114 ° . Differential of p = t2a 2 SECTION 3 115 116 = q2 ...
Página 10
... variable vector , p , and m a variable scalar , x , this equation may be written , p = xα · ( 2 ) which expresses that the locus of the variable point , B , is the indefinite straight line passing through the points O and A. The ...
... variable vector , p , and m a variable scalar , x , this equation may be written , p = xα · ( 2 ) which expresses that the locus of the variable point , B , is the indefinite straight line passing through the points O and A. The ...
Página 13
... variable vector and l m to be a variable ratio ; this last equation may be written , P = ха + ув ; x + y which expresses that the locus of the variable point C , the term of p , is the indefinite straight line AB ; which line it cuts ...
... variable vector and l m to be a variable ratio ; this last equation may be written , P = ха + ув ; x + y which expresses that the locus of the variable point C , the term of p , is the indefinite straight line AB ; which line it cuts ...
Página 72
... variable point and OB = OP = = P , it is evident that the locus of P is the surface of a sphere with centre O and radius T. OD = vTa . Equation ( 8 ) then becomes v2a P = КР Ꮭ Ko ; or , Ke = v2 . α α α ( 9 ) ( i ) . If , then , we meet ...
... variable point and OB = OP = = P , it is evident that the locus of P is the surface of a sphere with centre O and radius T. OD = vTa . Equation ( 8 ) then becomes v2a P = КР Ꮭ Ko ; or , Ke = v2 . α α α ( 9 ) ( i ) . If , then , we meet ...
Página 108
... variable , is also the equation of a Circle . What circle ? Comparing these equations with ( 9 ) of 75 ° , it is clear that p is the result of the positive conical rotation of ẞ round a through an angle = 20 = tr = 2t ( 1 ) , i.e. twice ...
... variable , is also the equation of a Circle . What circle ? Comparing these equations with ( 9 ) of 75 ° , it is clear that p is the result of the positive conical rotation of ẞ round a through an angle = 20 = tr = 2t ( 1 ) , i.e. twice ...
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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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