An Elementary Treatise on Quaternions |
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Page xiii
... to 8 . p = a + xB is the equation of a line drawn through the extremity of a and parallel to B. § 28 . p = ya + xB represents the plane through the origin parallel to a and B. § 29 . The condition that p , a , ẞ may terminate.
... to 8 . p = a + xB is the equation of a line drawn through the extremity of a and parallel to B. § 28 . p = ya + xB represents the plane through the origin parallel to a and B. § 29 . The condition that p , a , ẞ may terminate.
Page xiv
Peter Guthrie Tait. The condition that p , a , ẞ may terminate in the same line is Pp + qa + rB subject to the identical relation Similarly with = p + g + r 0 . pp + qa + rB + 87 0 , p + q + r + 8 = 0 , 0 , is the condition that the ...
Peter Guthrie Tait. The condition that p , a , ẞ may terminate in the same line is Pp + qa + rB subject to the identical relation Similarly with = p + g + r 0 . pp + qa + rB + 87 0 , p + q + r + 8 = 0 , 0 , is the condition that the ...
Page xix
... Condition of equilibrium of a rigid system is S. ẞda = 0 , where ẞ is a vector force , a its point of application . Hence the usual six equations in the form B = 0 , Vaß = 0. Central axis , & c . §§ 373-378 . For the motion of a rigid ...
... Condition of equilibrium of a rigid system is S. ẞda = 0 , where ẞ is a vector force , a its point of application . Hence the usual six equations in the form B = 0 , Vaß = 0. Central axis , & c . §§ 373-378 . For the motion of a rigid ...
Page 8
... condition of the following form must hold Hence and the equation y = aa + BB . P = ( x + za ) a + ( y + zb ) ß , @ = ( § + $ a ) a + ( n + 56 ) ß , p = w now requires only the two numerical conditions x + za = & + 5a , y + zb = n + 5b ...
... condition of the following form must hold Hence and the equation y = aa + BB . P = ( x + za ) a + ( y + zb ) ß , @ = ( § + $ a ) a + ( n + 56 ) ß , p = w now requires only the two numerical conditions x + za = & + 5a , y + zb = n + 5b ...
Page 10
... condition p + q + r = 0 identically . That is A homogeneous linear function of three vectors , equated to zero , expresses that the extremities of these vectors are in one straight line , if the sum of the coefficients be identically ...
... condition p + q + r = 0 identically . That is A homogeneous linear function of three vectors , equated to zero , expresses that the extremities of these vectors are in one straight line , if the sum of the coefficients be identically ...
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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