The Quarterly Journal of Pure and Applied Mathematics, Volume 11J.W. Parker, 1871 - Mathematics |
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Page 41
... meet at a point E on the cir- cumference of the fixed circle . It will be easily seen that the line TE passes through 0 , and is four times the radius ( c ) of the rolling circle , so that while the fixed locus of E is the circle of ...
... meet at a point E on the cir- cumference of the fixed circle . It will be easily seen that the line TE passes through 0 , and is four times the radius ( c ) of the rolling circle , so that while the fixed locus of E is the circle of ...
Page 47
The preceding result may be regarded as a generalisation of the theorem which we meet at the outset of the theory of forms , that the quadratic invariant of an odd function . vanishes and an even function is the evectant of its quad ...
The preceding result may be regarded as a generalisation of the theorem which we meet at the outset of the theory of forms , that the quadratic invariant of an odd function . vanishes and an even function is the evectant of its quad ...
Page 82
... the radical axis , which meets , suppose , the line of centres in M , then it is necessary that K shall be one of the anti - points of A , A ' ; or what is the same thing , the = distance KM must be into MA or MA ' ( 82 )
... the radical axis , which meets , suppose , the line of centres in M , then it is necessary that K shall be one of the anti - points of A , A ' ; or what is the same thing , the = distance KM must be into MA or MA ' ( 82 )
Page 102
... meet AC in C. Let AG = r , AA ' = ds , and let p be the radius of curvature of AA ' at A. Now GAC + AGA ' = exterior angle AnA ' ds cos therefore $ + ጥ therefore = GÂ ' C + AĈA ' ; аф ds = & + do + ds ; Р cos o 1 = -- . ( 1 ) . P Let p ...
... meet AC in C. Let AG = r , AA ' = ds , and let p be the radius of curvature of AA ' at A. Now GAC + AGA ' = exterior angle AnA ' ds cos therefore $ + ጥ therefore = GÂ ' C + AĈA ' ; аф ds = & + do + ds ; Р cos o 1 = -- . ( 1 ) . P Let p ...
Page 111
... meet the axis of rotation 00 ' in the point M , and let the projection of 00 ' on the plane of the conic be MN . Take P any point of the conic ; draw PQ in the plane of the conic , perpendicular to MN , and QR perpendicular to OO ...
... meet the axis of rotation 00 ' in the point M , and let the projection of 00 ' on the plane of the conic be MN . Take P any point of the conic ; draw PQ in the plane of the conic , perpendicular to MN , and QR perpendicular to OO ...
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Common terms and phrases
a+b+c action af-g angle angular velocities axes body Cayley centre circle coefficient columns common tangent concyclic cone confocal conic conicoids conjugate coordinates corresponding cubic curvature cusps denote differential dt dt elements ellipsoid envelope equal equation Euler's equations evectant evolute expression fixed point formulæ given curve greatest value Hence inflexion instantaneous axis integral intersection line IJ log mv magic square nodal normal obtain pairs parallel curve perpendicular points of contact pole quadric quartic surface radius reciprocal respectively shewn solenoid solution stationary tangent suppose tangent planes theorem torse triads unlike signs vertex w₁ whence WILLIAM WALTON zero square
Popular passages
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