The Quarterly Journal of Pure and Applied Mathematics, Volume 11J.W. Parker, 1871 - Mathematics |
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Page 40
... points of contact , the in- tersection E , of the normal is the instantaneous centre , and if TP = x , TQ = y , x and y are the coordinates of the carried locus of E , and since and OY = p = f ( $ ) , dp PY = = ƒ ' ( $ ) , аф TY = f ...
... points of contact , the in- tersection E , of the normal is the instantaneous centre , and if TP = x , TQ = y , x and y are the coordinates of the carried locus of E , and since and OY = p = f ( $ ) , dp PY = = ƒ ' ( $ ) , аф TY = f ...
Page 66
... points of contact being ( a cosa , b sina ) , ( a cosß , b sinß ) , and ( a cosy , b siny ) , the conditions that its angular points may lie on S ' are 12 a ( a2 b2 + b'2 1 ) a2 b2 +1 cosẞ cosy + +1 ) sin 8 siny -- 12 1 , & c . ... ( B ) ...
... points of contact being ( a cosa , b sina ) , ( a cosß , b sinß ) , and ( a cosy , b siny ) , the conditions that its angular points may lie on S ' are 12 a ( a2 b2 + b'2 1 ) a2 b2 +1 cosẞ cosy + +1 ) sin 8 siny -- 12 1 , & c . ... ( B ) ...
Page 67
... points of contact of the sides , then AABC : △ A'B'C ' is a constant ratio , which is also the ratio of the areas of the conics when they are ellipses , and is the ratio of the areas of the triangles inter- cepted between any tangent ...
... points of contact of the sides , then AABC : △ A'B'C ' is a constant ratio , which is also the ratio of the areas of the conics when they are ellipses , and is the ratio of the areas of the triangles inter- cepted between any tangent ...
Page 83
... point of contact , have , in fact , the above mentioned relation . And it thus appears that given two circles , the necessary and sufficient conditions for the coexistence of the properties mentioned in the theorem are that they shall ...
... point of contact , have , in fact , the above mentioned relation . And it thus appears that given two circles , the necessary and sufficient conditions for the coexistence of the properties mentioned in the theorem are that they shall ...
Page 155
... point of undulation , but of inflexion , since the stationary tangent passes through four consecutive points , two of which are coincident and correspond to the two con- secutive points of contact on the primitive curve lying on the ...
... point of undulation , but of inflexion , since the stationary tangent passes through four consecutive points , two of which are coincident and correspond to the two con- secutive points of contact on the primitive curve lying on the ...
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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
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