The Quarterly Journal of Pure and Applied Mathematics, Volume 11J.W. Parker, 1871 - Mathematics |
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Page 20
... ( X2 + Y2 ) — abZ * = 0 . This has four conic nodes ; viz . considering the equations X2 Y2 a + = 0 , aX + b2 - 2ZW = 0 , X2 + Y2 + Z2 = 0 , b -- and these give the point X = 0 , Y 20 On the Quartic Surfaces ( * XU , V , W ' ) 2 = 0 .
... ( X2 + Y2 ) — abZ * = 0 . This has four conic nodes ; viz . considering the equations X2 Y2 a + = 0 , aX + b2 - 2ZW = 0 , X2 + Y2 + Z2 = 0 , b -- and these give the point X = 0 , Y 20 On the Quartic Surfaces ( * XU , V , W ' ) 2 = 0 .
Page 21
and these give the point X = 0 , Y = 0 , Z = 0 four times ; four other points which are the nodes in question ; the point ( X = 0 , Y = 0 , Z = 0 ) is a singular point of a higher order ; the reduction caused by these singularities ...
and these give the point X = 0 , Y = 0 , Z = 0 four times ; four other points which are the nodes in question ; the point ( X = 0 , Y = 0 , Z = 0 ) is a singular point of a higher order ; the reduction caused by these singularities ...
Page 39
... give us any information about its direction . The introduction of a straight tube , which is sometimes employed in the explanation , is hardly satisfactory , seeing that we do not constantly carry straight tubes for the purpose of ...
... give us any information about its direction . The introduction of a straight tube , which is sometimes employed in the explanation , is hardly satisfactory , seeing that we do not constantly carry straight tubes for the purpose of ...
Page 41
... gives a proof of the known theorem , that if a para- bola touch the sides of a triangle , its directrix passes through the orthocentre . For , if S be the focus , which must be on the circum- scribing circle , KL is the tangent at the ...
... gives a proof of the known theorem , that if a para- bola touch the sides of a triangle , its directrix passes through the orthocentre . For , if S be the focus , which must be on the circum- scribing circle , KL is the tangent at the ...
Page 43
... operate with dx dx dx the devector symbols relative to x , y ; x , y ,; but since we shall have to differentiate with regard to a ,, it is only neces- sary to collect the terms which may give rise to Note on a Binary Evectant Form . 43.
... operate with dx dx dx the devector symbols relative to x , y ; x , y ,; but since we shall have to differentiate with regard to a ,, it is only neces- sary to collect the terms which may give rise to Note on a Binary Evectant Form . 43.
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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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