Quartic Surfaces With Singular Points
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In our eReader you can find the full English version of the book. Read Quartic Surfaces With Singular Points Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Quartic Surfaces With Singular Points
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The centres of these point-spheres are therefore the points M and M'. Hence the surface may be defined as the locus of the limiting points determined by Si and the tangent planes to Qi.
The points of Qi which give rise to real points of the cyclide are therefore those the tangent planes at which do not meet S t in real points. Taking the tangent planes common to Si and Qi we have a curve or curves determined on Qi denning the region on Qi which gives rise to real points of the cyclide.
Bitangen...t spheres whose centres lie on the same generator of a principal quadric.
The spheres which cut Si orthogonally and whose centres lie on a line p, a generator of Qi, will pass through the points of contact P, P' of the tangent planes to Si through p ; hence if G is the point of intersection of p and a plane through the centre of Si perpendicular to p, each of these spheres will pass through the circle whose centre is C and radius GP (or OP'). The circle lies on the cyclide ; for considering all the planes through p, the limiting points M, M' which arise in connection with Si, lie in the plane of this circle, also CM = CM' = GP = GP.
What to read after Quartic Surfaces With Singular Points?
You can find similar books in the "Read Also" column, or choose other free books by C M Charles Minshall Jessop to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
The centres of these point-spheres are therefore the points M and M'. Hence the surface may be defined as the locus of the limiting points determined by Si and the tangent planes to Qi.
The points of Qi which give rise to real points of the cyclide are therefore those the tangent planes at which do not meet S t in real points. Taking the tangent planes common to Si and Qi we have a curve or curves determined on Qi denning the region on Qi which gives rise to real points of the cyclide.
Bitangen...t spheres whose centres lie on the same generator of a principal quadric.
The spheres which cut Si orthogonally and whose centres lie on a line p, a generator of Qi, will pass through the points of contact P, P' of the tangent planes to Si through p ; hence if G is the point of intersection of p and a plane through the centre of Si perpendicular to p, each of these spheres will pass through the circle whose centre is C and radius GP (or OP'). The circle lies on the cyclide ; for considering all the planes through p, the limiting points M, M' which arise in connection with Si, lie in the plane of this circle, also CM = CM' = GP = GP.
What to read after Quartic Surfaces With Singular Points?
You can find similar books in the "Read Also" column, or choose other free books by C M Charles Minshall Jessop to read onlineMoreLess
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