On Models of Cubic Surfaces

On Models of Cubic Surfaces
W H William Henry Blythe
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When there is a node, C 2, the same kind of section B or C is obtained in either direc- tion.
Ill] MISCELLANEOUS 61 On the number of points necessary to determine a cubic surface.
We know that the equation of a cubic surface and therefore the twenty-seven straight lines upon it may be determined by 19 points upon the surface, not more than 9 being in the same plane, but a less number of points will be required if they are related to the surface in any special manner.
To take an illustration fro
...m conic sections.
Usually five points are required to determine a conic, but if we state that two given points are the extremities of the major axis we actually give four points, so only one other arbitrary point is required.
The tetrahedron in the following construction is taken from a figure in a paper by Mr H. M. Taylor already referred to.
Take the tetrahedron as ABCD cut by four planes Ix + My + Nz + Pu = 0, Lx my + Nz + Pu = 0, Lx + My nz + Pu = 0, Lx + My + Nz pu = Q, the planes of the tetrahedron being x = 0, y = 0, z = 0, n = 0.

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