 | Mathematics - 1850 - 318 pages
...of the curve of intersection : we arrive then at the important result, that " if two surfaces touch, the point of contact is a double point on their curve of intersection." We can prove that at such a point the curve of intersection has two tangents, by shewing that there... | |
 | George Salmon - Geometry, Analytic - 1862 - 490 pages
...invariants with regard to the pair of quadrics. 128. It is to be remarked that when two surfaces touch, the point of contact is a double point on their curve of intersection. In general, two surfaces of the m°* and nt" degrees respectively intersect in a curve of the mn°*... | |
 | Percival Frost - 1863 - 526 pages
...developable surface generated by the normal planes to a helix, is another helix. (8) If two surfaces touch, the point of contact is a double point on their curve of intersection. (9) Prove that in the common tangent plane of two surfaces which touch there are two directions, any... | |
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... intersection. If however the two surfaces should touch, every plane through the point of contact meets the surfaces in two curves which touch. Every such plane therefore passes through two coincident points of the curve of intersection : we arrive... 