One-sheeted hyperboloids and the generalization of their concept using the example of a system of conoprimas
Abstract
If it turned out that by choosing one linear prima in one diametral second and then arbitrarily another linear prima in an arbitrary other second, and thus constructing an infinite multitude of hyperboloids, we obtain that the entire aggregate of such hyperboloids is contained within a single third, which itself lies within a single linear quart, then we would be dealing with an entity representing a generalization of the concept of a hyperboloid; such a hyperboloid we could call a hyperboloid of the 4th degree system. The special third, possessing circular symmetry, which was just indicated in the article (“Symmetry of linear sets of conoprimas”) is precisely such a generalized hyperboloid in the system of conoprimes. Since in this system, which addresses an entirely different topic, it would be inappropriate to dwell on the consideration of this issue in all its details, this note has been dedicated specifically for this purpose.
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