More on special circles and spheres

Abstract

In these Notes (III 287), I devoted a brief article to this subject, in which I confined myself to a complete derivation of the geometric images pertaining thereto. The same derivation, of course, could be carried out by other means, which would necessarity lead to identical results. All conoprimas, for example, can be derived from circles by means of a collinear transformation, but also by the intersection of two projective primas of rays, and it is evident from elementary manuals that the latter example, if not more accurate, is at least more intuitive, and in this sense simpler (see the article). From the brief article mentioned at the beginning, it is clear that the existence of special circles and spheres introduces great disruption into the concepts of the circle that have become established, not merely over centuries, but over millennia. As proven herein, the notions of center and of equal radii must be completely eliminated from this concept.

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