Four studies of the lemniscate as GA 323 derives it — Steiner’s Cassini construction and its “out of space” branch, the sky-body correspondence, the Moon’s eclipse geometry, and the full seven-sphere system. Each carries its provenance in the Source Lens below.
The lemniscate as one frame of the Curve of Cassini. Sweep the focal distance and watch the oval pinch into the lemniscate, then split into two loops — the moment continuity “goes out of space.”
Source Lens · provenance
GA323, L9: “the lemniscate… is a special form of Curve of Cassini” (constant product).
GA323, L10: “I obtain the lemniscate when a=b, and the discontinuous curve when a is greater than b.”
GA323, L9: obliged “to go out of space… to preserve the continuity of the idea.” Rendered here as a projective circle-inversion — a representation, not a literal exit from 3-space.
Grounded in GA 323 lectures 8–12 (8–12 January 1921). These curves are teaching-forms offered for study, not an ephemeris.