Luke, The word 'analemma' has been used in a number of different ways, which you are mixing up in your question. The ancient use of the word refers more properly to what we might call today an orthographic projection.
For discussion of the various uses, fuller references, first use of the graphic figure 8, etc. see my article, "Of Analemmas, Mean Time and the Analemmatic Sundial" which appeared in two parts in the Bulletin of the British Sundial Society, Jun 1994, 94(2):2-6, and Feb 1995, 95(1):39-44. Fred Sawyer
