precisely that…complete with all its parts perfect

The formal divisions of a proposition

Proculs writes: Every problem and every theorem, which is complete with all its parts perfect, purports to contain in itself all of the following elements: enunciation, setting-out, definition or specification, construction or machinery, proof, conclusion.

Readers will notice that most propositions conclude, “Therefore, etc., Q.E.D.”

Q.E.D. stands for the Latin quod erat demonstrandum, that which was to have been demonstrated…. However, the meaning of the Greek is slightly different: a better translation would be, “precisely what was required to be proved.”

Euclid. Euclid’s Elements. Thomas L. Heath, trans. Dana Densmore, ed. Santa Fe, New Mexico: Green Lion Press, 2010. xxiii-xxiv.


Möbius strip

The Möbius strip or Möbius band (pronounced UK: /ˈmɜːbiəs/ or US: /ˈmoʊbiəs/ in English, [ˈmøːbi̯ʊs] in German) (alternatively written Mobius or Moebius in English) is a surface with only one side and only one boundary component. The Möbius strip has the mathematical property of being non-orientable. It can be realized as a ruled surface. It was discovered independently by the German mathematicians August Ferdinand Möbius and Johann Benedict Listing in 1858.[1][2][3]

The shape of the Möbius Strip probably dates to ancient times. An Alexandrian manuscript of early Alchemical diagrams contains an illustration with the visual proportions of the Möbius Strip. This image, on a page titled “The Chrysopoeia of Cleopatra”, has the appearance of an Ouroboros, and is referred to as the “One, All”.[4] Details »