QED

Jeff Miller heeft op zijn website lijsten van de vroegst bekende voorkomens van woorden en symbolen uit de wiskunde staan. Interessant is dat er bij veel woorden een uitgebreide bronnenlijst staat en een overzicht van de evolutie van de term. Over QED staat er:

Q. E. D. Euclid (about 300 B. C.) concluded his proofs with hoper edei deiksai, which Medieval geometers translated as quod erat demonstrandum (”that which was to be proven”).

According to Veronika Oberparleiter, the earliest known use in print of the phrase quod erat demonstrandum in a Euclid translation appears in the translation by Bartholemew Zamberti published in Venice in 1505.

In Dialogues Concerning Two New Sciences (1638) in Latin Galileo used quod erat intentum, quod erat demonstrandum, quod erat probandum, quod erat ostendendum, quod erat faciendum, quod erat determinandum, and quod erat propositum.

In 1665 Benedictus de Spinoza (1632-1677) wrote a treatise on ethics, Ethica More Geometrico Demonstrata, in which he proved various moral propositions in a geometric manner. He wrote the abbreviation Q. E. D., as a seal upon his proof of each ethical proposition.

Isaac Barrow used quod erat demonstrandum, quod erat faciendum (Q. E. F.), quod fieri nequit (Q. F. N.), and quod est absurdum (Q. E. A.).

Isaac Newton used the abbreviation Q. E. D.

[Martin Ostwald, Sam Kutler, Robin Hartshorne, David Reed]

Ook over magische vierkanten leren we iets bij:

MAGIC SQUARE is found in the title Des quassez ou tables magiques by Frenicle de Bessy (1605-1675).

The first citation in the OED2 is in 1704 in Lexicon technicum, or an universal English dictionary of arts and sciences by John Harris.

Benjamin Franklin used the term in his autobiography:

This latter station was the more agreeable to me, as I was at length tired with sitting there to hear debates, in which, as clerk, I could take no part, and which were often so unentertaining that I was induc’d to amuse myself with making magic squares or circles, or any thing to avoid weariness; and I conceiv’d my becoming a member would enlarge my power of doing good.

Franklin also used the term in a letter in which he wrote, “I make no question, but you will readily allow the square of 16 to be the most magically magical of any magic square ever made by any magician” (Cajori 1919, page 170).