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- quod erat demonstrandum used to convey that a fact or situation demonstrates the truth of one's theory or claim, especially to mark the conclusion of a formal proof; the Latin phrase, meaning literally ‘which was to be demonstrated’, is a translation of the Greek phrase used in a number of Euclid 's propositions.
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Where did quod erat demonstrandum come from?
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When was QED first used?
It was invented by Aristotle (384–322 B.C.) in Athens, and recorded in a group of writings known as the Organon. In one of these works, the Prior Analytics, Aristotle attempted to provide a complete analysis of the valid forms of reasoning.
The phrase quod erat demonstrandum is a translation into Latin from the Greek ὅπερ ἔδει δεῖξαι (hoper edei deixai; abbreviated as ΟΕΔ). The meaning of the Latin phrase is "that [thing] which was to be demonstrated" (with demonstrandum in the gerundive ).
The phrase quod erat demonstrandum is a translation into Latin from the Greek Greek, Ancient (to 1453);: ὅπερ ἔδει δεῖξαι (Greek, Ancient (to 1453);: hoper edei deixai; abbreviated as ΟΕΔ). Translating from the Latin phrase into English yields "that was to be demonstrated".
The earliest known use of the phrase quod erat demonstrandum is in the early 1600s. OED's earliest evidence for quod erat demonstrandum is from 1614, in the writing of William Bedwell, Arabist and mathematician.
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.
It originates from the Greek: hóper édei deîxai (ὅπερ ἔδει δεῖξαι), meaning "which had to be demonstrated". So the Latin Q.E.D. is a variation on the translation of the the expression used by the Greeks, namely, we know it was used by Euclid and Archimedes, and likely other Greek scholars who followed "suit."
The phrase originates from ancient Greek mathematics and philosophy, where demonstrating conclusions through rigorous proof was essential. In modern usage, Q.E.D. is still seen in academic writing, especially in mathematics, to affirm the validity of a proof.
