Full Form of QED:
Quod Erat Demonstrandum
QED Full Form is Quod Erat Demonstrandum. Quod Erat Demonstrandum, which is represented commonly in the abbreviated form Q.E.D, literally means “which is what had to be shown”. It is conventionally positioned at the end of a philosophical argument or mathematical proof when the original proposition has been verbatim stated as the demonstration’s conclusion. The use of abbreviation indicates the completion of the proof.
During the European Renaissance, great scholars used Latin and phrases like Q.E.D. were commonly used to conclude demonstrations. The most popular use of the phrase in any philosophical argument can be found in Baruch Spinoza’s book the Ethics that was published in the year 1766. The book was written in Latin and is regarded as one of the greatest works of Spinoza.
There is a similar Latin phrase bearing a slightly different connotation. It is Quod erat faciendum which means “which had to be done”. Euclid made use of this phrase to conclude those propositions that were essentially constructions, not proofs of theorems. Presently, there is no popular English equivalent of the phrase, though the phrases such as “as required” or “this completes the proof” or “hence proved” are commonly used as English substitutes of QED.