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Where did quod erat demonstrandum come from?
Where did QED come from?
Why did Euclid use quod erat faciendum?
When was QED used in philosophy?
Philippe van Lansberge's 1604 Triangulorum Geometriæ used quod erat demonstrandum to conclude some proofs; others ended with phrases such as sigillatim deinceps demonstrabitur, magnitudo demonstranda est, and other variants.
Euclid used the Greek original of Quod Erat Faciendum (Q.E.F.) to close propositions that were not proofs of theorems, but constructions of geometric objects. For example, Euclid's first proposition showing how to construct an equilateral triangle, given one side, is concluded this way. Equivalent forms
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.
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.
These initials stand for the Latin quod erat demonstrandum meaning, ‘what was to be demonstrated’. It was coined by Euclid in Greek c. 300 BC but it is better known in its Latin translation. The expression QED is typically used by mathematicians and philosophers to conclude proofs and arguments.
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.
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.
