What Did The Romans Ever Do For Us?

One may ask "What Did The Romans Ever Do For Us?" and part of the answer came in the well known Monty Python film entitled "The Life of Brian". Examples given included Aqueducts, sanitation and roads. Of course, it would have been an anachronism for the film scrip to have included "GCSE Latin" but we can certainly thank them for that legacy.

As far as mathematics goes, I have listed four examples re what the Romans gave to us mathematicians with help from the ancient Greeks. Out of deference, I have used lower case Greek letters for the four examples.

?) Q.E.D. is the initials of the Latin phrase quod erat demonstrandum, meaning "which is what had to be proven". The phrase is traditionally placed in its abbreviated form at the end of a mathematical proof or philosophical argument when what was specified in the enunciation-and in the setting-out-has been exactly restated as the conclusion of the demonstration. The abbreviation thus signals the completion of the proof.

?) Q.E.F. is another Latin phrase with a slightly different meaning, and less common in usage. Quod erat faciendum, originating from the Greek geometers` closing ???? ???? ??????? (hoper edei poiesai), meaning "which had to be done". Euclid used this phrase to close propositions which were not proofs of theorems, but constructions. For example, Euclid`s first proposition showing how to construct an equilateral triangle given one side is usually shortened to QEF

?) Reductio ad absurdum (Latin: "reduction to absurdity"; pl.: reductiones ad absurdum), also known as argumentum ad absurdum (Latin: argument to absurdity), is a common form of argument which seeks to demonstrate that a statement is true by showing that a false, untenable, or absurd result follows from its denial, or in turn to demonstrate that a statement is false by showing that a false, untenable, or absurd result follows from its acceptance. First recognized and studied in classical Greek philosophy (the Latin term derives from the Greek "??? ?????? ???????" or eis atopon apagoge, "reduction to the impossible", for example in Aristotle` s Prior Analytics), this technique has been used throughout history in both formal mathematical and philosophical reasoning, as well as informal debate.

?) pons asinorum In geometry, the statement that the angles opposite the equal sides of an isosceles triangle are themselves equal is known as the pons asinorum, which is Latin for "bridge of donkeys". This statement is Proposition 5 of Book 1 in Euclid`s Elements and is also known as the isosceles triangle theorem. Its converse is also true: if two angles of a triangle are equal, then the sides opposite them are also equal.