An introduction to Euclid - Latin terms

Index --- introduction --- definitions --- axioms and postulates --- propositions --- other

Euclid wrote in Greek, but several terms now used in Euclid are in Latin. Here are their meanings.

Latin	Translation	Comments
Pons Asinorum	Bridge of Asses	Name of Proposition 5. The name could be because the diagram ends up looking a little like a bridge, or because since it is slightly harder than previous proofs, this is the point that 'asses' fall off!
Q.E.D. (quod erat demonstrandum)	That which was to be proved	In other words - we've done it! It is the traditional end to a proof.
Q.E.F. (quod erat faciendum)	That which was to be done	In other words - we've done it! It is the traditional end to a construction.
Reductio ad absurdum	Reduced to the absurd	Proof by contradiction. The proof assumes the opposite of what must be proved, then shows this to be impossible, which proves the original statement. Proposition 6 uses Reductio ad absurdum.

There are various words that I have used in this website which are not used by Euclid. They are in general use, and they make understanding the ideas easier.

Words	Meaning	Euclid's description
180°	The angle which makes a straight line.	Two right angles
Congruent triangles	Both triangles have all corresponding sides and angles equal.	The two triangles are equal.
Opposite angles	When two straight lines cross, the pair of angles which oppose each other	Vertical angles