Euclid’s Elements terms

Enunciation

States what is given and what is sought

Setting-Out

Adapts what is given to serve the investigation

Definition or specification

States/clarifies what is particularly sought

Construction or machinery

Adds the needed reasoning/steps to find what is sought

Proof

Draws a conclusion “inference” by reasoning from the presented facts

Conclusion

Brings it back to the enunciation to confirm what has been demonstrated

Therefore, etc

Stands for an exact restatement of the enunciation

QED

“Precisely what was required to be proved:” placed at the end of a proof after the restatement of the enunciation

QEF

“Precisely what was required to be done:” placed at the end of propositions which are constructions

Porism

When another theorem emerges from the process of the initial demonstration, an incidental corollary

Lemma

An assumption made in order to prove something

Reductio ad Absurdum

When one reaches impossible conclusions as a result of false premises for the investigation

Figure

That which has a boundary

Boundary

The exterior bound of a figure, that which contains a figure

Same Ratio

Equimultiples

just number pairs in the same ratio, when both numbers of a pair are multipled by equal numbers the result is this

Same Ratio

The circumstance in which the relation of a pair of numbers is maintained no matter what they are multiplied by (it remains “alike” less than, greater, or equal)

Colonnade

A row of columns

Compound ratio

The ratio of one endpoint to another is the ______ of all the segments in between the two endpoints