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 |

© Jo Edkins 2010 - Return to Euclid index