![parallel postulate definition geometry parallel postulate definition geometry](https://image.slidesharecdn.com/postulates-geometry-131631/95/slide-15-1024.jpg)
Concerning the meaning of axiom, Aristotle says: “That which it is necessary for anyone to hold who is to learn anything at all is an axiom” and “It is ignorance alone that could lead anyone to try to prove the axiom.” Without going into the difficult question of the precise distinction to the Greek mind between axiom and postulate, we may take it that the character of being indisputable pertained to each. The earliest commentators found fault with this statement as being not self-evident. I wish to recall briefly the salient features of the story, and to state what seem to me its suggestions in regard to the teaching of elementary geometry.Įuclid's fifth postulate (called also the eleventh or twelfth axiom) states: “If a straight line falling on two straight lines makes the interior angles on the same side less than two right angles, the two straight lines if produced indefinitely meet on that side on which are the angles less than two right angles”. Its history is a long story with a dramatic climax and far-reaching in?uence on modern mathematical and general scientific thought.
![parallel postulate definition geometry parallel postulate definition geometry](https://i.ytimg.com/vi/0v2FvpTkW7I/maxresdefault.jpg)
This theorem does not depend on the parallel postulate. Like the famous problems of construction, Euclid's postulate concerning parallels is a thought that links the ages. Theorem: An exterior angle of a triangle is greater than either opposite interior angle.