  However, the fifth one sounds more like a statement of fact.  Euclid's text can be rendered in English as follows: “If a straight line [c] falling on two straight lines [a and b] makes the interior angles on the same side less than two right angles, the two straight lines [a and b], if produced indefinitely, meet on that side on which are the angles less than the two right angles” (terms in brackets added for clarity). This sounds far-fetched. Still, it can be readily paraphrased as a recipe for constructing triangles, (See Figure 1.) Every triangle is formed by three coplanar straight lines that meet, by pairs, at three points. Given any segment PQ, draw a straight line a through P and a straight line b through Q, so that a and b lie on the same plane; verify that the angles that a and b make with PQ on one of the two sides of PQ add up to less than two right angles; if this condition is satisfied, it should be granted that a and b meet at a point R on that same side of PQ, thus forming the triangle PQR. This request is known as “Euclid's Postulate”. If the request is rejected—say, because we believe that the world is finite and there is no room in it to accommodate vertex R if the interior angles in question add up to very little less than two right angles—then much of Euclid's system of geometry will not go through.