It is better educational policy, however, to assert this fact more definitely, and to state the additional assumption that figures may be moved about in space without deformation. The fourth of Euclid's postulates is often given as an axiom, following the idea of the Greek philosopher Geminus (who flourished in the first century B.C.), but this is because Euclid's distinction between axiom and postulate is not always understood. Proclus (410-485 A.D.) endeavored to prove the postulate, and a later and more scientific effort was made by the Italian geometrician Saccheri (1667-1733). It is very commonly taken as a postulate that all straight angles are equal, this being more evident to the senses, and the equality of right angles is deduced as a corollary. This method of procedure has the sanction of many of our best modern scholars. 5. _That, if a straight line falling on two straight lines make the interior angle 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 the two right angles._ This famous postulate, long since abandoned in teaching the beginner in geometry, is a remarkable evidence of the clear vision of Euclid. For two thousand years mathematicians sought to prove it, only to demonstrate the wisdom of its author in placing it among the assumptions.[49] Every proof adduced contains some assumption that practically conceals the postulate itself. Thus the great English mathematician John Wallis (1616-1703) gave a proof based upon the assumption that "given a figure, another figure is possible which is similar to the given one, and of any size whatever." Legendre (1752-1833) did substantially the same at one time, and offered several other proofs, each depending upon some equally unprovable assumption. The definite proof that the postulate cannot be demonstrated is due to the Italian Beltrami (1868). Of the alternative forms of the postulate, that of Proclus is generally considered the best suited to beginners. As stated by Playfair (1795), this is, "Through a given point only one parallel can be drawn to a given straight line"; and as stated by Proclus, "If a straight line intersect one of two parallels, it will intersect the other also." Playfair's form is now the common "postulate of parallels," and is the one that seems destined to endure. Posidonius and Geminus, both Stoics of the first century B.C., gave as their alternative, "There exist straight lines everywhere equidistant from one another." One of Legendre's alternatives is, "There exists a triangle in which the sum of the three angles is equal to two right angles." One of the latest attempts to suggest a substitute is that of the Italian Ingrami (1904), "Two parallel straight lines intercept, on every transversal which passes through the mid-point of a segment included between them, another segment the mid-point of which is the mid-point of the first."