![]() “If a line segment intersects two straight lines forming two interior angles on the same side that sum to less than two right angles, then the two lines, if extended indefinitely, meet on that side on which the angles sum to less than two right angles.”Īlthough the statement does not refer explicitly to parallel lines, the the fifth postulate is currently called “Parallel postulate”. The fifth postulate is however less obvious: As the sum of the interior angles α and β is less than 180°, according to the fifth postulate the two straight lines extended indefinitely, meet on that side. One of the reasons for this faith is that these postulates seem obvious: the first of them stipulates that a straight line passes between two points, the second that any line segment can be indefinitely prolonged in both directions, the third that, given a point and an interval, it is always possible to trace out a circle having the point for its center and the interval as its radius, the fourth that all right angles are equal to each other. These postulates would become the keystone for all of geometry, a system of absolute truths whose validity seemed irrefutable. In book I of the Elements, Euclid poses the five “requests” that, according to him, define planar geometry. In order to traverse curved Space, non-Euclidean Space.įrancis Ponge The oldest known fragment of Euclid’s Elements as part of the Oxyrhynchus papyri, dated from the Ptolemaic period and belonging to the famous Alexandrian Library That will allow us to put our trust in the Word, ![]() Thus we may perhaps, one day, create new Figures ![]() ![]() This post is an adaptation of a chapter of my book “ The Wraparound Universe” with many more illustrations. ![]()
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