 | Euclides - 1840 - 192 pages
...angles on the same side of it less than two right angles, those two straight lines, if produced, will meet on that side on which are the angles less than two right angles." This is evidently not an axiom, but a theorem requiring proof. We have therefore rejected it, and have... | |
 | Euclides - 1842 - 316 pages
...than two right angles, these straight lines, being continually produced, shall at length meet upon that side on which are the angles less than two right angles. AXIOMS. I. THINGS which are equal to the same are equal to one another. II. If equals be added to equals,... | |
 | Euclides - 1883 - 176 pages
...interior angles on the same side less than two right angles, the two straight lines, if produced, will meet on that side on which are the angles less than two right angles. If L KFG + L FGC are < 2 Us. To prove KP and CG will meet if produced towards K, C. If not, then KL... | |
 | Euclid - Mathematics, Greek - 1908 - 550 pages
...straight lines make 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 the ht'fl right angles. Although Aristotle gives a clear idea of what he understood by a postulate,... | |
 | Francis Rolt-Wheeler - Science - 1909 - 376 pages
...straight lines make 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 the two right angles. It will be noticed that the plane geometry is built on three elements, the point,... | |
 | David Eugene Smith - Geometry - 1911 - 360 pages
...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,... | |
 | Jacob William Albert Young - Mathematics - 1911 - 434 pages
...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 the two right angles." This is a consequence of our assumption, for let the rays AC and BD be such... | |
 | Duncan M'Laren Young Sommerville - Geometry, Non-Euclidean - 1914 - 291 pages
...straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side...which are the angles less than two right angles." 3. Attempts to prove the parallel-postulate. It seems impossible to suppose that Euclid ever imagined... | |
 | Duncan M'Laren Young Sommerville - Bell's mathematical series for schools and colleges - 1914 - 588 pages
...straight lines make the interior angles on the same side less than two right ingles, the two straight lines, if produced indefinitely, meet on that side...which are the angles less than two right angles." 3, Attempts to prove the parallel-postulate. It seems impossible to suppose that Euclid ever imagined... | |
 | Robert Édouard Moritz - Mathematics - 1914 - 434 pages
...straight lines make 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 the two right angles. — EUCLID. The Thirteen Books of Euclid's Elements [TL Heath] Vol. 1 (Cambridge,... | |
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That, if a straight line falling on two straight lines make 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 the two right angles. 
