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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. "
Monographs on Topics of Modern Mathematics, Relevant to the Elementary Field - Seite 93
herausgegeben von - 1911 - 416 Seiten
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Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840 - 192 Seiten
...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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 Seiten
...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,...
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 176 Seiten
...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...
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Introduction and books 1,2

Euclid - 1908 - 550 Seiten
...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,...
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The Science-history of the Universe, Band 8

Francis Rolt-Wheeler - 1909 - 376 Seiten
...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,...
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The Teaching of Geometry

David Eugene Smith - 1911 - 360 Seiten
...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,...
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Monographs on Topics of Modern Mathematics, Relevant to the Elementary Field

Jacob William Albert Young - 1911 - 434 Seiten
...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...
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The Elements of Non-Euclidean Geometry

Duncan M'Laren Young Sommerville - 1914 - 291 Seiten
...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...
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The Elements of Non-Euclidean Geometry

Duncan M'Laren Young Sommerville - 1914 - 588 Seiten
...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...
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Memorabilia Mathematica; Or, The Philomath's Quotation-book

Robert Édouard Moritz - 1914 - 434 Seiten
...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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