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" If a straight line meets two straight lines, so as to " make the two interior angles on the same side of it taken " together less than two right angles... "
Geometrical Researches on the Theory of Parallels
von Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 Seiten
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1810 - 554 Seiten
...X. Two straight lines cannot enclose a space. XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as...being continually " produced, shall at length meet upon that side on which are " the angles which are less than two right Angles. See the " notes on prop....
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814 - 560 Seiten
...two straight lines, so as to make " the two Lriterior angles on the same ade of it taken to" gether less than two right angles, these straight lines " being continually produced, shall at length meet upon " that side on which are the angles which are less than " two right angles. See the notes on Prop....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 350 Seiten
...before the llth is accounted the 10th. rfhe 12th Axiom of Euclid is, that " if a straight line meets two " straight lines, so as to make the two interior...lines being continually produced, shall at length meet upon that " side on which are the angles which are less than two right angles." Instead of this proposition,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 1046 Seiten
...cannot inclose a space. 11. AH right angles are equal to one another. 12." If a straight line meets two straight lines so as to make the two interior...lines being continually produced, shall at length meet upon that side on which are the angles which are lest than two right angles." Proposition I. Problem....
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 546 Seiten
...X. Two straight lines cannot inclose a space. XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as...being continually produced, shall at " length meet upon that side on which are the angles " which are less than two right angles." See the notes on Prop....
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Elements of Geometry: With Notes

John Radford Young - 1827 - 228 Seiten
...proportional." From this general proposition Legendre is enabled to demonstrate Euclid's twelfth axiom, viz. : If a straight line meet two straight lines so as to...lines being continually produced shall at length meet upon that side on which are the angles which are less than two right angles. Let the straight line...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 156 Seiten
...straight lines cannot inclose a space. 11. All right angles are equal. 12. If a straight line meets two straight lines so as to make the two interior...lines being continually produced, shall at length meet upon that side upon which are the angles which are less than two right angles. The last of these has...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - 1829 - 138 Seiten
...straight lines so as to make the two interior angles on the same side of it taken together, less tkau two right angles, these straight lines being continually produced, shall at length meet upon that side upon which are the angles which are less than two I right angles. The last of these...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 358 Seiten
...Axioms, and that which was before the llth is accounted the 10th. The 12th Axiom of Euclid is, that " if a straight line meet two " straight lines, so as..."lines being continually produced, shall at length meet upon that " side on which are the angles which are less than two right angles." Instead of this proposition,...
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Elements of Geometry with Notes

John Radford Young - 1833 - 240 Seiten
...straight line meet two straight lines so as to make the two interior angles on the same side \T> HAUM T> of it, taken together, less than two right angles,...lines being continually produced shall at length meet upon that side on which are the angles which are less than two right angles. Let the straight line...
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