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" If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... "
Elements of Geometry: With Notes - Page 172
by John Radford Young - 1827 - 208 pages
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...interior and opposite. In order to demonstrate this proposition, Euclid assumed it as an Axiom, that " if a "straight line meet two straight lines, so as to make the interior angles on " the same side of it less than two right angles, these straight lines being " continually...
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The Elements of Euclid

Euclid - Geometry - 1838 - 470 pages
...Two straight lines cannot enclose a space. XI. All right angles arc equal to one another. XII. •• If a straight line meet two straight lines, so as...right angles, these straight lines being continually pro" duced, shall at length meet upon that side on which are the angles " which are less than two right...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...X. Two straight linea cannot enclose a space, XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as...right angles, these straight lines being continually pro" duced, shall at length meet upon that side on which are the angles " which are less than two right...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...equal to one another. XII. " If a straight line meet two straight lines, which are " in the same plane, so as to make the two interior " angles on the same...than two right angles, these straight lines being " produced, shall at length meet upon that side on " which are the angles which are less than two "...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...from any centre, at any distance from that centre. IV. [Ax. XI.] V. And that if a straight line meets two straight lines, so as to make the two interior...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....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...interior and opposite. In order to demonstrate this proposition, Euclid assumed it as an Axiom, that " if a " straight line meet two straight lines, so as to make the interior angles on " the same side of it less than two right angles, these straight lines being " continually...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...Euclid is, that " if a straight line meets two straight " lines, so as to make the two interior anples on the same side of it taken " together less than...length meet upon that side on which are the angles AMONG the Axioms there have been made only two alterations. The 10th Axiom in Euclid is, that " two...
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...the necessity of a new axiom. Euclid's axiom alluded to is this : " If a straight line meet two other straight lines, so as to make the two interior angles...on the same side of it taken together less than two right-angles, these straight lines being continually produced, will at length meet on the side on which...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...to one another. |j 12. If a straight line meet two other straight lines which are in the same plane, so as to make the two interior angles on the same...together, less than two right angles, these straight lines shall at length meet upon that side, if they be continually produced.^ * ln this axiom and the following,...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...cannot enclose a space. xi. All right angles are equal to one another. xn. If a straight line falls upon two straight lines, so as to make the two interior angles on the same side of it together less than two right angles, those straight lines, being continually produced, shall at length...
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