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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 ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 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 the Philosophy of the Human Mind: In Two Parts, Part 1

Dugald Stewart - Psychology - 1847 - 666 pages
...Euclid's Elements. When it is assorted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the san»« side together equal to two right angles, these two straight lines, though indefinitely produced,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1849 - 332 pages
...therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight " lines, so as to make the two interior...shall at length meet upon that side on which are the angle* " which are less than two right angles." Instead of this proposition, which, though true, is...
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Prolegomena Logica: An Inquiry Into the Psychological Character of Logical ...

Henry Longueville Mansel - Logic - 1851 - 350 pages
...geometrical principles, " two straight lines cannot enclose a space," or, " if a straight line meets two straight lines, so as to make the two interior angles on the same side together less than two right angles, the two straight lines will meet if produced." As a matter of...
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The Elements of Euclid [book 1] for beginners, by J. Lowres

Euclides - 1852 - 48 pages
...inclose a space. 11. All right angles are equal to one another. 12. If a right line meet two other right lines, so as to make the two interior angles on the...it taken together less than two right angles, these two right lines being continually induced, shall at length meet on that side on which are the angles,...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...parallel to FG; but both cannot. »^^F/ — 1 5- jf" * 3. — To BK. I. PEOP. A. If a straight line cut two straight lines, so as to make the two interior angles on the same side of it together less than two right angles : then these two straight lines, being continually produced, shall...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...is the twelfth axiom, and is thus expressed in Euclid : — AXIOM XII. — If a straight line meets two straight lines, so as to make the two interior...than two right angles, these straight lines, being prolonged, shall at length meet upon that side on which are the angles that are less than two right...
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The Collected Works of Dugald Stewart, Esq. F.R.SS.: Elements of the ...

Dugald Stewart - 1854 - 454 pages
...Euclid's Elements. When it is asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never...
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The Collected Works of Dugald Stewart, Volume 3

Dugald Stewart - 1854 - 452 pages
...Euclid's Elements. When it is asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...cannot enclose a space. XI. All right angles are equal to one another. XII. If a straight line meets two straight lines, \ so as to make the two interior...being \ continually produced, shall at length meet ' V ' 'L upon that side on which are the angles -which \ are less than two right angles. It H admitted...
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