 | John Playfair - Euclid's Elements - 1832 - 358 pages
...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,... | |
 | John Radford Young - Geometry, Modern - 1833 - 240 pages
...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 make the two interior angles on the same side \T> HAUM T> of it, taken together, less than two right angles, these straight lines being continually... | |
 | Euclid - Euclid's Elements - 1833 - 216 pages
...equal to one another. 12. If a right line meet two right lines, so as to make See N. .the two internal angles on the same side of it taken together less than two right angles ; these right lines, being continually produced, shall at length meet upon that side on which are the angles,... | |
 | Euclid - 1835 - 540 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 upon that " side on which are the angles which are less than two right " angles. See the notes on Prop.... | |
 | Robert Simson - Trigonometry - 1835 - 544 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 upon that " side on which are the angles which are less than two right " angles. See the notes on Prop.... | |
 | John Playfair - Euclid's Elements - 1835 - 336 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 angles on the•same side of it taken " together less than two right angles, these straight lines being continually... | |
 | John Playfair - Geometry - 1836 - 148 pages
...may be produced until the perpendicular is greater than any given straight line. PROP. XIII. THEOR. 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. Let the straight line... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...of Euclid is, that " if a straight line " meets two straight lines, so as to make the two inte" rior angles on the same side of it taken together less " than two right angles, these straight lines oeing con" tinually produced, shall at length meet upon that side " on which are the angles which are... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...this proposition has been demonstrated by some writers in the following manner •. 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.* PROPOSITION I. PROBLEM.f To... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...by showing that the alternate Zs AGK, GKD are equal. PROPOSITION. " If a right line meet two right lines, so as to make the two interior angles on the...it taken together less than two right angles, these right lines being continually produced, shall at length meet on that side on which are the angles which... | |
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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... 
