| 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...taken together, less than two right angles, these** straight lines shall at length meet upon that side, if they be continually produced.* PROPOSITION I.... | |
| Euclides - 1838 - 264 pages
...subject, and which he calls an Axiom, is as follows. AXIOM XII. If a straight line meets two straight **lines so as to make the two interior angles, on the...taken together, less than two right angles, these** straight lines, being continually produced, shall at length meet upon that side on which are the angles... | |
| 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...taken together, less " than two right angles, these** straight lines being " produced, shall at length meet upon that side on " which are the angles which... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...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...taken " together less than two right angles, these** straight lines being continually " produced, shall at length meet upon that side on which are the angles... | |
| Euclides - 1842 - 320 pages
...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 angles on the...taken together, less than two right angles, these** straight lines, being continually produced, shall at length meet upon that side on which are the angles... | |
| James Bates Thomson - Geometry - 1844 - 268 pages
...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... | |
| 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 two right angles, these** straight lines being continually " produced, shall at length meet upon that side on which are the angles... | |
| Euclides - 1845 - 544 pages
...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 angles on the...it taken together less than two right angles, these** straight lines being continually produced, shall at length meet upon that side on which are the angles... | |
| Euclid - Geometry - 1845 - 218 pages
...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 angles on the...taken " together less than two right angles, these** straight " lines being continually produced, shall at length meet " upon that side on which are the... | |
| Euclid, James Thomson - Geometry - 1845 - 380 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...taken together, less than two right angles, these** straight lines shall at length meet upon that side, if they be continually produced.^ * ln this axiom... | |
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