 | 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... | |
 | Euclides - 1838 - 264 pages
...admitted before he can proceed with his subject, and which he calls an Axiom, is as follows. AXIOM XII. If a straight line meets two straight lines so as...are the angles which are less than two right angles. It is readily seen that this proposition is no other than the converse of Proposition xvii., which... | |
 | Euclid - Geometry - 1838 - 470 pages
...enclose a space. XI. All right angles arc equal to one another. XII. •• If a straight line meet two straight lines, so as to make the two " interior...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... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...cannot enclose a space, XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as to make the two . " interior...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... | |
 | 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 "... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...self-evident propositions. It is therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight " lines, so...the angles "which are less than two right angles." Instead of this proposition, which, though true, is by no means self-evident ; another that appeared... | |
 | Euclides - 1842 - 316 pages
...circle may be described 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...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.... | |
 | 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... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...progress of the understanding, it will certainly retard it AXIOMS. The 12th Axiom of 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... | |
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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... 
