| Euclid - 1837 - 410 Seiten
...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 - 1837 - 112 Seiten
...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 Seiten
...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 - 1838 - 478 Seiten
...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 - 1838 - 434 Seiten
...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 - 1841 - 378 Seiten
...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 - 1842 - 332 Seiten
...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 - 320 Seiten
...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 - 1844 - 237 Seiten
...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 - 1844 - 338 Seiten
...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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