| John Playfair - 1837 - 318 Seiten
...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... | |
| Euclid - 1838 - 416 Seiten
...Two straight lines cannot enclose a space. XI. All right angles arc equal to one another. XII. •• **If a straight line meet two straight lines, so as...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... | |
| Euclid, Robert Simson - 1838 - 416 Seiten
...X. Two straight linea cannot enclose a space, XI. All right angles are equal to one another. XII. " **If a straight line meet two straight lines, so as...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 - 1838
...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 to make the two interior...lines, being continually produced, shall at length meet** upon that side on which are the angles which are less than two right angles. It is readily seen that... | |
| Euclides - 1841 - 351 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 "... | |
| Euclides - 1842
...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 to make the two interior...lines, being continually produced, shall at length meet** upon that side on which are the angles less than two right angles. AXIOMS. I. THINGS which are equal... | |
| John Playfair - 1842 - 317 Seiten
...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... | |
| John Playfair - 1844 - 317 Seiten
...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...being continually " produced, shall at length meet** upon that side on which are the angles AMONG the Axioms there have been made only two alterations.... | |
| 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... | |
| Euclides - 1845
...cannot inclose 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...lines being continually produced, shall at length meet** upon that side on which are the angles which are less than two right angles. PROPOSITION I. PROBLEM.... | |
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