| John Playfair - Euclid's Elements - 1837 - 332 pages
...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 - Geometry - 1838 - 470 pages
...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... | |
| Robert Simson - Geometry - 1838 - 434 pages
...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 - 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 "... | |
| Euclides - 1842 - 316 pages
...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...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.... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...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 - 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...length meet upon that side on which are the angles** AMONG the Axioms there have been made only two alterations. The 10th Axiom in Euclid is, that " two... | |
| 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... | |
| Euclid, James Thomson - Geometry - 1845 - 382 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...together, less than two right angles, these straight lines** shall at length meet upon that side, if they be continually produced.^ * ln this axiom and the following,... | |
| Euclides - 1846 - 292 pages
...cannot enclose a space. xi. All right angles are equal to one another. xn. If a straight line falls upon **two straight lines, so as to make the two interior angles on the same side of it** together less than two right angles, those straight lines, being continually produced, shall at length... | |
| |