| Euclides - 1862
...X. Two straight lines cannot inclose a space. XI. All right angles are equal to one another. XII. ' **If a straight line meets two straight lines, so as...the angles which are less than two right angles.'** PROP. I. — PROBLEM. To describe an equilateral triangle upon a given finite straight line. •(References... | |
| Euclides - 1862
...cannot inclose a space. 11. All right angles are equal to one another. 12. If a straight line meet **two straight lines, so as to make the two interior...lines being continually produced, shall at length meet** on that side on which are the angles which are less than two right angles. EXPLANATION OF TERMS. A... | |
| Euclides - 1863
...angles measured by those equals must themselves be equal. 12. If a straight line meets two skaight **lines, so as to make the two interior angles on the...it taken together less than two right angles, these** two straight lines, being continually produced, shall at length meet upon that side on which the angles... | |
| Euclides - 1863
...part. j 11. All right angles are equal to one another. | 10. Two straight lines cannot enclose a space **to make the two interior angles on the same side of it,** \ 12. If a straight line meets two straight lines, so as straight lines, being continually produced,... | |
| Euclides - 1864
...part. X. Two straight lines cannot enclose a space. XL All right angles are equal to one another. XII. **If a straight line meets two straight lines, so as...are the angles which are less than two right angles.** PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given finitt straight line. Let... | |
| Euclides - 1865
...properties of parallel lines. Enclid gets over the difficulty by assuming the following as an axiom : — ' **If a straight line meets two straight lines, so as...right angles ; these straight lines being continually** prodnced, shall at length meet upon that side on which are the angles which are less than two right... | |
| Edward Clarke Lowe - 1866
...part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. **If a straight line meets two straight lines so as...are the angles which are less than two right angles.** BOOK II. • Definitions. 1. Every right-angled parallelogram is called a rectangle, and is said to... | |
| John Playfair - 1855 - 317 sider
...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 as...produced, shall at length meet upon that side on which are** th*i angles "which ire less than two right angles." Instead of this proposition, which, though true,... | |
| Matthew Ryan - 1866
...lines (AB, С D) which are in the same plane, so as to make the two interior angles (BA С, A С D) ore **the same side of it, taken together, less than two right angles, these** two straight lines (А В, С D) shall at length meet upon that side, if sufficiently produced. Draw... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight line meet **two straight lines, so as to make the two interior...lines, being continually produced, shall at length meet** on that side on which are the angles which are less than two right angles. PROPOSITION 1. PROBLEM.... | |
| |