| John Playfair - 1849 - 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...shall at length meet upon that side on which are the** angle* " which are less than two right angles." Instead of this proposition, which, though true, is... | |
| Henry Longueville Mansel - 1851 - 320 sider
...character, analogous to the geometrical principles, " two straight lines cannot enclose a space," or, " **if a straight line meets two straight lines, so as to make the two interior angles on the same side** together less than two right angles, the two straight lines will meet if produced." As a matter of... | |
| Euclides - 1852
...across the other two so as to 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."** [These are truths which no person can possibly doubt, who are others besides these, but these are sufficient... | |
| Euclides - 1852
...inclose a space. 11. All right angles are equal to one another. 12. If a right line meet two other right **lines, so as to make the two interior angles on the...it taken together less than two right angles, these** two right lines being continually induced, shall at length meet on that side on which are the angles,... | |
| Royal Military Academy, Woolwich - 1853
...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.** PROPOSITIONS. PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given finite straight... | |
| Euclides - 1853 - 147 sider
...part. X. Two straight lines cannot enclose a space. XI. 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 finiie straight line.... | |
| Euclides - 1853
...lines cannot inclose a space. All right angles are equal to one another. XII. " If a straight line meet **two straight lines, so as to make the two interior...the angles which are less than two right angles."** PROPOSITION I. — PROBLEM. To describe an equilateral triangle upon a given finite straight line.... | |
| Euclides - 1853
...parallel to FG; but both cannot. »^^F/ — 1 5- jf" * 3. — To BK. I. PEOP. A. If a straight line cut **two straight lines, so as to make the two interior angles on the same side of it** together less than two right angles : then these two straight lines, being continually produced, shall... | |
| Euclid - 1853 - 136 sider
...internal an£;^' '\ the same side, fS6g..£ ''• ' ^uol to two right I. 29, theor. . . I. 29, cor. . . **If a straight line meets two straight lines so as to make the two** internal angles on the same side together less than two right angles. {These '' stralgnt lines being... | |
| William Somerville Orr - 1854
...shall be meeting-lines. This is the twelfth axiom, and is thus expressed in Euclid : — AXIOM XII. — **If a straight line meets two straight lines, so as...than two right angles, these straight lines, being** prolonged, shall at length meet upon that side on which are the angles that are less than two right... | |
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