| Moffatt and Paige - 1879
...sides. 4. Three angles. Of these, Case 4 is the only one where the rule is not necessarily true. (d) **If a straight line meets two straight lines, so as...lines, being continually produced, shall at length meet** on that side on which are the angles which are less than two right angles. SECTION II. (Three Questions.)... | |
| Moffatt and Paige - 1879
...(10) Two straight lines cannot enclose a space, (n) All right angles are equal to one another. (12) **If a straight line meets two straight lines, so as...lines, being continually produced, shall at length meet** on that side on which are the angles that are less than two right angles. Proposition I. Problem. To... | |
| Rolla Rouse - 1879
...to one another. (This would be understood without making it an axiom.) Axiom 12. (See remark above.) **If a straight line meets two straight lines, so as...side of it taken together less than two right angles,** those straight lines being continually produced shall at length meet upon that side in which are the... | |
| Euclides - 1879
...angles are equal to one another. 12. If a straight line meet two straight lines, so as to make the **interior angles on the same side of it taken together...lines, being continually produced, shall at length meet** on that side on which are the angles which are less than two right angles. [Geometrical propositions... | |
| Moffatt and Paige - 1879
...are equal to two right angles, and therefore the angles BEF, EFD are less than two right angles. But **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, these straight lines, being continually produced, shall at length... | |
| Moffatt and Paige - 1879
...equal to two right angles (I. 29) ; therefore the angles BHF, HFE are less than two right angles. But **if a straight line meets two straight lines so as to make the** interior angles on the same side of it together less than two right angles, these straight lines being... | |
| Isaac Todhunter - 1880 - 400 Seiten
...cannot enclose a space. 11. All right angles are equal to one another. eJtV 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 32. A rhombus is thai all its sides... | |
| T S. Taylor - 1880
...still remain ev(.ry where the same distance apart. Euclid's twelfth Axiom. If a straight line meet **two straight lines, so as to make the two interior...side of it taken together less than two right angles,** those straight lines being continually produced, shall at length meet on that side on which are the... | |
| 1881
...that have been suggested, and explain the difficulty of assuming as an axiom (Euclid's axiom xn.) that **if a straight line meets two straight lines so as...angles on the same side of it taken together less than** right angles these straight lines continually produced shall meet. Explain what is meant by exterior,... | |
| Charles Scott Venable - 1881 - 366 Seiten
...then, since EFD + HFD = two right angles, we must have GEB — EFD. Therefore (3) AB is parallel to CD. **lines so as to make the two interior angles on the same side of it** less than two right angles, these straight lines being continually produced will meet on the side on... | |
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