 | Moffatt and Paige - 1879 - 378 pages
...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 - 428 pages
...(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 - 400 pages
...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 - 146 pages
...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 - 506 pages
...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 - 474 pages
...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 - Euclid's Elements - 1880 - 426 pages
...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 - 152 pages
...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... | |
 | Education, Higher - 1881 - 504 pages
...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 - 380 pages
...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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If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles... 
