| Education, Higher - 1881 - 504 pages
...and explain the difficulty of assuming as an axiom (Euclid's axiom xn.) that if a straight line meets **two straight lines so as to make the two interior...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... | |
| Euclides - Euclid's Elements - 1881 - 236 pages
...another. xn If a straight line meets two straight lines, no as to make the two interior angles on thr **same side of it, taken together, less than two right angles, these straight lines,** oeing continually produced, shall at length meet T upon that side on which are the angles which \ are... | |
| Marianne Nops - 1882 - 278 pages
...together equal to two right Zs .'. the Zs BGH, GHD are together less than two right ZB (I. 13). But **if a straight line meet two straight lines, so as to make the two interior** Z a on the same side of it, taken together, less than two rt. Z s, these straight lines being produced... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...two right angles ; [1. 18. therefore the angles BGH, GHD are together less than two right angles. But **if a straight line meet 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. [Axiom 12. Therefore the... | |
| Edward Royall Tyler, William Lathrop Kingsley, George Park Fisher, Timothy Dwight - United States - 1883 - 872 pages
...axiom from that given by Euclid, or put Euclid's axiom in a different form. Thus Euclid's axiom is, **"If a straight line meet 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. This axiom is a puzzling... | |
| Moffatt and Paige - 1883 - 516 pages
...(1. 13), therefore the angles BGH, GHD are less than two right angles. But if a straight line meets **two straight lines so as to make the two interior...than two right angles, these straight lines, being** continuallyproduced, shall at length meet on that side on which are the angles that are less than two... | |
| Science - 1892 - 448 pages
...at least one which is not axiomatic.3 This is the axiom of parallels, which reads as follows : — " **If a straight line meet two straight lines so as to...on the same side of it taken together less than two** right-angles, these straight lines, being continually produced, shall at length meet on that side on... | |
| Joseph Hughes - Education - 1883 - 568 pages
...; and also the two interior angles on the same side toeether equal to two right angles. Axiom xii. **If a straight line meet two straight lines so as to...on the same side of it taken together less than two** ri^ht angles, these straight lines being continually produced, îhall at length meet on that side on... | |
| Euclides - 1883 - 176 pages
...Note.— The converse of this proposition, that "if a straight line meeting two other straight lines **make the two interior angles on the same side of it taken together less than two right angles,** the two lines will, if produced tar enough) meet on that Bide on which are the angles less than two... | |
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