 | 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... | |
 | 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... | |
 | 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... | |
 | 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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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... 
