| 1880
...his six alrrjuara (requests) Euclid says : " Let it be granted that if a straight line meet two other **straight lines, so as to make the two interior angles...lines being continually produced shall at length meet** upon that side on which are the angles, which are together less than two right angles." This somewhat... | |
| T S. Taylor - 1880
...produced to any length, still remain ev(.ry where the same distance apart. Euclid's twelfth Axiom. **If a straight line meet 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 on that side on which are the... | |
| William Stanley Jevons - 1880 - 304 sider
...Give the logical opposites, converse and contrapositive, of Euclid's (so-called) twelfth axiom — **If a straight line meet two straight lines, so as to make the** interior angles on the same side of it taken together less than two right angles, those straight lines... | |
| 1881
...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 - 366 sider
...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 - 1881
...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
...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 - 1883 - 400 sider
...equal to one another. 9. The whole is greater than its part. 10. Two straight lines cannot enclose **a space. 11. All right angles are equal to one another....continually produced, shall at length meet on that** side on which are the angles which are less than two right angles. PROPOSITION I. PROBLEM. To describe... | |
| Edward Royall Tyler, William Lathrop Kingsley, George Park Fisher, Timothy Dwight - 1883
...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...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 one to... | |
| Moffatt and Paige - 1883
...(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... | |
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