| 1890
...in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet **two straight lines so as to make the two interior...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... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...— Prove this proposition independently of Prop. 27. Ax. 12. — If a straight line meet two other **straight lines so as to make the two interior angles on the same side of it** together less than two right angles, these two straight lines being continually produced shall at length... | |
| Edward Albert Bowser - 1890 - 393 sider
...straight line cut two other straight lines, (1) so as to make the exterior-interior angles equal, or (2) **so as to make the two interior angles on the same side** together equal to two right angles, then the two straight lines are parallel. xE (1) Hyp. Let the st.... | |
| Florian Cajori - 1890 - 400 sider
...less than two right-angles, these straight lines, being continually produced, shall at length meet on **that side on which are the angles which are less than two** right-angles." It has been validly urged against Euclid that this statement is far from being axiomatic.... | |
| Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 sider
...make equal alternate angles, he brings in the un wieldly postulate or axiom: " 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 angles." Do you wonder that succeeding... | |
| Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1892
...required for use before proposition 14 of his first book. Also the axiom, " 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 angles," is not required till proposition... | |
| 1892
...axiomatic.1 This is the axiom of parallel?, which reads as follows : — " If a straight line meet **two straight lines so as to make the two interior...on the same side of it taken together less than two** right-angles, these straight lines, being continually produced, shall at length meet oh that side on... | |
| 1892
...axiomatic.1 This id the axiom of parallels, which reads as follows : — " If a straight line meet **two straight lines so as to make the two interior...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... | |
| Euclid - 1892 - 518 sider
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If a straight line cut **two straight lines so as to make the two interior angles on the same side of it** together less than two right angles, these straight lines, being continually produced, will at length... | |
| Paul Carus - 1893
...which coincide with one another are equal to one another. Eleventh axiom : 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 angles. Twelfth axiom : Two straight... | |
| |