| James Gow - Mathematics - 1884 - 350 pages
...lines cannot enclose a space: 11. All right angles are equal: 12. If a straight line meet 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 will meet if produced on that side. Of these... | |
| Mathematics - 1885 - 150 pages
...it proved that all right angles are equal.* Axiom XII.: — " If a straight line meets two straight **lines, so as to make the two interior angles on the...taken together, less than two right angles, these** straight linos being continually produced, shall at length meet upon that side on which are the angles... | |
| New Zealand Institute - Science - 1886 - 530 pages
...parallel-axiom mentioned in my paper. Form (a), (Euclid's) is : — " If a straight line meets two straight **lines, so as to make the two interior angles on the same** I side of it taken together less than two right angles, these straight lines being continually produced... | |
| Benjamin Franklin Finkel - Mathematics - 1888 - 518 pages
...so as to make the two interior angles *For definitions of geometrical magnitudes, see Mensuration. **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 which are the angles... | |
| United States. Office of Education - Digital images - 1890 - 958 pages
...generally called the twelfth, by some the eleventh " axiom :" " 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, these straight lines, being continually produced, shall at length meet on that side on... | |
| Florian Cajori - Mathematics - 1890 - 422 pages
...generally called the twelfth, by some the eleventh "axiom :"* " 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, these straight lines, being continually produced, shall at length meet on that side on... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...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 - Geometry - 1890 - 418 pages
...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.... | |
| Nikolaĭ Ivanovich Lobachevskiĭ - Geometry, Non-Euclidean - 1891 - 142 pages
...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 angles on the...it taken together less than two right angles, these** straight lines, being continually produced, shall at length meet on that side on which are the angles... | |
| Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - Education - 1892 - 544 pages
...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 angles on the...taken together, less than two right angles, these** straight lines, being continually produced, shall at length meet on that side on which are the angles... | |
| |