| Euclides - 1884 - 182 pages
...much better, however, not to discuss it until we have made some further progress in the subject. 12. **If a straight line meet two straight lines so as to...together 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... | |
| James Gow - Mathematics - 1884 - 350 pages
...the last three are 10. Two straight lines cannot enclose a space: 11. All right angles are equal: 12. **If a straight line meet two straight lines, so as...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... | |
| National cyclopaedia - 1884 - 642 pages
...as stated by Euclid it is not a true axiom. It runs thus — 44 If a straight line meets two other **straight lines, so as to make the two interior angles on the same side of it, taken** j together, less than two right angles ; these straight lines, being continually produced, shall at... | |
| Mathematics - 1885 - 150 pages
...and thus is 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...together, less than two right angles, these straight** linos being continually produced, shall at length meet upon that side on which are the angles which... | |
| New Zealand Institute - Science - 1886 - 530 pages
...the 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
...assumption is a substitute for Euclid's famous eleventh (also called the twelfth) axiom which reads, **If a straight line meet two straight lines so as to make the two interior angles** *For definitions of geometrical magnitudes, see Mensuration. on the same side of it taken together... | |
| Florian Cajori - Mathematics - 1890 - 574 pages
...His assumption consists in what is generally called the twelfth, by some the eleventh " axiom :" " **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... | |
| United States. Office of Education - Digital images - 1890 - 958 pages
...His assumption consists in what is generally called the twelfth, by some the eleventh " axiom :" " **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... | |
| Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...— 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 - 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.... | |
| |