| 1885
...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 - 1886
...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 - 1888 - 481 sider
...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 - 1890 - 400 sider
...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... | |
| 1890
...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 - 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.... | |
| Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 50 sider
...cut by a transversal make equal alternate angles, he brings in the un wieldly postulate or axiom: " **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." Do you wonder that succeeding geometers... | |
| Nicholas Murray Butler, Frank Pierrepont Graves, William McAndrew - 1892
...to one another," is not required for use before proposition 14 of his first book. Also the axiom, " **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," is not required till proposition... | |
| 1892
...at least one which is not axiomatic.1 This is the axiom of parallel?, 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 oh that side on... | |
| |