 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Part. 10. Two Straight Lines cannot inclose a Space. 11. All Right Angles are equal to one another. 12. ' If a straight line meets two straight lines,...continually produced, shall at length meet upon that side on which are the angles 'which are less than two right angles.' * ie Elementary Theorems whose truth... | |
 | Nikolaĭ Ivanovich Lobachevskiĭ - Geometry, Non-Euclidean - 1891 - 142 pages
...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 - Education - 1892 - 544 pages
...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... | |
 | Euclid - Geometry - 1892 - 460 pages
...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 meet on that side on which are the angles which are together less than two right angles.... | |
 | Paul Carus - Electronic journals - 1893 - 720 pages
...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... | |
 | Florian Cajori - Mathematics - 1896 - 336 pages
...relatively to each other, namely, in proving proposi1 The parallel-postulate is : " 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." In the various editions... | |
 | William Stanley Jevons - Logic - 1896 - 344 pages
...to make the interior angles on the same side of it taken together less than two right angles, those straight lines being continually produced shall at length meet upon that side on which are the angles which are less than two right angles. makes the two interior angles upon the... | |
 | Hermann Schubert - Circle-squaring - 1899 - 163 pages
...Magnitudes 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... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...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 meet on that side on which are the angles which are together less than two right angles.... | |
 | Philosophy - 1903 - 750 pages
...conception of parallelism. So it was formulated axiomatically as follows : " If a straight line meet two straight lines, so as to make the two interior...continually produced, shall at length meet upon that side on which are the angles which are less than two right angles." This dogmatic statement (now commonly... | |
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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 two right angles... 
