 | 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
...as stated, AB would coincide with EF ; and thus is it proved that all right angles are equal.* Axiom XII.: — " If a straight line meets two straight...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
...equivalence of the three forms of 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
...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...lines being continually produced shall at length meet on that side< on which are the angles which are less than, two right angles. An axiom must possess... | |
 | United States. Office of Education - Digital images - 1890 - 958 pages
...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... | |
 | Florian Cajori - Mathematics - 1890 - 412 pages
...consists 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 - 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.... | |
 | 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... | |
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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... 
