 | Florian Cajori - 1890 - 412 Seiten
...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... | |
 | United States. Office of Education - 1890 - 958 Seiten
...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 Seiten
...— 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 - 418 Seiten
...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.... | |
 | Florian Cajori - 1890 - 412 Seiten
...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 less than two right-angles." It has been validly urged against Euclid that this statement is far from being axiomatic.... | |
 | Nikolaĭ Ivanovich Lobachevskiĭ - 1891 - 142 Seiten
...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 - 1892 - 544 Seiten
...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... | |
 | John Michels (Journalist) - 1892 - 448 Seiten
...axiomatic.1 This is the axiom of parallel?, which reads as follows : — " 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 oh that side on... | |
 | John Michels (Journalist) - 1892 - 446 Seiten
...axiomatic.1 This id the axiom of parallels, which reads as follows : — " 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... | |
 | Euclid - 1892 - 460 Seiten
...straight lines is based upon his twelfth Axiom, which we here repeat. AXIOM 12. If 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... | |
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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... 
