 | New Zealand Institute - 1886 - 530 Seiten
...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 - 518 Seiten
...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... | |
 | United States. Office of Education - 1890 - 958 Seiten
...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... | |
 | Florian Cajori - 1890 - 574 Seiten
...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 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.... | |
 | 1892 - 444 Seiten
...at least one which is not axiomatic.1 This id the axiom of parallels, 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 on that side on... | |
 | 1892 - 448 Seiten
...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... | |
 | Euclid - 1892 - 460 Seiten
...that all right angles are equal, admits of proof, and is therefore perhaps out of place as an Axiom.] 12. If a straight line meet two straight lines so as to make the interior angles on one side of it together less than two right angles, these straight lines will meet... | |
 | Michigan Schoolmasters' Club - 1894 - 554 Seiten
...any center with any radius. 4. That all right angles are equal. 6. 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 rig~ht angles, these two straight lines being continually produced shall at... | |
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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... 
