 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...  Educational Review - Page 38edited by - 1892Full view - About this book
 | Science - 1892 - 448 pages
...at least one which is not axiomatic.3 This is 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... | |
 | Euclides - 1883 - 176 pages
...Note.— The converse of this proposition, that "if a straight line meeting two other straight lines make the two interior angles on the same side of it taken together less than two right angles, the two lines will, if produced tar enough) meet on that Bide on which are the angles less than two... | |
 | Euclides - 1884 - 182 pages
...much better, however, not to discuss it until we have made some further progress in the subject. 12. If a straight line meet two straight lines so as to...together 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... | |
 | James Gow - Mathematics - 1884 - 350 pages
...the last three are 10. Two straight lines cannot enclose a space: 11. All right angles are equal: 12. If a straight line meet two straight lines, so as...make the two interior angles on the same side of it together less than two right angles, these straight lines will meet if produced on that side. Of these... | |
 | 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
...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 - Science - 1886 - 530 pages
...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
...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 - Mathematics - 1890 - 412 pages
...Euclid assumed it. His assumption consists in what is generally called the twelfth, by some the eleventh "axiom :" " If a straight line meet two straight lines...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 - Digital images - 1890 - 958 pages
...assumed it. His assumption consists in what is generally called the twelfth, by some the eleventh " axiom :" " If a straight line meet two straight lines...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... | |
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