 | Euclides - 1845 - 546 pages
...part. X. Two straight lines cannot inclose a space. XI. All right angles are equal to one another. XII. If a straight line meets two straight lines, so as...PROBLEM. To describe an equilateral triangle upon a given Jinite straight line. Let AB be the given straight line. It is required to describe an equilateral... | |
 | Euclid - Geometry - 1845 - 218 pages
...X. Two straight lines cannot inclose a space. XI. All right angles are equal to one another. XII. " If a straight line meets two straight lines, so as...the angles which are less " than two right angles." PROPOSITIONS. PROPOSITION I. PROBLEM. — To describe an equilateral triangle upon a given finite straight... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...to one another. |j 12. If a straight line meet two other straight lines which are in the same plane, so as to make the two interior angles on the same...together, less than two right angles, these straight lines shall at length meet upon that side, if they be continually produced.^ * ln this axiom and the following,... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...cannot enclose a space. XI. All right angles are equal to one another. XII. If a straight line meet two straight lines, so as to make the two interior...are the angles which are less than two right angles. A proposition is something either proposed to be done, or to be demonstrated, and iseither a problem... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...cannot enclose a space. XI. All right angles are equal to one another. XII. If a straight line meet two straight lines, so as to make the two interior...are the angles which are less than two right angles. A proposition is something either proposed to he done, or to he demonstrated, and iseither a problem... | |
 | Euclides - 1846 - 292 pages
...to two right angles, and therefore the angles BEF, EFD are together less than two right angles : But If a straight line meets 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, being continually produced, shall at length... | |
 | Euclides - 1847 - 128 pages
...impossible (Note on Definition 6). 11. All right angles are equal to one another. (See Definition 10.) 12. If a straight line meets two straight lines, so as...are the angles which are less than two right angles. An Axiom is a self-evident truth, and is so called from its being worthy (d£ioc) of universal acknowledgment.... | |
 | Dugald Stewart - Psychology - 1847 - 666 pages
...Euclid's Elements. When it is assorted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the san»« side together equal to two right angles, these two straight lines, though indefinitely produced,... | |
 | Euclides - 1848 - 52 pages
...cannot inclose a space. XI. All right angles are equal to one another. XII. If a straight line meet two straight lines, so as to make the two interior...are the angles which are less than two right angles. PROPOSITIONS. PROP. I. PROBLEM. To describe an equilateral triangle upon a given finite straight line.... | |
 | John Playfair - Euclid's Elements - 1849 - 332 pages
...self-evident propositions. It is therefore removed from among the Axioms. The 12th Axiom of Euclid is, that " if a straight line meets two straight " lines, so...shall at length meet upon that side on which are the angle* " which are less than two right angles." Instead of this proposition, which, though true, is... | |
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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... 
