 | Euclides - 1862 - 172 σελίδες
...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.' PROP. I. — PROBLEM. To describe an equilateral triangle upon a given finite straight line. •(References... | |
 | Euclides - 1862 - 140 σελίδες
...cannot inclose a space. 11. All right angles are equal to one another. 12. 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. EXPLANATION OF TERMS. A... | |
 | Euclides - 1863 - 74 σελίδες
...angles measured by those equals must themselves be equal. 12. If a straight line meets two skaight lines, so as to make the two interior angles on the...it taken together less than two right angles, these two straight lines, being continually produced, shall at length meet upon that side on which the angles... | |
 | Euclides - 1863 - 122 σελίδες
...part. j 11. All right angles are equal to one another. | 10. Two straight lines cannot enclose a space to make the two interior angles on the same side of it, \ 12. If a straight line meets two straight lines, so as straight lines, being continually produced,... | |
 | Euclides - 1864 - 448 σελίδες
...part. X. Two straight lines cannot enclose a space. XL All right angles are equal to one another. XII. If a straight line meets two straight lines, so as...are the angles which are less than two right angles. PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given finitt straight line. Let... | |
 | Robert Potts - 1865 - 528 σελίδες
...part. X. Two straight lines cannot enclose a space. XI. All right angles are equal to one another. xn. If a straight line meets two straight lines, so as...are the angles which are less than two right angles. PROPOSIT1ON I. PROBLEM. To describe an equilateral triangle upon a given finite straight line. Let... | |
 | Euclides - 1865 - 402 σελίδες
...properties of parallel lines. Enclid gets over the difficulty by assuming the following as an axiom : — ' If a straight line meets two straight lines, so as...right angles ; these straight lines being continually prodnced, shall at length meet upon that side on which are the angles which are less than two right... | |
 | Edward Clarke Lowe - 1866 - 172 σελίδες
...part. 10. Two straight lines cannot enclose a space. 11. All right angles are equal to one another. 12. If a straight line meets two straight lines so as...are the angles which are less than two right angles. BOOK II. • Definitions. 1. Every right-angled parallelogram is called a rectangle, and is said to... | |
 | John Playfair - 1855 - 350 σελίδες
...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 as...produced, shall at length meet upon that side on which are th*i angles "which ire less than two right angles." Instead of this proposition, which, though true,... | |
 | Matthew Ryan - 1866 - 50 σελίδες
...lines (AB, С D) which are in the same plane, so as to make the two interior angles (BA С, A С D) ore the same side of it, taken together, less than two right angles, these two straight lines (А В, С D) shall at length meet upon that side, if sufficiently produced. Draw... | |
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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... 
