 | John Playfair - 1849 - 332 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...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... | |
 | Henry Longueville Mansel - 1851 - 350 σελίδες
...character, analogous to the geometrical principles, " two straight lines cannot enclose a space," or, " if a straight line meets two straight lines, so as to make the two interior angles on the same side together less than two right angles, the two straight lines will meet if produced." As a matter of... | |
 | Euclides - 1852 - 152 σελίδες
...across the other two so as to 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." [These are truths which no person can possibly doubt, who are others besides these, but these are sufficient... | |
 | Euclides - 1852 - 48 σελίδες
...inclose a space. 11. All right angles are equal to one another. 12. If a right line meet two other right lines, so as to make the two interior angles on the...it taken together less than two right angles, these two right lines being continually induced, shall at length meet on that side on which are the angles,... | |
 | Royal Military Academy, Woolwich - 1853 - 400 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. PROPOSITIONS. PROPOSITION I. PROBLEM. To describe an equilateral triangle upon a given finite straight... | |
 | Euclides - 1853 - 176 σελίδες
...part. X. Two straight lines cannot enclose a space. XI. 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 finiie straight line.... | |
 | Euclides - 1853 - 146 σελίδες
...lines cannot inclose a space. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as to make the two interior...the angles which are less than two right angles." PROPOSITION I. — PROBLEM. To describe an equilateral triangle upon a given finite straight line.... | |
 | Euclides - 1853 - 334 σελίδες
...parallel to FG; but both cannot. »^^F/ — 1 5- jf" * 3. — To BK. I. PEOP. A. 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 : then these two straight lines, being continually produced, shall... | |
 | Euclid - 1853 - 176 σελίδες
...internal an£;^' '\ the same side, fS6g..£ ''• ' ^uol to two right I. 29, theor. . . I. 29, cor. . . If a straight line meets two straight lines so as to make the two internal angles on the same side together less than two right angles. {These '' stralgnt lines being... | |
 | William Somerville Orr - 1854 - 534 σελίδες
...shall be meeting-lines. This is the twelfth axiom, and is thus expressed in Euclid : — AXIOM XII. — If a straight line meets two straight lines, so as...than two right angles, these straight lines, being prolonged, shall at length meet upon that side on which are the angles that are less than two right... | |
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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... 
