 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...  The Element of Geometry - Seite 19von John Playfair - 1836 - 114 SeitenVollansicht - Über dieses Buch
 | Euclid, James Thomson - 1837 - 410 Seiten
...this proposition has been demonstrated by some writers in the following manner •. 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.* PROPOSITION I. PROBLEM.f To... | |
 | Euclides - 1837 - 112 Seiten
...by showing that the alternate Zs AGK, GKD are equal. PROPOSITION. " If a right line meet two right lines, so as to make the two interior angles on the...it taken together less than two right angles, these right lines being continually produced, shall at length meet on that side on which are the angles which... | |
 | John Playfair - 1837 - 332 Seiten
...interior and opposite. In order to demonstrate this proposition, Euclid assumed it as an Axiom, that " if a "straight line meet two straight lines, so as to make the interior angles on " the same side of it less than two right angles, these straight lines being " continually... | |
 | Euclid - 1838 - 470 Seiten
...Two straight lines cannot enclose a space. XI. All right angles arc equal to one another. XII. •• If a straight line meet two straight lines, so as...right angles, these straight lines being continually pro" duced, shall at length meet upon that side on which are the angles " which are less than two right... | |
 | Robert Simson - 1838 - 434 Seiten
...X. Two straight linea cannot enclose a space, XI. All right angles are equal to one another. XII. " If a straight line meet two straight lines, so as...right angles, these straight lines being continually pro" duced, shall at length meet upon that side on which are the angles " which are less than two right... | |
 | Euclides - 1841 - 378 Seiten
...equal to one another. XII. " If a straight line meet two straight lines, which are " in the same plane, so as to make the two interior " angles on the same...than two right angles, these straight lines being " produced, shall at length meet upon that side on " which are the angles which are less than two "... | |
 | Euclides - 1842 - 316 Seiten
...from any centre, at any distance from that centre. IV. [Ax. XI.] V. And that if a straight line meets two straight lines, so as to make the two interior...length meet upon that side on which are the angles less than two right angles. AXIOMS. I. THINGS which are equal to the same are equal to one another.... | |
 | John Playfair - 1842 - 332 Seiten
...interior and opposite. In order to demonstrate this proposition, Euclid assumed it as an Axiom, that " if a " straight line meet two straight lines, so as to make the interior angles on " the same side of it less than two right angles, these straight lines being " continually... | |
 | John Playfair - 1844 - 338 Seiten
...Euclid is, that " if a straight line meets two straight " lines, so as to make the two interior anples on the same side of it taken " together less than...length meet upon that side on which are the angles AMONG the Axioms there have been made only two alterations. The 10th Axiom in Euclid is, that " two... | |
 | James Bates Thomson - 1844 - 268 Seiten
...the necessity of a new axiom. Euclid's axiom alluded to is this : " If a straight line meet two other straight lines, so as to make the two interior angles...on the same side of it taken together less than two right-angles, these straight lines being continually produced, will at length meet on the side on which... | |
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