 | John Playfair - 1829 - 210 Seiten
...and the exterior angle equal to the interior and opposite angle on the same side of it; and likewise the two interior angles on the same side together equal to two right angles. AXIOM 10. Two straight lines which intersect each other cannot be both parallel to the same straight... | |
 | Dugald Stewart - 1829 - 418 Seiten
...asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never meet;" — is not the boundless... | |
 | Dugald Stewart - 1829 - 442 Seiten
...asserted, for example, that " if one straight line falls on two other straight lines, so as to make the two interior angles on the same side together equal to two right angles, these two straight lines, though indefinitely produced, will never meet ; " — is not the boundless... | |
 | Thomas Perronet Thompson - 1833 - 168 Seiten
...the exterior angle equal to the interior and opposite on the same side of the line ; or if it makes the two interior angles on the same side, together equal to two right angles ; those two straight lines shall be parallel. For First ; where the exterior angle EGA ,E is equal... | |
 | 1835 - 684 Seiten
...two right angles (2.). Therefore, if one straight line, falling upon two other straight lines, make the two interior angles, on the same side, together equal to two right angles, the two straight lines shall be parallel : and conversely. Cor. 4. (Eue. i. ax. 12.) If one straight... | |
 | Euclid - 1835 - 540 Seiten
...angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles. Let the straight line EF fall upon the parallel straight lines AB, CD; the alternate angles AGH, GHD are equal to one another... | |
 | John Playfair - 1836 - 148 Seiten
...parallel. COR. II. If a straight line falling on two other straight lines in the same plane, makes the two interior angles on the same side together equal to two right angles ; those two straight lines are parallel. . PROP. III. THEOR. If a straight line fall on two parallel... | |
 | Robert Mudie - 1836 - 542 Seiten
...alternate angles equal, the exterior angle equal to the interior and opposite on the same side, or the interior angles on the same side together equal to two right angles, we may always conclude that the two straight lines, which answer any of these conditions with the third... | |
 | Robert Mudie - 1836 - 524 Seiten
...alternate angles equal, the exterior angle equal to the interior and opposite on the same side, or the interior angles on the same side together equal to two right angles, we may always conclude that the two straight lines, which answer any of these conditions with the third... | |
 | Euclid, James Thomson - 1837 - 410 Seiten
...interior and remote, upon the same side of that line ; and (2.) if it make the interior angles upon the same side together equal to two right angles. Let the straight line EF, which falls upon the two straight lines AB, CD, make the exterior angle EGB E equal to the interior... | |
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... if a straight line, &c. QED PROPOSITION 29. — Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ;... 
