| Mathematics - 1835 - 684 pages
...equal to one another, or the exterior angle equal to the interior and opposite upon the same side, or **the two interior angles upon the same side together equal to two** right angles, those two straight lines are parallel . . . cor. 13 (e) And conversely, if a straight... | |
| Mathematics - 1836 - 472 pages
...straight lines are parallel to one another. XXIX. If a straight line fall upon two parallel straight **lines, it makes the alternate angles equal to one...interior angles upon the same side together equal to two** right angles. XXX. Straight lines which are parallel to the same straight line are parallel to one... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...AB is parallel to CD. PROPOSITION XXIX. THEOREM. If a straight line fall upon two parallel straight **lines, it makes the alternate angles equal to one...exterior 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... | |
| John Playfair - Geometry - 1837 - 332 pages
...will be parallel to each other. PROP. XXIX. THEOR. If a straight line fall upon two parallel straight **lines, it makes the alternate angles equal to one...exterior angle equal to the interior and opposite** upon the same side ; and likewise the two interior angles upon the same side together equal tu two... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...PROPOSITION XXIX. (Argument ad absurdum). Theorem. If a straight line fall upon two parallel straight **lines, it makes the alternate angles equal to one...exterior angle equal to the interior and opposite** upon the same side; and the two interior angles upon the same side together equal to two right angles.... | |
| Euclid - Geometry - 1837 - 410 pages
...one another ; (2.) the exterior angle equal to the interior and remote upon the same side ; and (3.) **the two interior angles upon the same side together equal to two** right angles, t Let the straight lines AB, CD be parallel, and let EF fall upon them ; then (1.) the... | |
| Euclides - 1838 - 264 pages
...conclusive, see NOTES at the end. PROP. XXIX. THEOR. If a straight line fall upon two parallel straight **lines, it makes the alternate angles equal to one...exterior angle equal to the interior and opposite** upon the tame side ; and likewise the two interior angles upon the same side together equal to two... | |
| Euclides - 1841 - 378 pages
...Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. If a straight line fall upon two parallel straight **lines, it makes the alternate angles equal to one...exterior 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... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...will be parallel to each other. PROP. XXIX. THEOR. If a straight line fall upon two parallel straight **lines, it makes the alternate angles equal to one...exterior 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... | |
| Euclides - 1842 - 320 pages
...Wherefore if a straight line, &c. QED PEOP. XXIX. THEOR. IF a straight line fall upon two parallel straight **lines it makes the alternate angles equal to one another...exterior 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... | |
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