| John Playfair - 1819 - 354 pages
...would in this manner be freed from all difficulty. PROP. III. 29. 1. Euclid. If a straight line fall on **two parallel straight lines, it makes the alternate angles equal to one another** ; the exterior equal to the interior * Prop. 1 1. Sup. The reference to this proposition involves nothing... | |
| William Nicholson - Natural history - 1821 - 406 pages
...straight line may be drawn parallel to that straight line, or that straight line produced. 14. Theorem IV. **If a straight line fall upon two parallel straight...exterior angle equal to the interior and opposite angle** on the same side ; and likewise the two interior angles upon the same side, together, equal to two... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 pages
...angles: therefore AB is parallel to CD. Wherefore,' if a straight line, &c. QED PROP. XXIX. THEOR. **IF a straight line fall upon two parallel straight...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... | |
| Peter Nicholson - Mathematics - 1825 - 1046 pages
...therefore AB is parallel to С D. Wherefore if a straight line, &c. OKD Proposition ХХГХ. Theorem, **If a straight line fall upon two parallel straight...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 - Circle-squaring - 1826 - 326 pages
...the alternate angles equal to one another; and the exterior angle equal to the interior and opposite **upon the same side ; and likewise the two interior...the same side together equal to two right angles.'** Let the straight line EF fall upon the parallel straight lines ABi CD; the alternate angles AGH, GHD... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...thts proposttton. * 15. 1. t 1 Ax. f2 Ax. * 13. 1. t 1 Ax. PROP. XXIX. THEOR. If a straight line Jail **upon two parallel straight lines, it makes the alternate...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 Radford Young - Euclid's Elements - 1827 - 228 pages
...a point between G and K, therefore, &c. PROPOSITION n. ,(29. I. Euclid.) If a straight line fall on **two parallel straight lines it makes, the alternate angles equal to one another** ; the exterior eqttal to the interior and opposite on the same side ; and likewise the two interior... | |
| Pierce Morton - Geometry - 1830 - 584 pages
...those two straight lines are parallel • . • cor. 13 (f) And conversely, if a straight line falls **upon two parallel straight lines, it makes the alternate angles equal to one another,** the exterior angle equal to the interior and opposite upon the same side, and the two interior angles... | |
| Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...interior angles &c. Which was to be demonstrated. PROPOSITION XXIX. THEOREM. — If a straight line falls **upon two parallel straight lines, it makes the alternate angles equal to one another.** Let the straight line EF fall upon the •? parallel straight lines AB, CD ; the alter- ^ - ^& - B... | |
| John Playfair - Euclid's Elements - 1833 - 346 pages
...angles ; therefore AB is parallel to CD. Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. **If a straight line fall upon two parallel straight lines, it makes the** alter' male angles equal to one another ; and the exterior angle equal to the interior and opposite... | |
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