| Euclides - 1874 - 342 pages
...3. AB is parallel to CD (I. 27). Wherefore, if a straight line, &c. QED PROPOSITION 29. — 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... | |
| Euclides - 1874 - 120 pages
...parallel to one another. PROPOSITION 29. THEOREM. If a straight line fall on two parallel straif/ht **lines, it makes the alternate angles equal to one...exterior angle equal to the interior and opposite angle** on the same side ; and also the two interior angles on the same side together equal to two right angles.... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...impossible.- (Lemma.) .-. L AFG is =. the alternate L FGD. Hence are easily deduced the following Theorems: **If a straight line fall upon two parallel straight lines, it makes the** exterior L. = the interior and opposite upon the same side. straight lines AB, CD; / Let HK fall upon... | |
| 1876 - 400 pages
...life and character of one of them. 3. Trace the descent of Queen Victoria from James I. EUCLID. — 1. **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... | |
| Edward Atkins - 1876 - 130 pages
...Therefore AB is parallel to CD (I. 27). Therefore, if a straight line, &c. QED Proposition 29. — Theorem. **If a straight line fall upon two parallel straight...exterior angle equal to the interior and opposite** upon the same side; and also the two interior angles upon the same side together equal to two right... | |
| Henry Major - 1876 - 784 pages
...exterior angle at the base of the triangle. 2. If a straight line fall upon two parallel straight Hues, **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 npon the same side together equal to two right... | |
| Euclides, James Hamblin SMITH - 1876 - 382 pages
...clear that they meet towards B, D, because GB lies between GN and HD. QED PROPOSITION XXIX. THKOBEM. **If a straight line fall upon two parallel straight lines, it makes the** two interior angles upon the same side together equal to two right angles, and also the alternate angles... | |
| Robert Potts - Geometry - 1876 - 446 pages
...lines make the alternate angles equal to each other, these two straight lines shall be parallel. 4. **If a straight line fall upon two parallel straight lines, it makes the** two interior angles upon the. same side together equal to two right angles. 5. Assuming Proposition... | |
| James Martin (of the Wedgwood inst, Burslem.) - 1876 - 334 pages
...triangle. NOTE. — The angles GAK, AKB, are called alternate angles, and when a straight line falls **upon two parallel straight lines, it makes the alternate angles equal to** each other (Euc. I. 29). Problem 25. To construct a triangle, having its base AB, its altitude CD,... | |
| Edward Atkins - 1877 - 72 pages
...line, .fee. QED Proposition 29. — Theorem. If a straight line fall upon two parallel straightlines, **it makes the alternate angles equal to one another, and the exterior angle** eyual to the interior and opposite upon the same side; and also the two interior angles upon the same... | |
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