 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; and likewise the two interior angles upon the same side together...  The Elements of Geometry, Symbolically Arranged - Page 39by Great Britain. Admiralty - 1846Full view - About this book
 | Edward Atkins - 1874 - 426 pages
...is parallel to CD (I. 27). Therefore, if a straight line, <fec. QE 2). 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... | |
 | Euclides - 1874 - 120 pages
...line, &c. QED PROPOSITION 28. THEOREM. If a straight line falling on two other straight lines, make the exterior angle equal to the interior and opposite angle on the same side of tlie line, or make the interior angles on the same side together equal to two right angles, the... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | Education Department,London - 1876 - 1010 pages
...parallel to those of the original triangle. 1. If a straight line falling on two other straight lines make the exterior angle equal to the interior and opposite angle on the same side of the line, the two straight lines shall be parallel to one another. 2. Parallelograms on the same... | |
 | 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,... | |
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