| J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...straight lines cut one another, the vortical or opposite angles shall be equal. Prop. 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 ; and... | |
| Euclides - 1865 - 402 pages
...The interior angles upon the same side together equal to two right angles ...... 2. And conversely, **if a straight line fall upon two parallel straight lines, it makes** — a. The alternate angles equal to one another . . .* A. The exterior angle equal to the interior... | |
| Aristotle - Fallacies (Logic) - 1866 - 278 pages
...result from various theses : for instance, parallels may be proved to meet both from the thesis that **if a straight line fall upon two parallel straight lines it makes the** exterior angle greater than the interior and opposite angle upon the same side10, and from the thesis... | |
| Robert Potts - 1868 - 434 pages
...therefore the remaining angle AGH is equal to the remaining angle GHD; (ax. 3.) PROPOSITION XXIX. 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 t/te interior and opposite upon the same side ; and... | |
| Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...greater side of every triangle is opposite to the greater angle and vice versa. (Eue. I., 18, 19.) 5. **If a straight line fall upon two parallel straight lines, it makes the alternate angles equal** to one another. (Eue. I., 29.) 6. If a side of a triangle be produced, the exterior angle is equal... | |
| Euclides - 1871 - 136 pages
...are not parallel. It is also cle ir that they meet towards B, D, because GB lies between GN and ///>. **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... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...clear that they meet towards B, D, because GB lies between GN and HD. <j. RD PROPOSITION XXIX. 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; and likewise... | |
| Henry Major - Student teachers - 1873 - 588 pages
...the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD. XXIX. — **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... | |
| 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 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... | |
| 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 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 also... | |
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