| Euclides - Euclid's Elements - 1837 - 112 pages
...AGH = alternate Z GHD, 3. and :. that AB |] CD. PROPOSITION XXIX. (Argument ad absurdum). 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 the... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...straight lines are perpendicular to a third line, they 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 another ; and the exterior angle equal to the interior and opposite upon the same side ; and... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...angle GHD ; and they are alternate angles ; therefore 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 another ; and the exterior angle equal to the interior and opposite upon the same side ; and... | |
| Robert Simson - Geometry - 1838 - 434 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 alternate angles equal** to one another; and the exterior angle equal to the interior and opposite upon the same side ; and... | |
| Euclides - 1838 - 264 pages
...geometrical, are nevertheless very ingenious and 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 another ; and the exterior angle equal to the interior and opposite upon the tame side ; and... | |
| Euclides - Geometry - 1841 - 378 pages
...alternate 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 alternate angles equal** to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...straight lines are perpendicular to a third line, they 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 another ; and the exterior angle equal to the interior and opposite upon the same side ; and... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...right angles ; AB is parallel to CD. But the 29th proposition assumes the converse of this, namely, **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 - 1842 - 316 pages
...alternate angles; therefore AB is parallel to CD. 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 ; and the exterior angle equal to the interior and opposite, upon the same side ; and... | |
| Euclid - Geometry - 1845 - 218 pages
...fore AB is parallelf to CD. Wherefore, if a straight line, &c. Q. i:. D. PROPOSITION XXIX. THEOR — **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 ;... | |
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