| Euclid - 1835 - 540 pages
...line," &c. QED PROP. XXVIII. THEOR. If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the fine ; or makes the interior angles upon the same side together equal to two right angles ;... | |
| Mathematics - 1836 - 488 pages
...together equal to two right angles ; the two straight lines are parallel to one another. XXIX. If a straight line fall upon two parallel straight lines,...exterior angle equal to the interior and opposite angle upon the same side ; and likewise the two interior angles upon the same side together equal to... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...= alternate Z GHD, 3. and :. that AB |] CD. PROPOSITION XXIX. (Argument ad absurdum). Theorem. If a straight line fall upon two parallel straight lines,...the interior and opposite upon the same side; and the two interior angles upon the same side together equal to two right angles. Steps of the Demonstration.... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...one another ; (2.) the exterior angle equal to the interior and remote upon the same side ; and (3.) the two interior angles upon the same side together equal to two right angles, t Let the straight lines AB, CD be parallel, and let EF fall upon them ; then (1.) the alternate angles... | |
| Andrew Bell - Euclid's Elements - 1837 - 290 pages
...to CD. PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the line, or makes the interior angles upon the same side together equal to two right angles, the... | |
| John Playfair - Euclid's Elements - 1837 - 332 pages
...parallel to CD. PROP. XXVIII. THEOR. If a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ;... | |
| 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,...angle equal to the interior and opposite upon the tame side ; and likewise the two interior angles upon the same side together equal to two right angles.... | |
| Robert Simson - Geometry - 1838 - 434 pages
...straight line, &c. QED PROP. XXVIII. THEOR. IF a straight line falling upon two other straight lines makes the exterior angle equal to the interior and opposite upon the same side of the line ; or makes the interior angles upon the same side together equal to two right angles ;... | |
| Euclides - Geometry - 1841 - 378 pages
...line, &c. QED PROP. XXVIII. THEOR. If a straight line, falling upon two other straight lines, makes the exterior angle equal to the interior and opposite upon the same side of the line: or make the interior angles upon the same side together equal to two right angles; the... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...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,...the same side together equal to two right angles. Now, the assertion contained in this theorem is both easy of comprehension and evident to the senses... | |
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