| Euclides - 1841 - 378 pages
...the third angle BAC to the third angle EDF. Therefore, if two triangles, &c. QED PROP. XXVII. THEOR. **If a straight line, falling upon two other straight lines, make the** alternate angles equal to one another, these two straight lines shall be parallel. Let the straight... | |
| Chambers W. and R., ltd - 1842 - 744 pages
...the exterior angle equal to the interior and opposite angle upon the same side of the line, or makes **the interior angles upon the same side together equal...two straight lines shall be parallel to one another.** To make this more clear, it may be as well to subjoin an example. Let the straight line EF, which E»... | |
| William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842
...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 equal to two right angles. Now,... | |
| Euclides - 1842 - 320 pages
...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 equal to two right angles. Let the... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...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 equal to two right angles. Let the... | |
| Education - 1844 - 688 pages
...equal sides are opposite. 3. Any two angles of a triangle are together less than two right angles. 4. **If a straight line falling upon two other straight lines make the** alternate angles equal to one another, these two straight lines shall be parallel. 5. The opposite... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...the exterior angle equal to the interior and remote, upon the same side of that line ; and (2) if it **make the interior angles upon the same side together equal to two right angles.** Let the straight line EF, which falls upon the two straight lines, AB, CD, make the exterior angle... | |
| Euclides - 1845 - 544 pages
...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 equal to two right angles. Let the... | |
| Euclid - Geometry - 1845 - 218 pages
...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 equal to two right angles. Let the... | |
| Great Britain. Admiralty - Geometry - 1846 - 130 pages
...manner it may be proved that they do not meet towards A, C ; .'. AB || CD ; ™. ss. GEOMETRY. PROP. **XXVII. THEOR. 28. 1 Eu. If a straight line falling...Let the str. line EF, which falls upon AB and CD,** make ext. /. EGB = /_ GHD, the int. and oppo. /. on the same side. Or int. l_ s on the same side, viz.... | |
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