 | Robert Gibson - Surveying - 1795 - 384 pages
...like we can prove of all other Lines but AB ; therefore AB is parallel to CD. Q.. ED r HE o. xii. . If two equal and parallel Lines AB, CD, be joined by two other Lines AD, EC, thnfe Jball be alfo equal and parallel. Fig. 3. Let Plate I. Let the Diameter or... | |
 | Robert Gibson - 1808 - 482 pages
...and the like we can prove of all other lines but AB ; therefore AB is parallel to CD. QED THEO. XII. If two equal and parallel lines AB, CD, be joined by two other lines AD, BC, those shall be also equal and parallel. Jig. 3. Plate I. Let the diameter or diagonal... | |
 | Robert Gibson - Surveying - 1814 - 558 pages
...we can prove of all other lines but AB ; therefore AB is parallel to CD. QED THEO. XII. PL. l.fg.3. If two equal and parallel lines AB, CD, be joined by two other Itnet AD, BC, those shall be also equal and parallel. Let the diameter or diagonal BDbe drawn,... | |
 | Nathaniel Bowditch - 1846 - 854 pages
...is equal to half the arc AFB, and AD huh'' the chord AB ; hence the proposition is manifest XLVII. If two equal and parallel lines, AB, CD, be joined by two others, AC, BD, these will be viso equal and parallel. To demonstrate this, join the two opposite angles A and D with... | |
 | Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...may be proved that half of AD is the sine of ABD, and the half of AB the sine of ADB. QED THEO. XI. If two equal and parallel lines AB, CD, be joined by two other lines AD, BC, those lines will be also equal and parallel. Let the diagonal BD be n drawn, and... | |
 | Nathaniel Bowditch - Nautical astronomy - 1888 - 704 pages
...is equal to half the arc AFP>, and AD half the chord AB; hence the proposition is manifest. •XXI. If two equal and parallel lines, AB, CD, be joined by two others, AC, BD, these will be also equal and parallel. To demonstrate this, join the two opposite angles A and D with... | |
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IEF=(FED)=AEF (by part 2. theo. 3.) a greater to a less, which is absurd, whence IK is not parallel ; and the like we can prove of all other lines but AB ; therefore AB is parallel to CD. QED THEO. XII. 