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" 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 the two interior angles upon the same side together... "
The Elements of Euclid: viz. the first six books, together with the eleventh ... - Page 26
by Robert Simson - 1835 - 513 pages
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 228 pages
...angles equal, the exterior angle equal to the interior opposite one, and the two interior angles on the same side together equal to two right angles. Let the straight line EFG fall upon the parallels AB and CD ; the alternate angles AGF and DFG are equal, the exterior angle...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...the exterior angle equal to the interior and opposite upon the same s1de of the line / or make the interior angles upon the same side together equal to two right angles : the two straight lines shall be parallel to one another. Let the straight line EF, which falls upon...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...equal to two right angles. — See figure on next page. Let the straight line EF intersect the two parallel straight lines AB, CD; the alternate angles AGH, GHD are equal, and the angles BGH, GHC are equal; and the two interior angles B •• M , GH D, on the same side...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...equal to one another, or the exterior angle equal to the interior and opposite upon the same side, or the two interior angles upon the same side together equal to two right angles, those two straight lines are parallel • . • cor. 13 (f) And conversely, if a straight line falls...
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Geometry Without Axioms; Or the First Book of Euclid's Elements. With ...

Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...straight line falls upon two parallel straight lines, it makes the alternate angles equal to one another. Let the straight line EF fall upon the •? parallel straight lines AB, CD ; the alter- ^ - ^& - B nate angles GHC, HGB are equal to one ~ - j^r - 5 another. ^F For, if the angle...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...equal to one another, or the exterior angle equal to the interior and opposite upon the same side, or the two interior angles upon the same side together equal to two right angles, those two straight lines are parallel . . . cor. 13 (e) And conversely, if a straight line falls upon...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...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 ; the two straight lines are parallel to one another. Let the straight line EF, which J falls upon...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...alternate angles equal to one another ; and the exterior angle equal to the interior and opposite angle upon the same side ; and likewise the two interior...the same side together equal to two right angles. XXX. Straight lines which are parallel to the same straight line are parallel to one another. XXXII....
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...angles, on the same side equal to two right angles. . v -. ^ •, Let the, straight line EF fall on the parallel; straight lines AB, CD ; the alternate- angles AGH, ' GHD are H\ D V ... •••Atf.-.-i...-- -.;,... equal, the exterior angle EGB is equal to the interior arid...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...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 tu two right angles. Let the straight line EF fall upon the parallel straight lines AB, CD ; the alternate...
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