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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... "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 38
by Euclides - 1838
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...angles upon the same side together equal to two right angles. .'. it. CD : the alternate angles Aim, GHD shall be equal to one another ; and the exterior angle EGB shall be equal to the interior and opposite, upon the same side, GHD; and the two interior angles BGH, g ^. . GHD upon the same side,...
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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
...equal to one another ; and the 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 two right angles. XXX. Straight lines which are parallel to the same straight line are parallel to one another. XXXII....
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...equal to one another, and the exterior angle equal to 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. Suppose that Z AGH ^ GHD, and that AGH > GHD, Then prove, on that supposition,...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...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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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...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 two straight lines shall be parallel to one another. Let the straight line EF, which falls upon...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...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...straight lines AB, CD ; the alternate angles, AGH, GHD are equal to one another; and the exterior angle EGB is equal to the interior and opposite upon the...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...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 two straight lines shall be parallel to one another. Let the straight line EF, which falls upon...
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