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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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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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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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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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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...angles equal to one another ; and the exterior angle equal to the interior and opposite upon the tame side ; and likewise the two interior angles upon the...straight lines AB, CD : the alternate angles AGH, GHD shall be equal to one another : and the exterior angle EGB shall be equal to the interior nnd opposite,...
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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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...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...are equal to one another ; and the exterior angle EG в is equal to the interior and opposite, upon the same side, GHD; and the two interior angles BGH,...
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Chambers's Information for the People, Volume 2

William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 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...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 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 are parallel to one another. Let the straight line EF, which falls upon the...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 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...line EF fall upon the parallel straight lines AB, CD. Then the alternate angles A GH, G HD shall be equal to one another ; the exterior angle EGB shall be...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 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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