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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... "
Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 100
by Euclides - 1858
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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...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...straight lines are parallel to one another. XXIX. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one...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...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...AB is parallel to CD. PROPOSITION XXIX. THEOREM. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one...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...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...will be parallel to each other. PROP. XXIX. THEOR. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one...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...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...PROPOSITION XXIX. (Argument ad absurdum). Theorem. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one...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....
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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...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...conclusive, see NOTES at the end. PROP. XXIX. THEOR. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one...exterior angle equal to the interior and opposite upon the tame side ; and likewise the two interior angles upon the same side together equal to two...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...Wherefore, if a straight line, &c. QED PROP. XXIX. THEOR. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...will be parallel to each other. PROP. XXIX. THEOR. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one...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...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...Wherefore if a straight line, &c. QED PEOP. XXIX. THEOR. IF a straight line fall upon two parallel straight lines it makes the alternate angles equal to one another...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...
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