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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... "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 48
by Euclides - 1871
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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
...exterior angle equal to the interior and remote, upon the same side of that line ; and (2.) if it make the interior angles upon the same side together equal to two right angles. Let the straight line EF, which falls upon the two straight lines AB, CD, make the exterior angle EGB...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...geometrical, are nevertheless very ingenious and conclusive, see NOTES at the end. PROP. XXIX. THEOR. If a straight line fall upon two parallel straight...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 right angles....
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...straight line, &c. QED PROP. XXVIII. THEOR. IF a straight line falling upon two other straight lines makes 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 ;...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - Geometry - 1841 - 378 pages
...line, &c. QED PROP. XXVIII. THEOR. If a straight line, falling upon two other straight lines, 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...
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Chambers's Information for the People, Volume 2

William Chambers, Robert Chambers - Encyclopedias and dictionaries - 1842 - 938 pages
...right angles ; AB is parallel to CD. But the 29th proposition assumes the converse of this, namely, if a straight line fall upon two parallel straight...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: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...alternate angles; therefore AB is parallel to CD. Wherefore if a straight line, &c. QED PEOP. XXIX. THEOR. IF a straight line fall upon two parallel straight...the same side together equal to two right angles. Let the straight line EF fall upon the parallel straight lines AB, CD; the alternate angles AGH, GHD...
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Chambers's information for the people, ed. by W. and R. Chambers, Volume 2

Chambers W. and R., ltd - 1842 - 744 pages
...proposition assumes the converse of this, namely, if a straight line fall upon two parallel straight hues, it makes the alternate angles equal to one another...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
...in this manner be freed from all difficulty. PROP. III. or 29. 1. Euclid. If a straight line fall on two parallel straight lines, it makes the alternate angles equal to one another ; the exterior equal to the interior and opposite on the same side ; and likewise the two interior...
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The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...vertical angles shall be equal. 4. If a straight line, falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line, or make the interior angles on the same side together equal to two right angles, the two...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...&c. QED PROPOSITION XXVIII. THEOREM. If a straight line falling upon two other straight lines, makes 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 iwo right angles ;...
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