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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, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...the exterior angle cqual 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 definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 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 to two right angles. PROP. XXX. THEOREM. Straight lines which are parallel to the same straight line are parallel to each...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...exterior angle equal to the interior and opposite on the same side; and the two interior angles on the same side together equal to two right angles. Let the straight line EF intersect the two parallel lines AB, CD; the alternate angles AGH, GHD are gle EGB is equal to the...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 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 egual to two right angles. Let the straight line EF fall upon the parallel straight lines AB, CD; the...
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The English Journal of Education, Volume 4

Education - 1850 - 488 pages
...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. 2. If one side of a triangle be produced,...
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The English Journal of Education, Volume 5

Education - 1851 - 502 pages
...other: and the exterior angle equal to the interior and opposite upon the same side : and likewiie the two interior angles upon the same side together equal to two right angles. 2. In a right-angled triangle, if a perpendicular be drawn from the right angle to the base, the triangles...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 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 first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...angles equal to one, another ; and tlie 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 rigM angles. LET the straight line ef fall upon the parallel straight lines ab, С d ; the alternate...
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The Assurance Magazine, and Journal of the Institute of Actuaries, Volume 3

Insurance - 1853 - 394 pages
...to 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. 30. Draw through a given point between two straight lines not parallel a straight line which shall...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 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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