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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... "
Practical geometry for art students - Page 21
by John Carroll (art master.) - 1881
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First Practical Lines of Geometrical Drawing ...

J. F. H. de Rheims - Geometrical drawing - 1865 - 336 pages
...straight lines cut one another, the vortical or opposite angles shall be equal. Prop. 29. — Theorem. 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...
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The College Euclid: Comprising the First Six and the Parts of the Eleventh ...

Euclides - 1865 - 402 pages
...The interior angles upon the same side together equal to two right angles ...... 2. And conversely, if a straight line fall upon two parallel straight lines, it makes — a. The alternate angles equal to one another . . .* A. The exterior angle equal to the interior...
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Aristotle on fallacies, or the Sophistici elenchi

Aristotle - Fallacies (Logic) - 1866 - 278 pages
...result from various theses : for instance, parallels may be proved to meet both from the thesis that if a straight line fall upon two parallel straight lines it makes the exterior angle greater than the interior and opposite angle upon the same side10, and from the thesis...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...therefore the remaining angle AGH is equal to the remaining angle GHD; (ax. 3.) PROPOSITION XXIX. THEOREM. 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 t/te interior and opposite upon the same side ; and...
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The Elements of Plane and Spherical Trigonometry ...

Alfred Challice Johnson - Spherical trigonometry - 1871 - 178 pages
...greater side of every triangle is opposite to the greater angle and vice versa. (Eue. I., 18, 19.) 5. If a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another. (Eue. I., 29.) 6. If a side of a triangle be produced, the exterior angle is equal...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...are not parallel. It is also cle ir that they meet towards B, D, because GB lies between GN and ///>. 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...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...clear that they meet towards B, D, because GB lies between GN and HD. <j. RD PROPOSITION XXIX. THEOREM. 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...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 588 pages
...the remaining angle GHD ; and they are alternate angles ; therefore AB is parallel to CD. XXIX. — 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...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...3. AB is parallel to CD (I. 27). Wherefore, if a straight line, &c. QED PROPOSITION 29. — Theorem. 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...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...is parallel to CD (I. 27). Therefore, if a straight line, <fec. QE 2). Proposition 29. — Theorem. 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 also...
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