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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 Geometry, Symbolically Arranged - Side 37
av Great Britain. Admiralty - 1846
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 sider
...line &c. QED PROPOSITION 28. THEOREM. If a straight line falling on two other straight lines, make the exterior angle equal to the interior and opposite angle on 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: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 sider
...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...equal to one another ; and the exterior angle equal to t/te interior and opposite upon the same side ; and likewise the two interior angles upon ihe same...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870
...same st. line are parallel to each other. DEM. — P. 29. If a st. line fall upon two parallel st. lines, it makes the alternate angles equal to one another ; and the exterior angle equal to the int. and opp. angle upon the same side ; and likewise the two int. angles upon the same side together...
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Elements of geometry, containing the first two (third and fourth ..., Del 1

Euclides - 1871
...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...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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The Elements of Plane and Spherical Trigonometry ...

Alfred Challice Johnson - 1871
...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...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 to the two interior...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 sider
...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...exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles up in t/ie tame side together equal to two...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...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...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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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...Proposition 28. — Theorem. If a straight line fall on two parallel straight lines, it makes — (1.) The exterior angle equal to the interior and opposite angle on the same side of the line ; (2.) The alternate angles equal ; and (3.) The two interior angles on the same side of...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...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...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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Pure mathematics, Volum 1

Edward Atkins - 1874
...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...exterior angle equal to the interior and opposite upon the same side; and also the two interior angles upon the same side together equal to two right...
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