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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 - Pagina 37
di Great Britain. Admiralty - 1846
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...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 tlie line, or make the interior angles on the same side together equal to two right angles, the...
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Euclidian Geometry

Francis Cuthbertson - 1874 - 349 pagine
...impossible.- (Lemma.) .-. L AFG is =. the alternate L FGD. Hence are easily deduced the following Theorems: If a straight line fall upon two parallel straight lines, it makes the exterior L. = the interior and opposite upon the same side. straight lines AB, CD; / Let HK fall upon...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pagine
...Therefore AB is parallel to CD (I. 27). Therefore, 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 also the two interior angles upon the same side together equal to two right...
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The Teachers' assistant and pupil teachers' guide, Volume 1

1876
...life and character of one of them. 3. Trace the descent of Queen Victoria from James I. EUCLID. — 1. 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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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876
...exterior angle at the base of the triangle. 2. If a straight line fall upon two parallel straight Hues, 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 npon the same side together equal to two right...
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Examination Christmas,1875

Education Department,London - 1876
...parallel to those of the original triangle. 1. 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, the two straight lines shall be parallel to one another. 2. Parallelograms on the same...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin SMITH - 1876 - 349 pagine
...clear that they meet towards B, D, because GB lies between GN and HD. QED PROPOSITION XXIX. THKOBEM. If a straight line fall upon two parallel straight lines, it makes the two interior angles upon the same side together equal to two right angles, and also the alternate angles...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 pagine
...lines make the alternate angles equal to each other, these two straight lines shall be parallel. 4. If a straight line fall upon two parallel straight lines, it makes the two interior angles upon the. same side together equal to two right angles. 5. Assuming Proposition...
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A graduated course of problems in practical plane and solid geometry

James Martin (of the Wedgwood inst, Burslem.) - 1876
...triangle. NOTE. — The angles GAK, AKB, are called alternate angles, and when a straight line falls upon two parallel straight lines, it makes the alternate angles equal to each other (Euc. I. 29). Problem 25. To construct a triangle, having its base AB, its altitude CD,...
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877
...line, .fee. QED Proposition 29. — Theorem. If a straight line fall upon two parallel straightlines, it makes the alternate angles equal to one another, and the exterior angle eyual to the interior and opposite upon the same side; and also the two interior angles upon the same...
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