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" Equal triangles on the same base, and on the same side of it, are between the same parallels. "
Euclid's Elements of Geometry: The Six First Books. To which are Added ... - Page 47
by Euclid, Rev. John Allen - 1822 - 494 pages
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Manual of Euclid: Books IV, V, VI, and Propositions 1-21 of Book XI

Euclid - 1868 - 141 pages
...to the triangle CDE (V. 9); and they are on the same base DE. But equal triangles on the same base and on the same side of it are between the same parallels (L 39). Therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III.—...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...to the triangle CDE: (v. 9.) and they are on the same base DE: but equal triangles on the same base and on the same side of it, are between the same parallels ; (I. 39.) therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III THEOREM....
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The Elements of Plane and Solid Geometry

Henry William Watson - Geometry - 1871 - 285 pages
...side of that line are between the same parallels. Corollary 2. — Equal triangles upon the same base and on the same side of it are between the same parallels. Corollary 3. — Equal parallelograms upon the same base and upon the same side of it are between the...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871
...base, and upon the same side of it, are between the same parallels. a Let the equal A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then must AD be II to BC. For if not, through A draw AO II to BC, so as to meet BD, or BD...
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Elements of geometry, with ... trigonometry

André Darré - 1872
...intersection of the diagonals, are equivalent. 3. Equivalent triangles or parallelograms on the same base and on the same side of it are between the same parallels. 4. If through any point in the diagonal of a parallelogram lines are drawn parallel to the sides, the...
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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 261 pages
...also equal (by Ax. 7). PROPOSITION XXXIX. THEOREM. Equal triangles (BAC and BDC) on the same base, and on the same side of it, are between the same parallels. For if AD be not parallel to BC, draw through the point A the right line AF parallel to BC, cutting...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...same base, and upon the same side of it, are between the same parallels. Let the equal A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then trntst AD be II to BC. For if not, through A draw AO II to BC, so as to meet BD, or BD...
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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873
...Therefore the triangles are equal, by Ax. 1. Proposition 39. — Theorem. Equal triangles on the same base and on the same side of it are between the same parallels. If ABC = DBC, AD is parallel to BC. If not, let DE be parallel to BC, and let it cut AC, or AC produced,...
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Pure mathematics, Volume 1

Edward Atkins - 1874
...DEF. Therefore, triangles, <fec. QED Proposition 89. — Theorem. Equal triangles upon the same base, and on the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base . BC, and on the same side of it ; They shall...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...on the other side of the base. QED Cor. — Hence it follows that if two isosceles triangles stand on the same base BC, and on the same side of it, the one triangle must be entirely within the other. For if not, let them stand as in the figure. Then...
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