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" DE : but equal triangles on the same base and on the same side of it, are between the same parallels ; (i. "
The First Six Books with Notes - Page 25
by Euclid - 1822 - 179 pages
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...triangles are on the same base DE and on the same side of it ; 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 3. THEOREM....
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Manual of Euclid: Books IV, V, VI.

Euclid - 1868 - 138 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 - 434 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 - 320 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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Euclid's Elements of Geometry

Euclid - Geometry - 1872 - 284 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 the side...
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Elements of geometry, with ... trigonometry

André Darré - 1872 - 226 pages
...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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Elementary Mathematics: Embracing Arithmetic Geometry, and Algebra

Lewis Sergeant - 1873 - 182 pages
...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 - 426 pages
...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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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 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 3. DE is parallel to BC. WTierefore, if a straight line, &c. QED PROPOSITION 3.—...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 pages
...DEF. Therefore, triangles, &c. QED Proposition 39. — 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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