| 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.—... | |
| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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... | |
| 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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