 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...join AE, BD intersecting at P ; shew that the angle APE is constant. 520. If any number of triangles on the same base BC, and on the same side of it have their vertical angles equal, and perpendiculars, intersecting at D, be drawn from B and C on the... | |
 | 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.—... | |
 | 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.... | |
 | 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... | |
 | Euclides - 1871 - 136 pages
...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 - 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... | |
 | 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... | |
 | Euclides, James Hamblin Smith - Geometry - 1872 - 376 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 - 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,... | |
 | 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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Equal triangles on the same base, and on the same side of it, are between the same parallels. 
