| Euclides - 1865 - 402 σελίδες
...BDE is equal 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 Kne, &c. QED PROP. m.— THEOREM.... | |
| Euclid, Isaac Todhunter - 1867 - 424 σελίδες
...[V. 9. And these 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.... | |
| Euclid, Isaac Todhunter - 1867 - 426 σελίδες
...[V. 9. And these 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.... | |
| Euclid - 1868 - 138 σελίδες
...triangle BDE is equal 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 σελίδες
...triangle BDEis equal 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 - 1871 - 320 σελίδες
...on the same 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... | |
| Dublin city, univ - 1871 - 366 σελίδες
...in every respect ? 2. Equal triangles, standing on equal bases, situated ?T? the same straight line, and on the same side of it, are between the same parallels ? 3. If a right line be divided, the sum of the squares of the \i hole line and of one segment is equal... | |
| Euclid - 1872 - 284 σελίδες
...Prop. 34), and therefore are 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... | |
| André Darré - 1872 - 226 σελίδες
...the point of 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... | |
| Lewis Sergeant - 1873 - 182 σελίδες
...Prop. 36. 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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