 | Euclides - 1864 - 448 pages
...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 ; (I. 39.) therefore DE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III.... | |
 | Euclides - 1865 - 402 pages
...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 - Euclid's Elements - 1867 - 424 pages
...[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 - Euclid's Elements - 1867 - 426 pages
...[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.... | |
 | Robert Potts - 1868 - 434 pages
...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.... | |
 | Euclid - 1868 - 138 pages
...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.—... | |
 | Henry William Watson - Geometry - 1871 - 320 pages
...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 pages
...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 - Geometry - 1872 - 284 pages
...AD is parallel to BC. PROPOSITION XL. THEOREM, Equal triangles (BAG and GDH) on equal bases, and at the same side of it, are between the same parallels. For if AD be not parallel to BH draw through Athe right line AF, p rallel A to BH, cutting one of the sides GD of the triangle GDH,... | |
 | André Darré - 1872 - 226 pages
...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... | |
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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. 
