 | Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...precaution is not taken, and give a proof in this case. Section 2. 1. Equal triangles on the same base, and on the same side of it, are between the same parallels. 2. If the square described upon one of the sides of a triangle be equal to the squares described upon... | |
 | 1856 - 428 pages
...figure, etc. QEBf PROPOSITION XL. THEOREM. Equal triangles upon equal bases in the same straight line, and on the same side of it, are between the same parallels. In fig. 40, let the equal triangles ABC and о в F be upon equal bases в с and в F, in the same... | |
 | W. Davis Haskoll - Civil engineering - 1858 - 422 pages
...two triangles of equal altitude, and on equal bases, are equal. Equal triangles upon the same base, and on the same side of it, are between the same parallels. If any two sides of any triangle are intersected by a line parallel to the third side, the intercepted... | |
 | Euclid - 1859 - 150 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—... | |
 | Royal college of surgeons of England - 1860 - 332 pages
...lines shall be parallel to one another. 5. Equal triangles on equal hases, in the same straight line and on the same side of it, are between the same parallels. 6. If a straight line be divided into any two parts, the squares of the whole line and one of the parts... | |
 | Euclides - 1861 - 464 pages
...us from any . in a side of а Д to divide it into two eq. parts. 39. 120. Eq. Д8 on the same base and on the same side of it are between the same parallels. The loci of the vertices of eq. Дз on the same base, form a st.linc 40. 121. Eq. дз on eq. bases... | |
 | Euclides - 1862 - 172 pages
...same are equal to one another,' (ax 7.) PROP. XXXIX.— THEOREM. Equal triangles upon the same base and on the same side of it, are between the same parallels. (References — Prop. i. 31,37; ax. !._) Let the equal triangles ABC, DEC, be upon the same base BC,... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...greater than the base of the other. 8. Equal triangles, on equal bases, in the same straight line, and on the same side of it, are between the same parallels. 9. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal... | |
 | Euclides - 1864 - 448 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.... | |
 | Euclides - 1865 - 402 pages
...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.... | |
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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. 
