 | Euclides - 1861 - 464 pages
...Prop. also enables 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
...halves of the 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
...angles ; and the three interior angles of every triangle are together equal to two right angles. 6. Equal triangles on the same base, and on the same side of it, are between the same parallels. 7. If a straight line be divided into any two parts, the rectangles contained by the whole and each... | |
 | Euclides - 1863 - 122 pages
...Therefore the triangle BDE is equal to the triangle CDE (V. 9) ; and they are en the same base DE. But equal triangles on the same base and on the same side of it arj between the same parallels (I 20). Therefore DE is parallel to BC. Wherefore, if a straight line,... | |
 | Euclides - 1864 - 448 pages
...therefore the 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
...therefore the 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 Kne, &c. QED PROP. m.— THEOREM.... | |
 | Robert Potts - 1865 - 528 pages
...therefore the 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, axe between the same parallels : (i. 39.) therefore DE is parallel to B C. Wherefore, if a straight... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...is equal to three times the arc AE. 230. The straight lines which bisect the vertical angles of all triangles on the same base and on the same side of it, and having equal vertical angles, all intersect at the same point. 231. If two circles touch each other... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...is equal to three times the arc AE. 230. The straight lines which bisect the vertical angles of all triangles on the same base and on the same side of it, and having equal vertical angles, all intersect at the same point. 231. If two circles touch each other... | |
 | Robert Potts - 1868 - 434 pages
...therefore the 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.... | |
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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. 
