 | Lewis Sergeant - 1873 - 182 pages
...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,... | |
 | Euclides - 1874 - 342 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 3. DE is parallel to BC. WTierefore, if a straight line, &c. QED PROPOSITION 3.—... | |
 | Edward Atkins - 1874 - 426 pages
...the triangle 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... | |
 | Edward Atkins - 1874 - 428 pages
...the triangle DEF. Therefore, triangles, &c. QED Proposition 39.— Theorem. Equal triangles upon tlie 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... | |
 | Robert Potts - Geometry - 1876 - 446 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 1iE is parallel to BC. Wherefore, if a straight line, &c. QED PROPOSITION III... | |
 | Edward Atkins - 1876 - 130 pages
...to the triangle DEF. Therefore, triangles, &c. QED Proposition 39. — 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... | |
 | Education Department,London - 1876 - 1010 pages
...point P within the triangle, such that the triangles РЛВ, PBC, PCA may be equal. 2. Equal triangles on the same base and on the same side of it are beUveen the same parallels. 3. The square on the sum of two lines is equal to the square on their difference... | |
 | Edward Harri Mathews - 1879 - 94 pages
...right-angled triangle, is equidistant from the two sides containing the right angle. 2. Equal triangles on the same base, and on the same side of it, are between the same parallels. The angular points of one triangle lie on the sides of another ; if the latter triangle be thus divided... | |
 | Euclides - 1879 - 146 pages
...of it. If CD meets AB in E, then CE, ED are also equal. PROPOSITION XXXIX. THEOREM. Equal triangles on the same base and on the same side of it are between the same parallels. Let the equal As ABC, DBC be on the same base BC, and on the same side of it. Then the As ABC, DBC... | |
 | Isaac Sharpless - Geometry - 1879 - 282 pages
...which the triangles will be halves, and apply Prop. 34.) Proposition 37. Theorem.—Equal triangles on the same base and on the same side of it are between the same parallels. Let ABC, DBC be equal triangles on the same base BC; they will be between the same parallels. For if... | |
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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. 
