| Euclides - 1871
...are taken such that BD = AE. Shew that the triangles CBD, ABE are equal. PROPOSITION XXXIX. THEOREM. **Equal triangles upon the same base, and upon the same side of it, are between the same parallels.** a Let the equal A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then must... | |
| Henry William Watson - Geometry - 1871 - 285 pages
...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 same parallels.** DEFINITIONS. 49. — If a rectangle be constructed having its adjacent sides respectively equal to... | |
| Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...Z>, Enre taken such that BD = AE. Shew that 'riangles CBD, ABE are equal. PROPOSITION XXXIX. THEOREM. **Equal triangles upon the same base, and upon the same...it, are between the same parallels. Let the equal** A s ABC, DBC be on the same base BC, and on the same side of it. Join AD. Then trntst AD be II to BC.... | |
| Euclid, Charles Peter MASON - Geometry - 1872
...parallel to the base upon which they stand.* * This proposition is generally stated thus: — "Equal As **upon the same base, and upon the same side of it, are between the same parallels."** The meaning of this is just what is stated above, but is less obvious to the beginner. For the construction... | |
| Euclides - 1874
...equal to the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION 39. — Theorem. **Equal triangles upon the same base and upon the same...upon the same base BC, and upon, the same side of it.** Then the triangles ABC, DBC shall be between the same parallels. Construction. Join AD ; then AD shall... | |
| Euclides - 1874
...between ike same parallels. * Let the equal triangles ABC, DBC be on the I • same base BC, and on **the same side of it : they shall be between the same parallels.** Q Join AD. AD shall be AK-- — 7\D «• parallel to BC. For if it is not, through A draw AE parallel... | |
| Edward Atkins - 1874
...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 be between the same parallels.** CONSTRUCTION. — Join AD ; AD shall be parallel to BC. - For if it is not, through A draw AE v°se-... | |
| Edward Atkins - 1876 - 119 pages
...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....equal triangles ABC, DBC be upon the same base BC, and** on the same side of it ; They shall be between the same parallels. CONSTRUCTION. — Join AD ; AD shall... | |
| Robert Potts - Geometry, Plane - 1876 - 403 pages
...THEOREM. Equal trianglei upon the tame base and upon the same tide of it, are between the tame parallel*. **Let the equal triangles ABC, DBC be upon the same base BC and upon the same side of it.** Then the triangles ABC, DBC shall be between the same parallels. AD Join AD; then AD shall be parallel... | |
| Henry Major - 1876
...lines drawn from the vertex, one bisecting the vertical angle, the other perpendicular to the base. 2. **Equal triangles upon the same base and upon the same side of it are between the same parallels.** ., Point out where the demonstration begins. Algebra.— 1. Simplify a — (&— c) — |6— (a—... | |
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