 | Henry William Watson - Geometry - 1871 - 320 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 - 376 pages
...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 side of 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... | |
 | Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...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... | |
 | Benjamin Greenleaf - Geometry - 1873 - 202 pages
...equilateral triangle, since its sides subtend ' EFA' m EXERCISES FOR ORIGINAL THOUGHT, ON REVIEW. 249. 1. Equivalent triangles upon the same base, and upon the same side of a straight line, are between the same parallels 2. The perimeter of an isosceles triangle is greater... | |
 | Euclides - 1874 - 342 pages
...the triangle DEF. Wherefore, triangles upon equal bases, &c. QED PROPOSITION 39. — Theorem. Equal triangles upon the same base and upon the same side of it, are between the same parallels. Let the equal triangles ABC, DBC be upon the same base BC, and upon, the same side of it. Then the... | |
 | Benjamin Greenleaf - Geometry - 1874 - 206 pages
...EFA, on the circumference (Theo. II. Bk. HI.). EXERCISES FOR ORIGINAL THOUGHT, ON REVIEW. 249. 1• Equivalent triangles upon the same base, and upon the same side of a straight line, are between the same parallels. 2. The perimeter of an isosceles triangle is greater... | |
 | Richard Wormell - 1876 - 268 pages
...parallel straight lines, towards the same parts, are also themselves equal and parallel. . . 59 39. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. .. .. .. .. .. .. 141 40. Equal triangles upon the same side of equal bases, that are in the same straight... | |
 | Henry Major - 1876 - 784 pages
...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—... | |
 | Elias Loomis - Conic sections - 1877 - 458 pages
...having a vertical angle equal to ACB. PROPOSITION V. 46. Required the locus of the vertices of all equivalent triangles upon the same base and upon the same. side of it. . . . Let AB be the given base ; let ABC be a triangle c P having the given area, and let it be situated... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...the same base and on opposite sides of it. If CD meets AB in E, then CE, ED are also equal. 39. Equal triangles upon the same base, and upon the same side of it, are between the same parallels. AB, CD are parallel straight lines ; AD, BC meet in E, and CD is produced to F, so that the triangles... | |
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Equal triangles upon the same base, and upon the same side of it, are between the same parallels. 
