| Richard Wormell - 1876
...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... | |
| Edward Atkins - 1877
...Therefore, triangles, &c. QED Proposition 39. — Theorem. Equal triangles upon the same base, and on tJie **same side of it, are between the same parallels. Let...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... | |
| Elias Loomis - Geometry - 1877 - 443 pages
...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... | |
| Moffatt and Paige - 1879
...equal to the triangle DE F. Therefore, triangles upon equal bases, etc. QED Proposition XXXIX. 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. Join AD ; then AD shall be parallel... | |
| W J. Dickinson - Geometry - 1879 - 36 pages
...on 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... | |
| Euclides - 1879
...&c. QED PROPOSITION XL. THEOREM. Equal triangles, on equal bases in the same straight line, and on **the same side of it, are between the same parallels. Let the** = As ABC, DEF be on == bases EC, EF, in the same straight line BF, and on the same side of it. Then... | |
| 1880
...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. — i. Simplify — a — (bc)- {b-(ac}} — [a—... | |
| 1880 - 144 pages
...lines, make the alternate angles equal to each other ; the two straight lines shall.be parallel. 5. **Equal triangles upon the same base and upon the same side of it, are between the same parallels.** 6. If the square described upon one of the sides of a triangle, be equal to the squares described upon... | |
| Pupil teachers - 1880
...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... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...triangles &c. QED PROPOSITION 40. THEOREM. Equal triangles, on equalbases,in the same straight line, and on **the same side of it, are between the same parallels. Let the equal triangles ABC,** DEF be on equal bases BC, EF, in the same straight line BF, and on the same side of it : they shall... | |
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