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" EQUAL triangles upon the same base, and upon the same side of it, are between the same parallels. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 40
by Euclides - 1841 - 351 pages
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Modern geometry [ed.] with an appendix by W.B. Jack

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...
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Elements of geometry, based on Euclid, book i

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...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

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...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

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...
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A complete set of male pupil teachers' examination questions in Euclid [book ...

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...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

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...
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Papers for teachers

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—...
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The student's guide to the University of Durham, with information respecting ...

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...
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The pupil teachers' handy mathematical and grammatical question-book, with key

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...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

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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