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" Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity. "
The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose - Page 11
by Euclides - 1853
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877 - 72 pages
...have a different situation, as EG, GF, Then upon the same base, and on the same side of it, there will be two triangles, which have their sides terminated in one extremity of the base equal to one another, and likewise their sides, which are terminated in the other extremity. But this is...
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Euclid, book i., propositions i. to xxvi., with exercises and alternative ...

Euclides - 1877 - 58 pages
...CA do not coincide with the sides ED, FD, they wil have a different situation as EG, FG : but then on the same base and on the same side of it there will be two triangles having their sides which are terminated in the one extremity of the base equal...
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An introduction to the Elements of Euclid, being a familiar explanation of ...

Stephen Thomas Hawtrey - 1878 - 202 pages
...method, with the aid of the following explanation. Euclid proves first, in the seventh Proposition, that on the same base and on the same side of it there cannot be two triangles, having the two sides ending in one extremity of the base equal to each other, and likewise the two...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879 - 428 pages
...etc. QED COR. Hence every equiangular triangle is also equilateral. Proposition VII. Theorem. Upon the same base, and on the same side of it, there cannot be two triangles which have their sides that are terminated in one extremity of the base equal to one another, and also those that are terminated...
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Erchomenon, or, The republic of materialism. By ****[H.C.M. Watson].

Henry Crocker M. Watson - Utopias - 1879 - 280 pages
...MAESTON, SBAKLB, & RIVINGTON, CROWN BUILDINGS, 188, FLEET STREET. 1879. [All rights reserved. ] . " Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and...
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A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - Geometry - 1879 - 44 pages
...What proposition is the converse of this. Show that every equiangular triangle is equilateral. 7. Upon the same base and on the same side of it there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879 - 94 pages
...EUCLID. \Capitalletters, and not numbers, must be used in Hie diagrams .\ 1. On the same straight line, and on the same side of it, there cannot be two triangles which have there sides terminated in one extremity of the base equal to one another, and likewise their sides...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879 - 146 pages
...sides BA, AC do not coincide with the sides ED, DF, but have a different situation as EG, FG ; Then, on the same base and on the same side of it there can be two As which have their sides which are terminated at one extremity of the base equal to one...
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Ten years' Queen's scholarship questions, 1870-9, with answers to arithmetic ...

Education Ministry of - 1880 - 238 pages
...be used in the diagrams. Not more than ten questions to bo answered. 1. On the same straight line, and on the same side of it, there cannot be two triangles...sides terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity. 2. Show how to bisect...
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First principles of Euclid: an introduction to the study of the first book ...

T S. Taylor - 1880 - 152 pages
...THEOREM (Euclid I. 7). Assumed here as an axiom and explained. Proved on page 96. General Enunciation. On the same base, and on the same side of it, there cannot be two triangles having the two sides terminated in one extremity of the base equal, and likewise those terminated in...
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