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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 first three books of Euclid's Elements of geometry, with theorems and ... - Side 11
av Euclid, Thomas Tate - 1849 - 108 sider
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - 1872 - 216 sider
...that, on the same base, and on the same side of it, there can be two As, having the sides terminating in one extremity of the base equal to one another, and likewise those terminating in the other extremity of the base equal to one another. PROPOSITION VIII. If two triangles...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 376 sider
...position, as GE, GF, then upon the same base and upon the same side of it there can be two A s which have their sides which are terminated in one extremity of the base equal, and their sides which are terminated in the other extremity of the base also equal : which is impossible....
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873 - 580 sider
...a different situation as EG, FG, then upon the same base EF, and on the same side of it, there can be two triangles that have their sides which are terminated...extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible ; therefore, if the base BC...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 sider
...as EG, GF: Then, upon the same base, and upon the same side of it, there can be two triangles which have their sides which are terminated in one extremity...the base, equal to one another, and likewise those sides which are terminated in the other extremity ; but this is impossible (I. 7). Therefore If the...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 sider
...situation as EG, FG; then on the same base and on the same side of it there will be two triangles having their sides which are 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 impossible. [I. 7.] Therefore...
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Pure mathematics, Volum 1

Edward Atkins - 1874 - 426 sider
...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 impossible (I. 7). . BA, AC Therefore,...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1876 - 382 sider
...AB-AC. QED NOTE 13. Euclid's Proof of I. 7. Upon (he same base and on Hie so/me tide of it, tJie.rc cannot be two triangles that have their sides which...one extremity of the base equal to one another, and their sides which are terminated in the other extremity of the base equal also. If it be possible,...
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 268 sider
...Upon the same base and on the same side of it, there cannot be two triangles that have their sides terminated in one extremity of the base equal to one...those which are terminated in the other extremity, equal to one another. 17. Any two angles of a triangle are together less than two right angles. .....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 446 sider
...as EG, GF: then, upon the same base, and upon the same side of it, there can be two triangles which have their sides which are terminated in one extremity...the base, equal to one another, and likewise those sides which are terminated in the other extremity; but this is impossible. (1. 7.) Therefore, if the...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 130 sider
...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 impossible (I. 7), .". EA, AC...
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