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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 Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 sider
...different situation as EG, FG; then, upon the same base EF, and upon 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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Chambers's information for the people, ed. by W. and R. Chambers, Volum 2

Chambers W. and R., ltd - 1842 - 744 sider
...logicians call • dilemma. It is stated in the proposition that, upon the same base, and ou the same side of it, there cannot be two triangles that have their...another, and likewise those which are terminated in the otlu-r extremity equal to one another. This is proved by examining separately every possible position...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 sider
...FG ; then, upon the same base EF, and upon the same side of it, there can be two triangles EDF.EGF, that have their sides which are terminated in one...extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible (7. 1.) ; therefore, if the...
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Chambers's Information for the People, Volum 2

William Chambers, Robert Chambers - 1842 - 938 sider
...It is stated in the proposition that, upon the am« base, and on the same side of it, there cantol be two triangles that have their sides which are terminated in one extremity of the base equal to one uotber, and likewise those which are terminated in tbeodwrntremiry equal to one another. This is proved...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 sider
...EG, FG, then, upon the same base EF, and upon the same side of it, there can be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity : But this is impossible (7. 1.); therefore, if the base...
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Report to the Trustees of the Dick Bequest for the Benefit of the ..., Volum 2

1844 - 456 sider
...upon the same base, and on the same side of it, there cannot be two triangles which have the sides terminated in one extremity of the base equal to one...those which are terminated in the other extremity equal. 2. Upon a given straight lino, to describe a segment of a circle which shall contain an angle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1844 - 338 sider
...then, upon the same base EF, and upon the same side of it, there can be two triangles EDF, EGF.that have their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity ; but this is impossible (7. 1.); therefore, if the base...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 218 sider
...different situation as EG, FG, then upon the same base EF, and upon 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 impossiblef; therefore, * 7. i. if the base...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 sider
...as EG, FG: 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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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclides, James Thomson - 1845 - 382 sider
...FG ; then, upon the same base EF, and upon the same side of it, there would be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise their sides terminated in the other extremity; but (I. 7) this is impossible: therefore, if the base...
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