 | Euclides - 1842 - 316 sider
...DBC is equal (4. 1.) to the triangle ACB, the less to the greater; which is absurd. Therefore A в is not unequal to AC, that is, it is equal to it....the same side of it, there cannot be two triangles having their sides which are terminated in one extremity of the base equal to one another, and likewise... | |
 | Chambers W. and R., ltd - 1842 - 744 sider
...which 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...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... | |
 | 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... | |
 | 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... | |
 | 1844 - 456 sider
...of another, of which the solidity is three times that of the former ; 1841. GEOMETRY. 1 . Prove that 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 another, and likewise those... | |
 | 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... | |
 | 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... | |
 | Euclid, 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... | |
 | Sir J. Butler Williams - 1846 - 368 sider
...the triangle possesses this property is evident from the theorem, (Euclid, 7, I.) which proves that, "Upon the same base, and on the same side of it, there...triangles that have their sides which are terminated at one extremity of the base equal to one another, and likewise those which are terminated in the other... | |
 | Euclid, John Playfair - 1846 - 334 sider
...FG ; then, upon the same base EF, and upon the same side of it, there can he 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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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... 
