 | Euclid, Charles Peter Mason - 1872 - 216 pàgines
...&c.) Cor. It follows from this that all the sides of an equi-angular A are equal. PROPOSITION VII. Upon the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated in the one extremity of the base equal to one another, and... | |
 | Euclides, James Hamblin Smith - 1872 - 376 pàgines
...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.... | |
 | Henry Major - 1873 - 588 pàgines
...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... | |
 | Lewis Sergeant - 1873 - 182 pàgines
...Hence it follows that an equiangular triangle is also equilateral. Proposition 13. — Theorem. On the same base, and on the same side of it, there cannot be two triangles having tlie sides terminated by one extremity of the base equal, and also the sides terminated by the... | |
 | Euclides - 1874 - 342 pàgines
...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... | |
 | Henry Evers - 1874 - 216 pàgines
...geometric figure that cannot alter its form without altering the length of its sides. It is Euclid I., 7. " Upon the same base, and on the same side of it, there cannot be two triangles which have their two sides terminated in one extremity on the base equal, and likewise those terminated... | |
 | Euclides - 1874 - 120 pàgines
...aho bisects the angle A and OA, BO and CO are all equal to one another. PROPOSITION 7. THEOREM. On the same base, and on the same side of it, there cannot be two triangles which have their sides which are terminated in one extremity of the base, equal to one another, and... | |
 | Edward Atkins - 1874 - 426 pàgines
...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,... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pàgines
...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,... | |
 | Richard Wormell - 1876 - 268 pàgines
...line. .. 28 3. From the greater of two given straight lines to cut off a part equal to the less. 28 7. 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 another, and likewise those which are terminated... | |
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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... 
