 | John Playfair - 1837 - 332 sider
...then, upon the same base EF, and upon the same side of it, there can be two triangles EOF, 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... | |
 | Euclid, James Thomson - 1837 - 410 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 * Or, if the three aides of one triangle be equal to the three sides of another,... | |
 | Andrew Bell - 1837 - 290 sider
...equal to it. COR. — Hence every equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot he two triangles that have their sides which are terminated in one extremity of the base equal to one... | |
 | Robert Simson - 1838 - 434 sider
...Therefore AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles / &c. a ED *1) Cor. Hence every equiangular triangle is also equilateral....those which are terminated in the other extremity. * If it be possible, let there be two triangles ACB, ADB, upon the same base AB, and upon the same... | |
 | Euclides - 1838 - 264 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; *7' a- therefore, if the base... | |
 | Great Britain. Committee on Education - 1853 - 1218 sider
...ability, will suffice for the highest class of certificates. Section 1. 1. Upon the same base and upon the same side of it there cannot be two triangles...one another, and likewise those which are terminated at the other extremity. 2. The greater side of every triangle is opposite to the greater angle. 3.... | |
 | Euclides - 1840 - 82 sider
...them are also equal. COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base, and on the same side of it, there cannot be two triangles having their conterminous sides at both extremities of the base, equal to each other. PROP. VIII. THEOR.... | |
 | Euclides - 1840 - 192 sider
...— Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base (AB), and on the same side of it, there cannot be two triangles having their conterminous sides (AC and AD, BC and BD) at both extremities of the base, equal to each... | |
 | Euclides - 1841 - 378 sider
...AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. QED COR.—Hence every equiangular triangle is also equilateral. PROP....the same side of it, there cannot be two triangles thai have 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... | |
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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. 
