 | Euclides - 1840 - 192 σελίδες
...— 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 σελίδες
...two angles, &c. QED COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on 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 σελίδες
...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... | |
 | John Playfair - 1842 - 332 σελίδες
...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... | |
 | William Chambers, Robert Chambers - 1842 - 938 σελίδες
...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... | |
 | Euclides - 1842 - 316 σελίδες
...if two angles, &c. QED COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. UPON the same base, and on 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... | |
 | John Playfair - 1844 - 338 σελίδες
...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... | |
 | 1844 - 456 σελίδες
...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 σελίδες
...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 σελίδες
...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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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, equal to one another. 
