 | Isaac Todhunter - 1867 - 426 pages
...&c. QED Corollary. Hence every equiangular triangle is also equilateral. PROPOSITION 7. THEOREM. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise... | |
 | 1867 - 224 pages
...magnitudes said to coincide? What name is given to a triangle which has three unequal sides ? 2. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise... | |
 | Robert Potts - 1868 - 434 pages
...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... | |
 | Euclides - 1870 - 270 pages
...PROP. 7. — THEOR. Upon the same base and upon the same side of it there cannot be two triangles t/iat have their sides, which are terminated in one extremity...the base, equal to one another, and likewise those equal which are terminated in the other extremity. CONS. — Pst. 1. A st. line may be drawn from one... | |
 | Euclides - 1871 - 136 pages
...may be shewn that AB is not less than AC ; .: AB=AC. QED NOTE XIII. Euclid-s Prop. VII. of Book I. Upon the same base and on the same side of it, there...their sides which are terminated in one extremity qf the base equal to one another, and their sides which are terminated in the other extremity of the... | |
 | Henry William Watson - 1871 - 320 pages
...equal to AC, and EB + ED is equal to DB, therefore AC + DB is greater than AB + DC. PROPOSITION 4. Upon the same base and on the same side of it there cannot be two triangles having the two sides terminated in one extremity of the base equal to each other, and at the same time... | |
 | Euclid, Charles Peter Mason - 1872 - 216 pages
...&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 pages
...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 - 586 pages
...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 pages
...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... | |
| |
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. 
