| Euclides - 1842 - 316 pages
...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 - Euclid's Elements - 1844 - 338 pages
...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... | |
| Church schools - 1844 - 456 pages
...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 - Geometry - 1845 - 218 pages
...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 pages
...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... | |
| Euclides, James Thomson - Geometry - 1845 - 382 pages
...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 - Geodesy - 1846 - 368 pages
...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 - Euclid's Elements - 1846 - 334 pages
...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... | |
| Euclides - 1846 - 292 pages
...If two angles %c. QED COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOK. **Upon the same base, and on the same side of it, there cannot be two triangles** which have their sides terminated in one extremity of the base equal to one another, and also those... | |
| Euclides - 1847 - 128 pages
...subtraction, AB = AC. Wherefore, if, when two sides of a A &c. — Q, ED PROP. VII. THEOR. GEN. ENUN. — **Upon the same base, and on the same side of it, there...those which are terminated in the other extremity.** PART. ENUN. — Let the two AS ACB, ADB be upon the same base AB, and the same side of it, and let... | |
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