 | 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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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. 
