 | Euclid, 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... | |
 | John Playfair - Euclid's Elements - 1847 - 340 pages
...is, it is equal to it. COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there...which are terminated in one extremity of the base equai to one another, and likewise those which are terminated in the other extremity, equal to one... | |
 | Euclides - 1848 - 52 pages
...equal to one another. COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOREM. Upon the same base, and on the same side of it, there...those which are terminated in the other extremity. PROP. VIII. THEOREM. If two triangles have two sides of the one equal to two sides of the other, each... | |
 | Euclid, Thomas Tate - 1849 - 120 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 impossible (i. 7.) ; therefore, if the base... | |
 | 1852 - 316 pages
...Taylor. EUCLID. DIVISION I. SECTION I. 1. Upon the same base and upon the same side of it there canuot be two triangles that have their sides which are terminated...one another, and likewise those which are terminated at the other extremity. 2. The greater side of every triangle is opposite the greater angle. 3. To... | |
 | Sir Henry Edward Landor Thuillier - Surveying - 1851 - 826 pages
...the triangle possesses this property is evident from the Theorem (Euclid 7. 1.) 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... | |
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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. 
