 | Sir J. Butler Williams - 1846 - 368 pagina’s
...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 cannot be two triangles that have their sides which are terminated at one extremity of the base equal to one another, and likewise... | |
 | Euclid, John Playfair - 1846 - 334 pagina’s
...equal to that of the triangle (4. 1.) ACB, the less to the greater ; which is absurd. Therefore, AB is not unequal to AC, that is, it is equal to it. COR. Hence every equiangular triangle is also equilateral. PR0B. VII. THEOR. •» Upon the same base,... | |
 | Euclides - 1847 - 128 pagina’s
...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 cannot be two triangles that have their sides, which are terminated in one extremity of the base, equal to one another, and... | |
 | Euclides - 1848 - 52 pagina’s
...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 cannot be two triangles that have their sides which are terminated in one extremity of the base, equal to one another, and... | |
 | Euclid, Thomas Tate - 1849 - 120 pagina’s
...triangle DBC is equal to the triangle (i. 4.) ACB, the less to the greater; which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it....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... | |
 | Elias Loomis - 1849 - 252 pagina’s
...triangle DBC is equal to the triangle ACB (Prop. VI.), the less to the greater, which is absurd. Hence AB is not unequal to AC, that is, it is equal to it. Therefore, if two angles, &c. Cor. Hence, every equiangular triangle is also equilateral. PROPOSITION... | |
 | Great Britain. Committee on Education - 1850 - 790 pagina’s
...rule for determining the surface of a sphere. GEOMETRY. Section 1 . 1. Upon the same base, and upon the same side of it, there cannot be two triangles having their two sides terminated at one extremity of the base equal, and likewise their two sides terminated at... | |
 | Sir Henry Edward Landor Thuillier - 1851 - 826 pagina’s
...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 cannot be two triangles that have their sides, which are terminated at one extremity of the base, equal to one another, and... | |
 | 582 pagina’s
...3i per cents, at 97, and what change in income rould be thus effected ? EUCLID. « SECTION I. '• Upon the same base and on the same side of it, there cannot be two "angles, which have their sides which arc terminated in one extremity of the 'ase cqual to one another,... | |
 | Euclides - 1852 - 152 pagina’s
...triangle DBC is equal to the triangle b ACB, the less to the greater; which is absurd. Therefore AB is not unequal to AC ; that is, it is equal to it. Wherefore, if two angles, &c. QED COK. Hence every equiangular triangle is also equilateral. [To exhibit the truth of this, draw first... | |
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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... 
