 | 1836 - 488 σελίδες
...equal to one another, the sides which subtend, or are opposite to them, are also equal to one another. VII. Upon the same base, and on the same side of it,...those which are terminated in the other extremity, equal to one another. VIII. If two triangles have two sides of the one equal two sides of the other,... | |
 | John Playfair - 1836 - 488 σελίδες
...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...be two triangles, that have their sides which are terminal ed in one extremity of the base equal to one another, and likewise those which are terminated... | |
 | Euclides - 1837 - 112 σελίδες
...2. that .'. Aflisnot =/= AC, ie, that AB = AC. PROPOSITION VII. (Argument ad Absurdum.) Theorem. On the same base, and on the same side of it, there cannot be two triangles that have their sides terminated in one extremity of the base equal to each other, and likewise those terminated in the other... | |
 | John Playfair - 1837 - 332 σελίδες
...then, upon the same base EF, and upon the same side of it, there can be two triangles EOF, 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... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...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 * Or, if the three aides of one triangle be equal to the three sides of another,... | |
 | Andrew Bell - 1837 - 290 σελίδες
...equal to it. COR. — Hence every equiangular triangle is also equilateral. PROPOSITION VII. THEOREM. Upon the same base, and on the same side of it, there cannot he two triangles that have their sides which are terminated in one extremity of the base equal to one... | |
 | Robert Simson - 1838 - 434 σελίδες
...in which the vertex of one triangle is upon a side of the other, needs no demonstration. Therefore upon the same base, and on the same side of it, there...those which are terminated in the other extremity. QED PROP. VIII. THEOR. IF two triangles have two sides of the one equal to two sides of the other,... | |
 | Euclides - 1838 - 264 σελίδες
...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; *7' a- therefore, if the base... | |
 | Great Britain. Committee on Education - 1853 - 1218 σελίδες
...ability, will suffice for the highest class of certificates. Section 1. 1. Upon the same base and upon the same side of it there cannot be two triangles...one another, and likewise those which are terminated at the other extremity. 2. The greater side of every triangle is opposite to the greater angle. 3.... | |
 | Euclides - 1840 - 82 σελίδες
...them are also equal. COR.—Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. On the same base, and on the same side of it, there cannot be two triangles having their conterminous sides at both extremities of the base, equal to each other. PROP. VIII. THEOR.... | |
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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. 
