 | Robert Potts - 1860 - 380 σελίδες
...as EG, GF: 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. (l. 7.) Therefore, if the... | |
 | Euclides - 1860 - 288 σελίδες
...then, upon- the same base EF, and upon the -same side of it, there can be two triangles EDF and 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 (I. 7); therefore if the base... | |
 | Royal college of surgeons of England - 1860 - 332 σελίδες
...HEY. G. FBOST, MA 1. Give Euclid's definitions of the different kinds of three sided figures. 2. On 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... | |
 | Popular educator - 1860 - 536 σελίδες
...upon the same base E p, and upon the same side of it, there can be two triangles having their sides terminated in one extremity of the base, equal to one another, and likewise those terminated in the other extremity; but this, by the precedin-* proposition, is impossible. Wherefore,... | |
 | War office - 1861 - 714 σελίδες
...years at . per cent, per annum, simple interest. 10. Extract the square root of 13277-9529. Euclid. 1. Upon the same base, and on the same side of it there cannot be two triangles which have their sides which are terminated in one extremity of the base equal to one another, and... | |
 | Euclides - 1861 - 464 σελίδες
...similar segments of a circle, is the same in principle with the 7th of Book I., which says, that, " on 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, and likewise those terminated... | |
 | Euclides - 1862 - 172 σελίδες
...two angles, &c. QED Cor. Hence every equiangular triangle is also equilateral. PROP. VII.^ THEOREM. Upon the same base and on the same side of it, there...are terminated in one extremity of the base equal to each other, and likewise those which are terminated in the other extremity. (References — Prop. i.... | |
 | 1862 - 428 σελίδες
...the arc PQ, and upon the same side of it, there would be two spherical triangles having their sides terminated in one extremity of the base equal to one another and also those terminated in the other extremity. But if the elements LM, MN be in the same straight line,... | |
 | Euclides - 1862 - 140 σελίδες
...sides BA, AC, do not coincide with the sides ED, DF, but have a different situation, as EG, GF, 7. Then upon the same base, and on the same side of it, there will be two triangles, which have their sides terminated in one extremity of the base equal to one... | |
 | Euclides - 1863 - 74 σελίδες
...making an observation with a quadrant of altitude. PROP. 7. — THEOR. Upon the same base and upon the same side of it there cannot be two triangles...the base equal to one another, and likewise those equal which are terminated in the other extremity. CON.— Pst. 1, Pst. 2.— DEM —P. 6, Ax. 9. E.... | |
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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. 
