 | Robert Simson - 1806 - 546 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»; therefore, if the base BC... | |
 | John Playfair - 1806 - 320 σελίδες
...FG; 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 Book I. another, and likewise their sides terminated in the other \^f>fn^ extremity : but this is impossible*... | |
 | Euclid - 1810 - 554 σελίδες
...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 that have their sides see which are terminated in one extremity of the base equal to one another, and likewise those which... | |
 | John Mason Good - 1813 - 722 σελίδες
...which subtend, or arc. opposite to» the equal angles, shall be equal to one another. Prop. VII. Theor. Upon the same base, and on the same side of it, there...those which are terminated in the other extremity. Prop. VIII. Theor. If two triangles have two sides of the one equal to two sidfs of the other, each... | |
 | Charles Butler - 1814 - 528 σελίδες
..." for if -4EB do not coincide with CFD, it must fall otherwise (as in the figure to prop. 23.) then upon the same base, and on the same side of it, there will be two similar segments of circles not coinciding with one another, but this has been shewn (in... | |
 | Euclides - 1816 - 588 σελίδες
...• ent 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*; • 71 1. therefore, if the... | |
 | John Playfair - 1819 - 350 σελίδες
...&c. Q, ED 33 " " " ~ 0 COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the same base, and on the same side of it, there...those which are terminated in the other extremity, equal to one another. Let there be two triangles ACB, ADB, upon the same base AB, and upon the same... | |
 | John Playfair - 1819 - 354 σελίδες
...two angles, &c. QED II C COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the. same base, and on the same side of it, there caitnot be two triangles, that have their sides which are terminated in one extremity of the base equal... | |
 | Euclid, Robert Simson - 1821 - 514 σελίδες
...triangle is upon a side of the other, needs no demonstration. "** Therefore upon the same base, and^on the same side of it, there cannot be two triangles...one another, and likewise those which are terminated in'the other extremity: QED PROP. VIII. THEOR. IF two triangles have two sides of the one equal to... | |
 | Euclides - 1821 - 294 σελίδες
...every equiangular triangle is equilateral ; vide, Elrington. PROP. 7. THEOR. i On the same right line and on the same side of it there cannot be two triangles formed whose conterminous sides are equal. If it be possible that there can, 1st, let the vertex of... | |
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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. 
