 | 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... | |
 | 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... | |
 | 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
...(ol)tothe angle BDC; but BCD has been proved to be greater than the. same BCD; 'which is impossible. The case in which the vertex of one triangle is upon...no demonstration. "** Therefore upon the same base, and^on the same side of it, there cannot be two triangles that have; their sides which are terminated... | |
 | 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... | |
 | Rev. John Allen - 1822 - 508 σελίδες
...it are equal, and therefore the sides opposite to them. PROP. VII. THEOR. Upon the same base (AB), and on the same side of it, there cannot be two triangles (ACB, ADB), whose conterminous sides are equal, (namely AC to AD, and BC to BD). For, if possible,... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...(3.1.) to angle BCD ; but BDC has been proved to be greater than the same BCD ; which is impossible. The case in which the vertex of one triangle is upon a side of the other, needs uo demonstration. Therefore, upon the same base, and on the same side of it, there cannot be two triangles,... | |
 | Euclid, John Playfair - 1826 - 326 σελίδες
...BCD; bnt BDC. has been proved to be greater than the same BCD; whieh is impossible. The ease in whieh the vertex of one triangle is upon a side of the other,...Therefore, upon the same base, and on the same side of it, thereeasnot be two triangles that have their sides whieh are terminated in one extremity of the base... | |
 | Robert Simson - 1827 - 546 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 can- See N. not be two triangles that have their sides which are terminated in one extremity of the... | |
 | Thomas Perronet Thompson - 1833 - 168 σελίδες
...CA, AB are all equal to one another. PROPOSITION VII. THEOREM. — Upon the same given straight line and on the same side of it, there cannot be two triangles...their sides which are terminated in one extremity of it equal to one another, and also those which are terminated in the other See Note. extremity. For... | |
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Therefore, 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 extretnity equal... 
