| Euclid - Geometry - 1810 - 518 pages
...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 - Mathematics - 1814
..." 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 - 317 pages
...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 - Mathematics, Greek - 1821 - 516 pages
...(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
...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 - Astronomy - 1822 - 494 pages
...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 - Mathematics - 1825 - 372 pages
...(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,... | |
| John Playfair - Euclid's Elements - 1826 - 320 pages
...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 - Trigonometry - 1827 - 513 pages
...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 - Euclid's Elements - 1833 - 150 pages
...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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