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. Introduction and books 1,2 - Page 259by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...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 - Trigonometry - 1806 - 311 pages
...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, Robert Simson - 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... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...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...the base equal to one another, and likewise those** which are terminated in the other extremity. Prop. VIII. Theor. If two triangles have two sides of... | |
| Euclides - 1814
...equiangular triangle is also equilateral. PROP. VII. THEOR. UP0N the same base, and on the same side of 5 **it, there cannot be two triangles that have their...the base equal to one another, and likewise those** which are terminated in the other extremity. If it be possible, let there be two triangles ACB, ADB,... | |
| 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... | |
| Euclides - Geometry - 1816 - 528 pages
...• 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 - 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
...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...the base, equal to one another, and likewise those** which are terminated in'the other extremity: QED PROP. VIII. THEOR. IF two triangles have two sides... | |
| 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... | |
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