| Robert Simson - Trigonometry - 1806 - 546 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 - Euclid's Elements - 1806 - 320 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 - Geometry - 1810 - 554 pages
...Therefore AB is not D unequal to AC, that is, it is equal to it. J — Wherefore, if two angles, &c. QED **CoR. Hence every equiangular triangle is also equilateral....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 - 714 pages
...the sides also 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...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... | |
| Euclides - 1814 - 560 pages
...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...those which are terminated in the other extremity.** If it be possible, let there be two triangles ACB, ADB, upon the same base AB, and upon the same side... | |
| Charles Butler - Mathematics - 1814 - 528 pages
..." 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 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 - 354 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 another, and likewise** their sides terminated in the other extremity ; but this is impossible (7. 1.) ; therefore, if the... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 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...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 pages
...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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