| 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*... | |
| John Mason Good - 1813 - 714 pages
...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 - 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 - Circle-squaring - 1819 - 350 pages
...&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 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... | |
| 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... | |
| Rev. John Allen - Astronomy - 1822 - 508 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 - 1046 pages
...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...triangles, that have their sides which are terminated** >n one extremity of the base equal to one another, and likewise those which are terminated in the other... | |
| John Playfair - Circle-squaring - 1826 - 326 pages
...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 equal to one another, and likewise those** whieh are terminated iu the other extremity equal to one another, QED ~f PROP. VIII. THEOR. If two... | |
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