 | Euclid - Geometry - 1810 - 554 pages
...\i b4.i er: which is absurd. 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...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... | |
 | 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 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... | |
 | 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
...triangle DBC is equal to the triangle13 ACB, the less to the greater ; which is absurd. Therefore AB is not unequal to AC, that is. it is equal to it Wherefore,...THEOR. UPON the same base, and On the same side of S««.N. it, there cannot be two triarrgles that have their * sides which are terminated in one extremity... | |
 | John Playfair - 1819 - 354 pages
...equal to that of the triangle (4. 1.) ACB, the less to the greater ; which is absurd. Therefore, AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. QED II C COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon the. same base,... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...equal to that of the triangle (4. 1.) ACB, the less to the greater ; which is absurd. Therefore, AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. Q, ED 33 " " " ~ 0 COR. Hence every equiangular triangle is also equilateral. PROP. VII. THEOR. Upon... | |
 | Euclid, Robert Simson - Geometry - 1821 - 514 pages
...Therefore AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. Q,. E, D. BC COR. Hence every equiangular triangle is also equilateral,...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... | |
 | 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
...triangle DBC, is equal to the triangle (4.1.) ACB the less to the greater ; which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it....QED COR. Hence every equiangular triangle is also equal equilátera. Proposition Vll. Theorem. Upon the same base, and on the same side of it, there... | |
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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... 
