 | 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 - 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 - 1825 - 1058 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 - 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... | |
 | Robert Simson - 1827 - 546 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... | |
 | Jared Sparks, Henry Cabot Lodge, Edward Everett, James Russell Lowell - 1828 - 598 pages
...right angles, the lines AI, BD, produced, will meet.' The other is from Simson's Euclid, prop. 7, b. 1. 'Upon the same base and on the same side of it,...those which are terminated in the other extremity.' Now we presume there can be no doubt, which of these two methods is best adapted to the conception... | |
 | Jared Sparks, Henry Cabot Lodge, Edward Everett, James Russell Lowell - 1828 - 598 pages
...right angles, the lines AI, BD, produced, will meet.' The other is from Simson's Euclid, prop. 7, b. 1 . ' Upon the same base and on the same side of it,...those which are terminated in the other extremity.' Now we presume there can be no doubt, which of these two methods is best adapted to the conception... | |
 | Thomas Perronet Thompson - 1833 - 168 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... | |
 | Euclides - 1834 - 518 pages
...triangle is also equilateral. PROPOSITION VII. See N. THEOR. — Upon the same base, and on the mine side of it, there cannot be two triangles that have their sides which arc terminated in one extremity of the base, equal to one a not her, and likewise those which are terminated... | |
 | Euclid - 1835 - 540 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 imposa 7. 1. sible " ; therefore, if the... | |
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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, equal to one another. 
