 | Rev. John Allen - 1822 - 508 σελίδες
...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 - 372 σελίδες
...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... | |
 | Euclid, John Playfair - 1826 - 326 σελίδες
...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 - 513 σελίδες
...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, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...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, there...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, Edward Everett, James Russell Lowell, Henry Cabot Lodge - 1828 - 598 σελίδες
...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, there...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 - 150 σελίδες
...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 σελίδες
...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 σελίδες
...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... | |
 | Robert Simson - 1835 - 513 σελίδες
...in which the vertex of one 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 trianyles that have tfieir sides which are terminated in one extremity of the base equal to one another,... | |
| |
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. 
