 | 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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...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 triangles that have thtir sides, which are terminated in one extremity of the base, equal to another, and likewise those... | |
 | Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 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, 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 - American fiction - 1828 - 598 pages
...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... | |
 | Euclid, Robert Simson - Geometry - 1829 - 548 pages
...therefore the base DC is equal to the base AB, and the triangle DBC is equal to the triangle (4. 1.) ACB, the less to the greater; which is absurd. Therefore...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... | |
 | Thomas Perronet Thompson - Euclid's Elements - 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... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...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,... | |
 | Mathematics - 1836 - 488 pages
...one another, the sides which subtend, or are opposite to them, are also equal to one another. VII. Upon the same base, and on the same side of it, there...terminated in the other extremity, equal to one another. VIII. If two triangles have two sides of the one equal two sides of the other, each to each, and have... | |
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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... 
