 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...is equal to that of the triangle (4. l.)ACB,the less to the water; •whieh is absurd. Therefore, AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, See. QED B CKR'. Henee every equiangular triangle is also equilateral. 4 PROP. VII, THEOR. Upon the... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...further from the straight line AB, and then comes nearer to it, which is also impossible : therefore FE is not unequal to AC, that is, it is equal to it. PROP. II. If two equal straight lines AC, BD be each at right angles to the same straight line AB ;... | |
 | 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 cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise... | |
 | 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 cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise... | |
 | Euclid, Robert Simson - Geometry - 1829 - 548 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....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... | |
 | John Playfair - Euclid's Elements - 1832 - 358 pages
...DBCisequal 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....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... | |
 | John Playfair - Euclid's Elements - 1833 - 346 pages
...AB is not unequal to AC, that is, it is equal to it. Wherefore, if two angles, &c. QED 33 . C COE. 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... | |
 | 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 that have their sides which are terminated in one extremity of it equal to one another, and also those... | |
 | Robert Simson - Trigonometry - 1835 - 544 pages
...triangle DBC is equal to the triangleb ACB, the less to the greater; which is absurd. Therefore AB is not unequal to AC, that is, it is equal to it....equiangular triangle is also equilateral. PROP. VII. THEOR. See N. Upon the same base, and on the same side of it, there cannot be two triangles that have their... | |
 | Euclid - 1835 - 540 pages
...farther from the straight line AB, and then comes nearer to it; which is also impossible. Therefore FE is not unequal to AC, that is, it is equal to it. PROP. II. IF two equal straight lines, AC, BD le each at right angles to the same straiglit line AB... | |
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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... 
