 | John Playfair - Euclid's Elements - 1833 - 346 pages
...much more is the angle ABC greater than ACB. Therefore the greater side, &c. QED PROP. XIX. THEOR. The greater angle of every triangle is subtended by...opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB. For, if it be... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...triangle &c. Which was to be demonstrated. PROPOSITION XIX. THEOREM. — The greater angle in any triangle has the greater side opposite to it, Let ABC be a triangle, of which the angle B is greater than the angle C. The side AC is greater than the side AB. For, if it be not greater, AC must either be... | |
 | Euclides - 1834 - 518 pages
...D. PROPOSITION XIX. THEOR. — The greater angle of every triangle is subtended by the greater tide, or has the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA : the side AC shall be greater than the side AB. For if it be not... | |
 | Euclid - 1835 - 540 pages
...much more is the angle ABC greater than ACB. Therefore, " the greater side," &c. QED PROP. XIX. THEOR. The greater angle of every triangle -is subtended...opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA; the side AC is likewise greater than the side AB. For, if it be... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB. PROP. XII. THEOR. The greater angle of every triangle is subtended by the greater side, or has the givater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle... | |
 | Mathematics - 1836 - 488 pages
...right angles. XVIII. The greater side of every triangle has the greater angle opposite to it. XIX. The greater angle of every triangle is subtended by...greater side, or has the greater side opposite to it. XX. Any two sides of a triangle are together greater than the third side. XXI. If from the ends of... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...angle ABD is likewise greater than the angle ACB ; wherefore the angle ABC is still greater than ACB. PROPOSITION XIX. THEOREM. The greater angle of every...opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA ; the side AC is like- -*• wise greater than the side AB. For,... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...greater than the angle ACB ; wherefore much more is the angle ABC greater than ACB PROP. XIX. THEOR. The greater angle of every triangle is subtended by...opposite to it. Let ABC be a triangle, of which the angle ABC is greater than the angle BCA ; the side AC is likewise greater than the side AB. For, if it be... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...ADB, 2. that Z ABD > Z ACS, 3. £Aa£ /. much more Z ^BC > Z PROPOSITION XIX. (Argument ad absurdum). Theorem. The greater angle of every triangle is subtended...greater side, or has the greater side opposite to it. Steps of the Demonstration. 1. Prove that AC cannot be = AB, 2. that AC cannot be < AB, 3. that :.... | |
 | Euclides - 1838 - 264 pages
...greater than ACB. Therefore the greater side, &c. QED PROP. XIX. THEOR. The greater angle of eeery triangle is subtended by the greater side, or has...opposite to it. Let ABC be a triangle of which the angle ABC w greater than the angle BCA: the side AC shall be greater than the side AB. For, if it be not... | |
| |
The greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. 
