 | Euclid - 1835 - 540 pages
...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 the...greater, AC must either be equal to AB, or less than it ; iris not equal, because then the angle ABC a 5. 1. would be equal * to the angle ACB; but it is not;... | |
 | Mathematics - 1836 - 472 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 the...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 - 240 pages
...than the angle ACB ; wherefore the angle ABC is still greater than ACB. PROPOSITION XIX. THEOREM. The greater angle of every triangle is subtended by the...ABC is greater than the angle BCA ; the side AC is like- -*• wise greater than the side AB. For, if it be not greater, AC must either be equal to AB,... | |
 | Euclid - Geometry - 1837 - 410 pages
...Let A BC be a triangle, of which the angle B is greater than C; the side AC is likewise greater than AB. For if it be not greater, AC must either be equal...AB, or less than it. It is not equal, because then (I. 5.) the angle B * Let the learner compare this proposition and the following with the 5th and 6th... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...ABD > Z ACS, 3. ŁAaŁ /. much more Z ^BC > Z PROPOSITION XIX. (Argument ad absurdum). Theorem. The greater angle of every triangle is subtended by the...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 :.... | |
 | Robert Simson - Geometry - 1838 - 434 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 the...than the side AB. For, if it be not greater, AC must A either be, equal to AB, or less than it ; it is not equal, because then the angle ABC would be equal... | |
 | 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...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 greater,... | |
 | Euclid - Geometry - 1838 - 478 pages
...more is the angle ABC greater than ACB. Therefore the greater side, &c. Q,. ED PROP. XIX. THEOR. THE greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it. For, if it be not greater, AC must either be, equal to AB, or less than it ; it is not equal, because... | |
 | Euclides - 1841 - 378 pages
...Therefore the greater side, &c. QED PROP. XIX. THEOR. greater than the angle BCA; the side AC shall be greater than the side AB. For, if it be not greater,...must either be equal to AB, or less than it; it is r.ot equal, because then the angle ABC would be equal* to the angle ACB; but it * 5. I. is not; therefore... | |
 | Chambers W. and R., ltd - 1842 - 744 pages
...that the greater angle of every triangle has the greater side opposite to it. In the annexed triangle, the angle ABC is greater than the angle BCA. The side AC, being opposite to the larger angle, is longer than the side AB, which is opposite to the smaller angle.... | |
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THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. 
