| 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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