| Euclides - 1845 - 544 pages
...angle ABC greater than the angle ACB. Therefore the greater side, &c. QED PROPOSITION XIX. THEOREM. The **greater angle of every triangle is subtended by the...which the angle ABC is greater than the angle BCA.** Then the side AC shall be greater than the side AB. For, if AC be not greater than AB, AC must either... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...Therefore, if two sides, &c. PROP. XIX. THEOR. — If two angles of a triangle be unequal, the greater angle **has the greater side opposite to it. Let ABC 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... | |
| Euclides - 1846 - 292 pages
...the angle ABC greater than the angle ACB. Wherefore, The greater side %c. QED PROP. XIX. THEOR. The **greater angle of every triangle is subtended by the...triangle, of which the angle ABC is greater than the angle** ACB : the side AC is also greater than the side AB. For, if it be not greater, it must either be equal... | |
| Great Britain. Admiralty - Geometry - 1846 - 130 pages
...ACB, much more is /_ ABC > L ACB. Therefore the greater side, &c. PROP. XVIII. THEOR. 19. lEu. The **greater angle of every triangle is subtended by the...greater side; or has the greater side opposite to it.** If ABC be a ^, of which L ABC > L BCA; then AOAB. BC For AC must be either >, =, or < AB. 1st. If AC... | |
| Euclides - 1847 - 128 pages
...ACB; and that as DC is > or < AC, the L BAC is > or < the / ABC. PROP. XIX. THEOR. GEN. ENUN. — The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** PART. ENUN. — Let ABC be a A, of which the Z ABC is > the Z ACB; then the side AC shall be > AB.... | |
| Euclides - 1848 - 52 pages
...THEOREM. The greater side of every triangle is opposite to the greater angle. PROP. XIX. THEOREM. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** PROP. XX. THEOREM. Any two sides of a triangle are together greater than the third side. PROP. XXI.... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...is the angle ABC greater than ACB. Therefore the greater side, etc. QED PROPOSITION XIX. THEOR. The **greater angle of every triangle is subtended by the...the angle BCA ; the side AC is likewise greater than** tie side AB. For, if it be not greater, AC must either be equal to AB or less than it; it is not equal,... | |
| Euclides - Geometry - 1853 - 334 pages
...then the side opposite to the greater angle shall be greater than the side opposite to the less angle. **Let ABC be a triangle, of which the angle ABC is greater than the angle BCA.** Then the side AC shall be greater than the side AB. For if it be not greater, AC A must either be equal... | |
| Euclides - Geometry - 1853 - 176 pages
...the angle abС than a С b. Therefore the greater side, <fee. QED PROPOSITION XIX. — THEOREM. The **greater angle of every triangle is subtended by the greater side, or** IMS tlie greater side opposite to it. LET abС be a triangle, of which the angle ab С is greater than... | |
| William Somerville Orr - Science - 1854 - 532 pages
...side, &c. QED PROPOSITION XIX.— THEOREM. The greater angle of every triangle (А В С) is stdtended **by the greater side, or has the greater side opposite to it. Let** the angle В be greater than C; then AC shall be greater thanAB. О For, if it be not greater, AC must... | |
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