| Euclides - 1862
...greater than the side which is opposite to the less. (References— Prop. i. 5, 18.) Let ABC be any **triangle, of which the angle ABC is greater than the angle BCA.** Then the side AC shrill be greater than the side AB. For, if AC be not greater than AB, AC must either... | |
| Euclides - 1863
...and X greater than Y. much more is X greater than Z. PROP. 19. — THKOE. (Converse of the 18th.) The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** O DEM.— P. 5. P. 18. E. li Hyp. 21 Cone. In A ABC let £ ABC be > L ACB; then side AC is > side /... | |
| Euclides - 1864
...AB C greater than the angle ACB. Therefore the greater side, &c. QED PROPOSITION XIX. THEOREM. The **greater angle of every triangle is subtended by the...side, or, has the greater side opposite to it. Let** AB C be a triangle of which the angle ABC is greater than the angle BCA. Then the side AC shall be... | |
| Euclides - 1864
...QED PROPOSITION XIX. THEOREM. The greater angle of every triangle is subtended by the greater aide, **or, has the greater side opposite to it. Let ABC be a triangle of which the angle** ABCis greater than the angle BCA. Then the side AC shall be greater than the side AB. For, if AC be... | |
| Euclides - 1865
...3. The greater side of every triangle is opposite to the greater angle . . . . . . . . I. 18. 4. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it** * . . . L 19. 5. Any two sides of a triangle are together greater than the third . . . . . . . . .... | |
| Euclides - 1865
...greater ; therefore AB is equal to AC. PROPOSITION XX. TIIEOR. The greater angle of every 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 also greater than the side AB. For if it be not greater,... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...ACB. [Axiom 9. . .., Wherefore, the greater side &c. QED l( * • '' 7 PROPOSITION 19. THEOREM. 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 not, AC must be either equal to AB or less... | |
| Euclid, Isaac Todhunter - 1867 - 400 sider
...greater than the angle ACB. " [Axiom 9. Wherefore, the greater side &c. QED PROPOSITION 19. THEOREM. The **greater angle of every triangle is subtended by the greater side, or** Itat the greater side opposite to it. Let ABC be a triangle, of which the angle ABC is greater than... | |
| Robert Potts - 1868 - 410 sider
...QED PROPOSITION XIX. THEOREM. The greater angle of every triangle is subtended by the greater tide, **or, has the greater side opposite to it. Let ABC be...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, Charles Peter MASON - 1872
...true. Either the side * This proposition is often expressed thus : — " The greater £ of every A **is subtended by the greater side, or has the greater side opposite to it."** The meaning of this is precisely the same as what is given above. -f Let the beginner carefully distinguish... | |
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