 | 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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THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. 
