| Euclides - 1879 - 146 pages
...more is L ABC greater than L ACB. Therefore, the greater side, &c. QED PROPOSITION XIX. THEOREM. The **greater angle of every triangle is subtended by the...has the greater side opposite to it. Let ABC be A** of which Z. ABC is greater than Then AC is greater than AB. Dem. For if AC be not greater than AB,... | |
| W J. Dickinson - Geometry - 1879 - 44 pages
...triangle. Prove that the greater side of every triangle is opposite to the greater angle. 19-. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** Same proposition. Hence show that the perpendicular is the shortest straight line that can be drawn... | |
| Moffatt and Paige - 1879 - 378 pages
...may be proved by a method similar to that employed in the 4th proposition of the first book. 2. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** Write out the converse of this proposition, and show that one of the two propositions is proved directly,... | |
| Isaac Sharpless - Geometry - 1879 - 282 pages
...ABD>ACB; therefore still more ABC>ACB. Proposition 21. Thewem.—The greater angle of every triangle **has the greater side opposite to it. Let ABC be a triangle** in -which the angle ABC is greater than the angle A CB; then will AC be greater than AB. For, if not,... | |
| Noah Knowles Davis - Logic - 1880 - 316 pages
...proposed before now ; but no such theory has ever been proposed ; hence, none can be framed. 50. The **greater angle of every triangle is subtended by the...opposite to it. Let ABC be a triangle, of which the angle** B is greater than the angle C ; then the side AC is likewise greater than the side A B. For if AC be... | |
| Education - 1906 - 716 pages
...in one of the old geometries one would find following the theorem and figure something like this : **Let ABC be a triangle of which the angle ABC is greater...the side AC is likewise greater than the side AB.** This in the first paragraph is followed by the demonstration in the next, beginning with " For." The... | |
| Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...&c. QED PROPOSITION 19. THEOREM. TJie greater angle of every triangle is subtended l)y the fjreater **side, or has the greater side opposite to it. Let...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... | |
| Noah Knowles Davis - Logic - 1880 - 344 pages
...theory could be framed to explain the estab50. The greater angle of every triangle is subtended by thc **greater side, or has the greater side opposite to it. Let ABC be a triangle, of which the angle** B is greater than the angle C ; then the side AC is likewise greater than the side A B. For if AC be... | |
| Euclides, Frederick Burn Harvey - Geometry - 1880 - 178 pages
...opposite to the greater angle in any triangle is greater than the side which is opposite to the less. **Let ABC be a triangle, of which the angle ABC is greater than the angle** ACB. Then, it is to be proved that The side AC is greater than the side AB. A PROOF. — If the side... | |
| Moffatt and Paige - 1881 - 176 pages
...draw a straight line at a given angle to a given straight line, from a given point in the same. 2. The **greater angle of every triangle is subtended by the...greater side, or has the greater side opposite to it.** 3. If D, E, F are points taken in the sides BC, CA, AB of an equilateral triangle ABC, so that BD =... | |
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