 | 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 - 344 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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THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it. 
