 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...if one Bide, <SeQED 4 PROP. XVII. t HEOR. Any two angles of a triangle are together less than twfl right angles. Let ABC be any triangle; any two of...its angles together are less than two right angles. Produee BC to D ; and beeause ACD is the exterior angle of the triangle ABC, ACD, is greater (16. 1.)... | |
 | George Lees - 1826 - 276 pages
...that the angle BCG, that is, ACD% is e 5. 1. greater than ABC. Therefore, if one side, &c. QED Cor. Any two angles of a triangle, are together less than two right angles. For, since by the proposition, the exterior angle ACD is greater than the interior and opposite angle... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...be bisected, and AC be produced to G, it may be demonstrated I * 15. 1. that the angle BCG, that is, the angle * ACD, is greater than the angle ABC. Therefore,...ABC be any triangle; any two of its angles together shall be less than two right angles. Produce BC toD; and because ACD is the exterior angle of the triangle... | |
 | Pierce Morton - Geometry - 1830 - 584 pages
...the one equal to the three sides of the other, each to each, are equul in all respects . . 7 (•7) Any two angles of a triangle are together less than two right angles 7 (A} A triangle cannot have more than one right angle, or more than one obtuse angle . . nor. 7 (i)... | |
 | Augustus De Morgan - 1831 - 108 pages
...than two right angles, is not an assumption but a consequence of his proposition, which shews that any two angles of a triangle are together less than two right angles, and which is established before any mention is made of parallels. It has been found by the experience... | |
 | Euclides - 1833 - 304 pages
...line. For then an external angle would be = to an internal and opposite, which is absurd. PROP. 17, THEOR. Any two angles of a triangle are together less than two right angles. Produce any side ; then the external angle is greater than either of the internal remote angles ; but... | |
 | Thomas Perronet Thompson - Euclid's Elements - 1833 - 168 pages
...And by parity of reasoning, the like may be proved in every other triangle. Wherefore, universally, any two angles of a triangle are together less than two right angles. Which was to be demonstrated. COH. 1. A triangle cannot have more than one right angle; nor more than... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...that the angle BCG, that is (8. 1.) the angle ACD, is greater than the angle ABC. PROP. X. THEOR. Aw) two angles of a triangle are together less than two...Produce BC to D ; and because ACD is the exterior ano-le of the triangle ABC, ACD is greater (9. 1.) than the interior and opposite angle ABC ; to each... | |
 | Euclid - 1835 - 540 pages
...d 15. 1. greater than the angle ABC. Therefore, " if one side" &c. QED PROP. XVII. THEOR. Any tico angles of a triangle are together less than two right...right angles. Produce BC to D ; and because ACD is the exteriorangle of the triangle ABC, ACD is greater3 than the interior and , opposite angle ABC; to each... | |
 | Mathematics - 1835 - 684 pages
...Therefore, Sic. Cor. The two triangles are equal in every respect. (4. & 4 Cor.) PROP. 8. (Eue. i. 17.) Any two angles of a triangle are together less than two right angles. Let А В С be any triangle : any two of its angles, ABC and ACB, shall be together less than two right... | |
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ANY two angles of a triangle are together less than two right angles. 
