 | Robert Simson - 1827 - 546 σελίδες
...the angle * ACD, is greater than the angle ABC. Therefore, if one side, &C. QED PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. Let ABC be any triangle; any two of its angles together shall be less than two right angles. Produce BC toD; and... | |
 | Pierce Morton - 1830 - 584 σελίδες
...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 σελίδες
...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... | |
 | John Playfair - 1832 - 358 σελίδες
...the angle ACD, is greater than the angle ABC. Therefore if one side, &c. QED PROP. XVII. THEOR. Jlny two angles of a triangle are together less than two right angles. Let ABC be any triangle; any two of its angles together are less than two right angles. Produce BC to D ; and... | |
 | Euclides - 1833 - 304 σελίδες
...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... | |
 | Euclid - 1835 - 540 σελίδες
...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 angles. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce BC to D ; and... | |
 | 1835 - 684 σελίδες
...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... | |
 | 1836 - 488 σελίδες
...be produced, the exterior angle is greater than either of the interior, and opposite angles. XVII. Any two angles of a triangle are together less than two right angles. XVIII. The greater side of every triangle has the greater angle opposite to it. XIX. The greater angle... | |
 | John Playfair - 1836 - 488 σελίδες
...is1', the angle ACD, is greater than the angle ABC. Therefore, if one side, &c. QED PROP. XVII. THEOR. Any two angles of a triangle are together less than two right angles. Book I. Let ABC be any triangle ; any two of its angles together are less than two right angles. Produce... | |
 | George Darley - 1836 - 172 σελίδες
...together. Hence the angles BCA, ABC, BAC together are equal to -^ \* v two right angles. This, &c. ART. 38. Any two angles of a triangle are together less than two right angles ; and if any angle of a triangle be obtuse or right, the other two are acute ; also, if two angles... | |
| |
Any two angles of a triangle are together less than two right angles. 
