| Euclides - 1834
...from the vertex to the point of section, divides the outward angle of the triangle into tlvo equal **angles. Let ABC be a triangle, and let one of its sides** BA be produced to E ; and let the outward angle CAE be divided into two equal angles by the straight... | |
| 1835
...(o) The three angles of a triaugle are together equal to two right angles; and if one of the sides **be produced, the exterior angle is equal to the two interior and opposite angles** . 14 (/>) In a right angled triaugle — 1. One of the angles, viz. the right angle, is equal to the... | |
| John Playfair - 1836 - 114 sider
...therefore, also, the angles CBA, BAC, ACB, are equal to two right angles. Wherefore, if a side of a tqangle **be produced, the exterior angle is equal to the two...angles of every triangle are equal to two right angles.** Which was to be proved. COR. I. All the interior angles of any rectilineal figure, together with four... | |
| 1836 - 472 sider
...Straight lines which are parallel to the same straight line are parallel to one another. XXXII. If a side **of any triangle be produced, the exterior angle is equal to the two interior and** op. posite angles ; and the three interior angles of every triangle are equal to two right angles.... | |
| Euclides - 1837
...through a given point parallel to a g - f, given straight line. PROPOSITION XXXII. Theorem. If a side **of any triangle be produced, the exterior angle is...angles of every triangle are equal to two right angles.** Steps of the Demonstration. 1. Prove that the altern. Z BAC = alternate Z ACE, And since AB, CD are... | |
| John Playfair - 1837 - 318 sider
...drawn through the given point A parallel to the given straight line BC. PROP. XXXII. THEOR. / If a side **of any triangle be produced, the exterior angle is...interior angles of every triangle are equal to two** rightfmgles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the exteripr angle... | |
| Euclid - 1837 - 390 sider
...to that which is described by either extremity of the base.* BOOK I. PROP. XXXII. THEOR. IF a side **of any triangle be produced, the exterior angle is equal to the two interior and** remote angles ; and the three interior angles of every triangle are together equal to two right angles.... | |
| C. Reiner - 1837 - 215 sider
...the exterior angle is greater than either of the interior and opposite angles. 7. If one side of a **triangle be produced, the exterior angle is equal to the two interior and opposite angles.** 8. If each of the sides of a triangle be produced, the three exterior angles are, together, equal to... | |
| Andrew Bell - 1837 - 240 sider
...A parallel to the given straight line BC. PROPOSITION XXXII. THEOREM. If a side of any triangle he **produced, the exterior angle is equal to the two interior and opposite angles ; and** vie three interior angles of every triangle are equal to two right angles. Let ABC he a triangle, and... | |
| Euclid - 1838 - 416 sider
...point A parallel to the given straight line BC. Which was to be done. PROP. XXXII. THEOR. Ir a side **of any triangle be produced, the exterior angle is...angles of every triangle are equal to two right angles.** ROOK I. triangle, viz. ABC, BCA, CAB, are together equal to two right angles. Through the point C draw... | |
| |