| Institution of Civil Engineers of Ireland - 1906
...abbreviations may be used, but the method of proof must be geometrical.] 1. If a side of a triangle is **produced, the exterior angle is equal to the two interior...and the three interior angles of every triangle are** together equal to two right angles. If the side BC of a triangle ABC is produced both ways, and the... | |
| Saskatchewan. Dept. of Education - 1906
...line and surface. Illustrate by reference to a cube. 2. (a) If a side of any triangle be produced, (1) **the exterior angle is equal to the two interior and opposite angles; and** (2) the three interior angles of the triangle are together equal to two right angles. — I. 32. (6)... | |
| University of Calcutta - 1907
...figures in the margin indicate full marks. 1. If u side of any triangle be produced, the exterior anirlo **is equal to the two interior and opposite angles ;...and the three interior angles of every triangle are** together eqnal to two right angles. The bisectors of the exterior angles of any quadrilateral form... | |
| Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
...assumption of the uniqueness of the parallel. PROPOSITION 32. In any triangle, if one of the sides **be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of** the triangle are equal to two right angles. Let ABC be a triangle, and let one side of it BC be produced... | |
| Herbert Spencer - 1910
...foregoing theorem is inconveniently long. We shall find a titter one in Proposition xxxii. " If the side **of any triangle be produced, the exterior angle is...and the three interior angles of every triangle are** together equal to two right angles. " Let ABC be a triangle, and let one of its sides BC be produced... | |
| David Eugene Smith - 1911 - 339 sider
...is equal to two right angles. Euclid stated this as follows : " In any triangle, if one of the sides **be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of** the triangle are equal to two right angles." This states more than is necessary for the basal fact... | |
| G.E. Martin - 1997 - 512 sider
...to draw a straight line parallel to a given straight line. 32. In any triangle, if one of the sides **be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of** the triangle are equal to two right angles. 33. The straight lines joining equal and parallel straight... | |
| Mary Tiles - 1991 - 188 sider
...have been Aristotle's favourite example (Euclid 1926 pp. 320-1). In any triangle, if one of the sides **be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of** the triangle are equal to two right angles. Figure 1 O BCD Construction Let ABC be a triangle and let... | |
| Proclus - 1992 - 355 sider
...theorems, in that our geometer himself does so later in the case of equal angles: "In any triangle **the exterior angle is equal to the two interior and opposite angles, and the three** angles of a triangle are equal to two right angles."136 So here they think it appropriate in a similar... | |
| Saul Stahl - 1993 - 298 sider
...claim in the subsequent chapters of this book. Proposition 32. In any triangle, if one of the sides **be produced, the exterior angle is equal to the two...opposite angles, and the three interior angles of** the triangle are equal to two right angles. Proposition 47. In right-angled triangles the square on... | |
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