| Euclid - Euclid's Elements - 1904 - 456 pages
...three interior angles of a triangle are together equal to two right angles. A Let ABC be a triangle, **and let one of its sides BC be produced to D. Then** (i) the exterior angle ACD shall be equal to the sum of the two interior opposite angles CAB, ABC ;... | |
| Herbert Spencer - Psychology - 1906
...foregoing theorem is inconveniently long. We shall find a fitter one in Proposition xxxii. " If the **side of any triangle be produced, the exterior angle...every triangle are together equal to two right angles.** " Let ABC be a triangle, and let one of its sides BC be produced to D ; then the exterior angle ACD... | |
| Institution of Civil Engineers of Ireland - Civil engineering - 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...every triangle are together equal to two right angles.** If the side BC of a triangle ABC is produced both ways, and the bisectors of the exterior angles so... | |
| Saskatchewan. Department of Education - 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 ;...three interior angles of every triangle are together** eqnal to two right angles. The bisectors of the exterior angles of any quadrilateral form a qnadrilateral... | |
| Association of Ontario Land Surveyors - Surveying - 1907
...to a given rectilineal figure and having an angle equal to a given rectilineal angle. 3. Prove that **the three interior angles of every triangle are together equal to two right angles.** 4. Inscribe an equilateral triangle in a given circle; trisect a right angle. 5. To divide a given... | |
| Euclid - Mathematics, Greek - 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 - Philosophy - 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...every triangle are together equal to two right angles.** " Let ABC be a triangle, and let one of its sides BC be produced to D; then the exterior angle ACD... | |
| David Eugene Smith - Geometry - 1911 - 339 pages
...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... | |
| Freemasonry - 1913
...Forty-seventh Problem, there are several other equally important problems ascribed to him. Among these are: the **interior angles of every triangle are together equal to two right angles;** that the only polygons which fill up the whole space about a given point are the equilateral triangle,... | |
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