 | Proclus - 1992 - 432 Seiten
...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 case to... | |
 | Saul Stahl - 1993 - 320 Seiten
...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 interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. Proposition 47. In right-angled triangles... | |
 | Troels Kardel - 1994 - 270 Seiten
...together in any manner are greater than the remaining one. I. 32. In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. I. 34. In parallelogrammic areas the... | |
 | John R Cole - 1995 - 374 Seiten
...historique et critique, 3d ed. (Rotterdam, 1720), sv "Pascal." 5. "In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles." 6. VMP, 13-15. There is no independent... | |
 | James Clerk Maxwell - 1990 - 836 Seiten
...annotations on the flyleaf by Maxwell, is in Maxwell's library (Cavendish Laboratory, Cambridge). (Theorem) ' If one side of a triangle be produced, the exterior angle is greater than either of the interior, and opposite angles' (Elements: 20). the angle ADB (Prop. 5).... | |
 | Peter Machamer - 1998 - 474 Seiten
...scientific demonstrations. Using Proclus's analysis of Euclid I, 32 [In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles are equal to two right angles) as an example for a noncausal demonstration he claimed... | |
 | Reinhard Laubenbacher, David Pengelley - 2000 - 292 Seiten
...Euclid's theorem on the angle sum of triangles. PROPOSITION 32. In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and 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... | |
 | Nick Huggett - 1999 - 292 Seiten
...the given straight line BC. QEF 8 c ^O Figure 2.5 PROPOSITION 32 In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. [Fig. 2.5] Let ABC be a triangle, and... | |
 | Douglas M. Jesseph - 1999 - 440 Seiten
...an opinion on the topic, is Euclid's proof of the theorem that "in any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles" (Elements 1, prop. 32). The theorem... | |
 | Victor J. Katz - 2000 - 284 Seiten
...Heath (1861-1940, English) of Heiberg's text: Proposition 32. In any triangle, if one of the sides be produced, the exterior angle is equal to the two interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. B D FIGURE 2 The figure is a little... | |
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If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. 
