 | Mary Tiles - Mathematics - 1991 - 210 pages
...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 - Mathematics - 1992 - 432 pages
...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 - Geometry, Non-Euclidean - 1993 - 320 pages
...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... | |
 | Troels Kardel - Medical - 1994 - 270 pages
...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...opposite angles, and the three interior angles of the triangle are equal to two right angles. I. 34. In parallelogrammic areas the opposite sides and... | |
 | John R Cole - Biography & Autobiography - 1995 - 374 pages
...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...opposite angles, and the three interior angles of the triangle are equal to two right angles." 6. VMP, 13-15. There is no independent confirmation of... | |
 | Peter Machamer - Biography & Autobiography - 1998 - 474 pages
...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...and opposite angles, and the three interior angles are equal to two right angles) as an example for a noncausal demonstration he claimed it could not... | |
 | Douglas M. Jesseph - Mathematics - 1999 - 440 pages
...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...opposite angles, and the three interior angles of the triangle are equal to two right angles" (Elements 1, prop. 32). The theorem is, obviously enough,... | |
 | Nick Huggett - Philosophy - 1999 - 292 pages
...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...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 let one side of it... | |
 | Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...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...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... | |
 | Victor J. Katz - Mathematics - 2000 - 284 pages
...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...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 different from the... | |
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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 equal to two right angles. 
