| G.E. Martin - Mathematics - 1997 - 512 pages
...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 - Mathematics - 1991 - 188 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 - Philosophy - 1992 - 355 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 - Mathematics - 1993 - 298 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, Nicolaus Steno - Medical - 1994 - 252 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 - 349 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 - Philosophy - 1998 - 462 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... | |
| Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 278 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... | |
| Nick Huggett - Science - 1999 - 274 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... | |
| Douglas M. Jesseph - Mathematics - 1999 - 419 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,... | |
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