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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. "
The geometry of the three first books of Euclid, by direct proof from ... - Seite 24
von Euclides - 1856
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A Commentary on the First Book of Euclid's Elements

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...
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The Poincaré Half-plane: A Gateway to Modern Geometry

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...
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Steno on Muscles

Troels Kardel, Nicolaus Steno - 1994 - 252 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...
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Pascal: The Man and His Two Loves

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...
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The Scientific Letters and Papers of James Clerk Maxwell: Volume 1, 1846-1862

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)....
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The Cambridge Companion to Galileo

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...
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Mathematical Expeditions: Chronicles by the Explorers

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...
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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

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...
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Squaring the Circle: The War Between Hobbes and Wallis

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...
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Using History to Teach Mathematics: An International Perspective

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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