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Bøker Bok 151160 av 164If a side of any triangle be produced, the exterior angle is equal to the two interior...
" 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. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Side 41
av John Playfair - 1832 - 333 sider
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Steno on Muscles

Troels Kardel - 1994 - 252 sider
...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...
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Pascal: The Man and His Two Loves

John R Cole - 1995 - 349 sider
...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...
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The Cambridge Companion to Galileo

Peter Machamer - 1998 - 462 sider
...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...
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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - 1999 - 419 sider
...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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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

Nick Huggett - 1999 - 274 sider
...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...
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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - 2000 - 278 sider
...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...
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The Unfinished Mechanics of Giuseppe Moletti: An Edition and English ...

Giuseppe Moleti, Walter Roy Laird - 2000 - 222 sider
...right angle' (Euclid, Elements, 3.31, tr. Heath, 2:61-5). 64 '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' (Euclid, Elements, 1.32, tr. Heath, 1:316-22). 65 'If two...
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Using History to Teach Mathematics: An International Perspective

Victor J. Katz - 2000 - 261 sider
...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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Philosophy and Geometry: Theoretical and Historical Issues

L. Magnani - 2001 - 249 sider
...valid solution of the problem (Kant, 1929, A716-B744, pp. 578-579)." PROP. XXX11. THEOR. 1f a side of any triangle be produced, the exterior angle is equal to the two interiar and oppasite angles ; and the three interior angles af eDery triangle are equal to two right...
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Philosophy and Geometry: Theoretical and Historical Issues

L. Magnani - 2001 - 256 sider
...A716-B744, pp. 578-579).13 PROP. XXXII. THEOR. If a side of any triangle be produced, the exterior angle if equal to the two interior and opposite angles ; and...three interior angles of every triangle are equal to tico right angles. Let ABC be a triangle, and let one of its sides BC be produced to D ; the exterior...
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