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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. "
Report on the examination for admission to the Royal military academy at ... - Pagina 19
di Woolwich roy. military acad - 1861
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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - 1999 - 419 pagine
...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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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - 2000 - 278 pagine
...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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Using History to Teach Mathematics: An International Perspective

Victor J. Katz - 2000 - 261 pagine
...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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The Unfinished Mechanics of Giuseppe Moletti: An Edition and English ...

Giuseppe Moleti, Walter Roy Laird - 2000 - 222 pagine
...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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Philosophy and Geometry: Theoretical and Historical Issues

L. Magnani - 2001 - 249 pagine
...universally 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 pagine
...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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The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Mathematical Association, Mathematical Association of America - 2003 - 541 pagine
...exterior angles on the same side equal to two right angles. Prop. 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. Prop. 38: Triangles which are on equal bases and in the...
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The Cambridge Companion to Kant and Modern Philosophy

Paul Guyer, Jonathan Nelson Professor of Humanities and Philosoph Paul Guyer - 2006 - 722 pagine
...exhibit their concepts in intuition actually to think them. 27. "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, p. 316. 28. Because of space limitations,...
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