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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. "
National Society's Monthly Paper - Página 107
1855
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Mathematics and the Image of Reason

Mary Tiles - 1991 - 210 páginas
...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...
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A Commentary on the First Book of Euclid's Elements

Proclus - 1992 - 432 páginas
...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...
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - 1993 - 320 páginas
...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...
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Steno on Muscles: Introduction, Texts, Translations

Troels Kardel - 1994 - 270 páginas
...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 - 374 páginas
...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 - 474 páginas
...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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Mathematical Expeditions: Chronicles by the Explorers

Reinhard Laubenbacher, David Pengelley - 2000 - 292 páginas
...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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Space from Zeno to Einstein: Classic Readings with a Contemporary Commentary

Nick Huggett - 1999 - 292 páginas
...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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Squaring the Circle: The War Between Hobbes and Wallis

Douglas M. Jesseph - 1999 - 440 páginas
...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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The Unfinished Mechanics of Giuseppe Moletti: An Edition and English ...

Giuseppe Moleti, Walter Roy Laird - 2000 - 252 páginas
...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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