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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. "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 52
by Euclides - 1871
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The Foundations of Geometry and the Non-Euclidean Plane

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...
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Mathematics and the Image of Reason

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...
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A Commentary on the First Book of Euclid's Elements

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

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...
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Steno on Muscles

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...
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Pascal: The Man and His Two Loves

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...
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The Cambridge Companion to Galileo

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...
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Mathematical Expeditions: Chronicles by the Explorers

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

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

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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