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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. "
Elements of Geometry and Conic Sections - Page 30
by Elias Loomis - 1857 - 226 pages
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Using History to Teach Mathematics: An International Perspective

Victor J. Katz - Mathematics - 2000 - 284 pages
...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 different from the...
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Shop Reference for Students and Apprentices

Christopher J. McCauley - Science - 2000 - 532 pages
...the right angle. a2 = b2 + c2 Geometrical Propositions If one side of a triangle is produced, then the exterior angle is equal to the sum of the two interior opposite angles. Angle D = angle A + angle B If two lines intersect, then the opposite angles formed...
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Key Maths: 8, Volume 8

David Baker - Mathematics - 2001 - 546 pages
...85) = 45° Then MS* the exterior angle = 180 - 45° angles on a straight line = 135° The link is: The exterior angle is equal to the sum of the two interior angles ie 135° = 50° + 85° Framework for teaching mathematics Year 7 Shape, space and measures Geometrical...
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Philosophy and Geometry: Theoretical and Historical Issues

L. Magnani - Gardening - 2001 - 280 pages
...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 the 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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Designing Experiments & Games of Chance: The Unconventional Science of ...

William R. Shea - History - 2003 - 374 pages
...of the three interior angles of a triangle is equal to two right angles after realizing that if any side of a triangle is produced, the exterior angle...to the sum of the two interior and opposite angles. This property follows from Proposition 29 of Book I, which uses the postulate of parallel lines to...
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The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Chris Pritchard - Mathematics - 2003 - 572 pages
...angles. Prop. 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. 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 - History - 2006 - 760 pages
...to think them. 27. "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." Euclid, Elements, p. 316. 28. Because of space limitations,...
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