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" If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles. "
The first six books of the Elements of Euclid, with numerous exercises - Σελίδα 13
των Euclides - 1853 - 147 σελίδες
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Geometry: A Comprehensive Course

Daniel Pedoe - 1988 - 468 σελίδες
...another, they make the vertical angles equal to one another. 16 In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. 17 In any triangle two angles taken together in any manner are less than two right...
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The Poincaré Half-plane: A Gateway to Modern Geometry

Saul Stahl - 1993 - 298 σελίδες
...students' memory, Euclid's proof is summarized below. Proposition 16. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. PROOF: Let ABC be a triangle, and let one side of it BC be produced to D (Fig....
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The Irish Law Times and Solicitors' Journal, Τόμος 37

1903 - 960 σελίδες
...numbers is 13, the difference of their squares is 39. Find the numbers. SECOND PAPEK. EUCLID. 2. I f any side of a triangle be produced, the exterior angle is greater than either of the interior non-adjacent angles. 1. Prove that, it at a point in a right liiic, two other right lines on opposite...

Steno on Muscles

Troels Kardel, Nicolaus Steno - 1994 - 252 σελίδες
...respectively, namely those which the equal sides subtend. I. 16. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. I. 18. In any triangle the greater side subtends the greater angle. I. 20. In...

The Scientific Letters and Papers of James Clerk Maxwell: Volume 1, 1846-1862

James Clerk Maxwell - 1990 - 776 σελίδες
...and annotations on the flyleaf by Maxwell, is in Maxwell's library (Cavendish Laboratory, Cambridge). (Theorem) ' If one side of a triangle be produced,...exterior angle is greater than either of the interior, and opposite angles' (Elements: 20). the angle ADB (Prop. 5). Upon AB describe a segment of a circle...
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Tradition, Transmission, Transformation: Proceedings of Two Conferences on ...

F. Jamil Ragep, Sally P. Ragep, Steven John Livesey - 1996 - 591 σελίδες
...the three propositions quoted by Thabit b. Qurra. Theorem I,16: In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles.35 Table I 36 35 Heath [1956], vol. l,p. 279. 36 Since Thabit omitted here the...
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Foundations and Fundamental Concepts of Mathematics

Howard Whitley Eves - 1997 - 344 σελίδες
...line. Let us briefly consider, for example, Proposition I 16: In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. A precis of Euclid's proof runs as follows. Let ABC (Figure 2.2) be the given...
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A Course in Modern Geometries

Judith Cederberg - 2004 - 441 σελίδες
...another, they make the vertical angles equal to one another. 16. In any triangle if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. 17. In any triangle two angles taken together in any manner are less than two...
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The Changing Shape of Geometry: Celebrating a Century of Geometry and ...

Mathematical Association, Mathematical Association of America - 2003 - 541 σελίδες
...they make the vertical angles equal to one another. Prop. 16: In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. Prop. 19: In any triangle the greater angle is subtended by the greater side....
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