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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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Introduction and books 1,2

Euclid - 1908
...generally given in the text-books as Corollary 2. 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. Let ABC be a triangle, and let one side of it BC be produced to D ; 5 I say that...

A School Geometry, Μέρη 1-4

Henry Sinclair Hall - 1908
...are equal in all respects. 24 THEOREM 8. [Euc. I. 16.] If one side of a triangle is produced, then the exterior angle is greater than either of the interior opposite angles. 28 COR. 1. Any two angles of a triangle are together less than two right angles. 29 COR. 2. Every triangle...

Monographs on Topics of Modern Mathematics: Relevant to the Elementary Field

Jacob William Albert Young - 1911 - 416 σελίδες
...angles the two rays will be in the same line with 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 • leas than two...

Treasure

William Henry Williamson - 1915 - 360 σελίδες
...working at his lessons. George Harvey learnt axioms and postulates, how to demonstrate clearly that if one side of a triangle be produced the exterior angle is greater than the interior and opposite angle, and the two interior and opposite angles taken together are less than...

The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - 1997 - 512 σελίδες
...the vertical angles equal to one another. (Theorem 14.11) 16. In any triangle, if one of the sides be produced, the exterior angle is greater than either of the interior and opposite angles. (Theorem 17.9) 17. In any triangle two angles taken together in any manner are...
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Geometry: A Comprehensive Course

Daniel Pedoe - 1988 - 449 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
...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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