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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. "
The geometry of the three first books of Euclid, by direct proof from ... - Seite 24
von Euclides - 1856
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Principles of psychology

Herbert Spencer - 1910 - 780 Seiten
...theorem is inconveniently long. We shall find a titter one in Proposition xxxii. " If the side of any triangle be produced, the exterior angle is equal...the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles. " Let ABC be a triangle,...
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The Teaching of Geometry

David Eugene Smith - 1911 - 360 Seiten
...is equal to two right angles. Euclid stated this as follows : " 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." This states more than is necessary...
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The Teaching of Mathematics in the United Kingdom

Great Britain. Board of Education - 1912
...and the included angle of another triangle, the triangles are equal in all respects. 2. Prove that if one side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles. 3. From the angular points B, C of a triangle ABC, perpendiculars...
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Special Reports on Educational Subjects, Bände 26-27

Great Britain. Board of Education - 1912 - 1032 Seiten
...and the included angle of another triangle, the triangles are equal in all respects. 2. Prove that if one side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles. 3. From the angular points S, C of a triangle ABC, perpendiculars...
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Treasure

William Henry Williamson - 1915 - 376 Seiten
...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...
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The Teaching of Geometry in Schools: A Report Prepared for the Mathematical ...

Mathematical Association - 1923 - 88 Seiten
...draw a straight line parallel to a given straight line. I. 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. I. 47 : In right-angled triangles the...
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The Atlantic Monthly, Band 124

1919 - 896 Seiten
...of age the old lady died, but not without leaving a profound impress on the future Proposition 16, "If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles." ' Concerning the attachment between the lad and...
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The Foundations of Geometry and the Non-Euclidean Plane

G.E. Martin - 1997 - 536 Seiten
...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 interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. 33. The straight lines joining equal...
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Annual Report

Saskatchewan. Department of Education - 1910
...(c) What circumstances concurred to give the Midland Dialect predominance ? . GEOMETRY. 1. (a) If a side of a triangle be produced the exterior angle...the two interior and opposite angles; and the three interior angles of the triangle are together equal to two right angles. I. 32. (6) Eind the number...
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Mathematics and the Image of Reason

Mary Tiles - 1991 - 210 Seiten
...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 interior and opposite angles, and the three interior angles of the triangle are equal to two right angles. Figure 1 O BCD Construction Let ABC...
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