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" F, which is the common vertex of the triangles ; that is, together with four right angles. Therefore all the angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides. "
The First Six Books: Together with the Eleventh and Twelfth - Seite 38
von Euclid - 1781 - 520 Seiten
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Elementary Plane Geometry: Inductive and Deductive

Alfred Baker - 1903 - 144 Seiten
...From the result reached in the previous question, show that all the interior angles of any polygon are equal to twice as many right angles as the figure has angles (or sides), less four right angles. 5. How many right angles is the sum of all the angles in...
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A Text-book of Euclid's Elements for the Use of Schools, Bücher 1

Euclid - 1904 - 456 Seiten
...with the angles at F, which are equal to four right angles. I. 15, Cor. Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right COROLLARY 2. If the sides of a rectilineal figure, which has no re-entrant angle, are produced in order,...
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The Colliery Manager's Handbook

Caleb Pamely - 1904
...tested by Euclid, for, " The sum of all the interior angles of any rectilinear figure, together with 4 right angles, are equal to twice as many right angles as the figure has sides." This is not so thorough a test as the plotting, because it checks only the angles taken and...
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A text-book of engineering drawing and design

Sidney Herbert Wells - 1905
...depends upon Corollary I. of Euclid i., 32, which says, that " the interior angles of any straight lined figure together with four right angles are equal to twice as many right angles as the figure has sides." The most common of the regular polygons used in engineering designs are the pentagon (five-sided),...
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Annual Report - Dept. of Education

Saskatchewan. Department of Education - 1906
...right angles. — I. 32. (6) What is a Corollary ? Show that all the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. (c) Derive the magnitude of an angle of a regular octagon. (d) If the exterior vertical angle...
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A School Geometry, Teile 1-4

Henry Sinclair Hall - 1908
...parallel to the base. -ve* f1 — 44 GEOMETRY. COROLLARY 1. ^M <Ae interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. Let ABCDE be a rectilineal figure of & sides. It is required to prove that all the interior...
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Books 10-13 and appendix

Euclid - 1908
...course be arranged so as not to assume the proposition that the interior angles of a convex polygon together with four right angles are equal to twice as many right angles as the figure has sides. Let there be any convex polyhedral angle with V as vertex, and let it be cut by any plane meeting...
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On Intelligence

Hippolyte Taine - 1998 - 588 Seiten
...together equal to four right angles ; hence it follows that the polygon contains a number of angles which, together with four right angles, are equal to twice as many right angles as there are sides. — Here the explanatory intermediate is a character comprised in all the elements...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1851
...THOSE ON PHYSICAL SCIENCE AND MECHANICS.) Section 1. 1. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. 2. Equal triangles upon equal bases, in the same straight line, and towards the same parts,...
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The Sanitary Record, Band 19

1897
...every triangle are together equal to two right angles. And, all the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. And, all the exterior angles of any rectilineal figure are together equal to four right angles....
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