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" 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. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Page 56
by Euclid - 1765 - 464 pages
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Pure mathematics, Volume 1

Edward Atkins - 1874
...figure, are equal to twice as many right angles as the figure has sides. But all the interior angles, together with four right angles, are equal to twice as many right angles as the figure has sides (I. 32, Cor. 1) ; Therefore all the interior angles, together with all the exterior angles, are...
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Pure mathematics, Volume 1

Edward Atkins - 1874
...Therefore, if a side of any triangle, &c. QED COROLLARY 1. — All t/ie interior angks of any rectilineal figure, together with four right angles, are equal to twice as many riff hi angles as tlie figure /ias sides. For any rectilineal figure ABCDE can, . by drawing straight...
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Elements of Euclid [selections from book 1-6] adapted to modern methods in ...

Euclides - 1874
...O, which together are equal to four right angles (I. 10, cor.); therefore the angles of the figure are equal to twice as many right angles as the figure has sides, less four right angles. — If the figure be a regular polygon, the magnitude of each angle,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1876 - 403 pages
...if a side of any triangle be produced, &c. QED, Con. 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. D For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides,...
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SYLLABUS OF PLANE GEOMETRY

1876
...triangle the two acute angles are complementary. THEOR. 26. All the interior angles of any polygon together with four right angles are equal to twice as many right angles as the figure has sides. COR. All the exterior angles of any convex polygon are together equal to four right angles....
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 pages
...figure, are equal to twice as many right angles as the figure has sides. But all the interior angles, together with four right angles, are equal to twice as many right angles as the figure has sides (I. 32, Cor. 1) ; Therefore all the interior angles, together with all the exterior angles, are...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 413 pages
...Book, of which the above is a corollary, and prove 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. Each angle of a regular polygon contains of a right angle ; what is the number of sides of...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 443 pages
...angles as the figure has sides. Let ABCDE be any polygon ; then all its interior angles A, B, C, D, E, together with four right angles, are equal to twice as many right angles as the figure has sides. 3 O For, from any point, F, within it, draw lines FA, FB, FC, etc., to all the angles. The...
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Elements of geometry, based on Euclid, book i

Edward Atkins - 1877
...figure, are equal to twice as many right angles as the figure has sides. But all the interior angles, together with four right angles, are equal to twice as many right angles as the figure has sides (I. 32, Cor. 1) ; Therefore all the interior angles, together with all the exterior angles, are...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878
...triangles are equal to twice as many right angles as the figure has sides. 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. Cor. 2. All the exterior angles of any rectilineal Jigure, made by producing the sides successively...
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