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" Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon... "
Elements of Geometry and Trigonometry - Page 31
by Adrien Marie Legendre - 1837 - 359 pages
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An Elementary Geometry and Trigonometry

William Frothingham Bradbury - Geometry - 1872 - 262 pages
...the sum of the angles of all the triangles, that is, the sum of the interior angles of the polygon, is equal to twice as many right angles as the polygon has sides minus two. PRACTICAL QUESTIONS. 1. Do two lines that do not meet form an angle with each other ? Two...
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Treatise on Plane and Solid Geometry for Colleges, Schools, and Private Students

Eli Todd Tappan - Geometry - 1873 - 288 pages
...among the equal parts. SUM OF THE ANGLES. 423. Theorem. — The sum of all the angles of a polygon is equal to twice as many right angles as the polygon has sides, less two. For the polygon may be divided into as many triangles as it has sides, less two (417); and...
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A Treatise on Special Or Elementary Geometry

Edward Olney - Geometry - 1872 - 472 pages
...re.entrant angle. FIG. 186. PROPOSITION XT. 253. Theorem. — The sum of the inferior angles of a polygon s* equal to twice as many right angles as the polygon has sides, less four right angles. DEM. — Let n be the number of sides of any polygon; then the sum of its angles...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...inscribed in a circle, the sum of the angles in the segments exterior to the polygon, together with two right angles, is equal to twice as many right angles as the polygon has sides. 20. Draw the common tangents to two given circles. 21. From a given point draw a straight line cutting...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...inscribed in a circle, the stun of the angles in the segments exterior to the polygon, together with two right angles, is equal to twice as many right angles as the polygon has aides. SO. Draw the common tangents to two given circles. 21. From a given point draw a straight line...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...similar. For, the corresponding angles in each are equal, because any angle in F( >C either polygon is equal to twice as many right angles as the polygon has sides, less four right angles, divided by the number of angles (B. I, P. XXVI , C. 4); and further, the corresponding...
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The elementary geometry of the right line and circle

William Alexander Willock - Circle - 1875 - 196 pages
...corresponding external is equal to two right angles, the sum of all the internal and all the external is equal to twice as many right angles as the polygon has angles, or sides. If we take from this latter sum the four right angles to which the external angles...
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Dublin examination papers

Dublin city, univ - 1876 - 420 pages
...EUCLID AND TRIGONOMETRY. i . Prove that the sum of the internal angles of any polygon, together with four right angles, is equal to twice as many right angles as the figure has sides. Trisect an angle of 45o. 2. Construct a square equal to a given rectilinear figure....
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Manual of Geometry and Conic Sections: With Applications to Trigonometry and ...

William Guy Peck - Conic sections - 1876 - 412 pages
...angles of each triangle is two right angles ; hence, the sum of all the angles of all the triangles is equal to twice as many right angles as the polygon has sides. But, the sum of the angles of the polygon is equal to the sum of all the angles of all the triangles...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 382 pages
...Edition of Euclid. COB. 1. The sum of the interior angles of any rectilinear figwre together withfow right angles is equal to twice as many right angles as the figure has sides. Let ABCDE be any rectilinear figure. Take any pt. F within the figure, and from F...
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