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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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The Mathematical Monthly, Volume 2

John Daniel Runkle - Mathematics - 1860
...figure must be aliquot parts of the circle or of four right angles. All the angles of any such figure are equal to twice as many right angles as the figure has sides minus four right angles, or if be the number of sides, the sum of all the angles is (2 n —...
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A course of geometrical drawing

William Schofield Binns - 1861
...let the required polygon be a pentagon. From Euc. I., 32, Cor. 1, "All the angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides." From this corollary, we can deduce a formula for finding the angle of any polygon. Let x equal...
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ELEMENTS OF GEOMETRY AND CONIC SECTIONS

ELIAS LOOMIS, LL.D. - 1861
...there are sides of the polygon BCDEF. Also, the anGEOMETRY. gles of the polygon, together with lour right angles, are equal to twice as many right angles as the figure has sides (Prop. XXVIII., BI) ; hence all the angles of the triangles are equal to all the angles of the...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862
...all the triangles, are equal to four right angles, (i. 15, cor. 2) 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. Att the exterior angles of any rectilineal figure are together equal to four right angles....
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862
...with its adjacent exterior angle ABD, are equal to two right angles. (I. 13.) angles of the figure, are equal to twice as many right angles as the figure has sides. 3. But all the interior angles, together with four right angles, are equal to twice as many...
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Responsions

University of Oxford - Education, Higher - 1863
...fall on it from the opposite angle, and the acute angle. 4. 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. 5. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863
...point F within the Cor. 1.—All the interior angles (ABC, BCD, &c.) of any rectilineal figure (ABCDE) together with four right angles are equal to twice as many right angles as the figure has sides. ., figure to each of its angles. \ Because the three interior angles of a triangle are equal...
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A Practical Treatise on the Science of Land and Engineering Surveying ...

Henry S. Merrett - Surveying - 1863 - 317 pages
...sides. It has been proved by the foregoing corollary that all the interior angles, together with the four right angles, are equal to twice as many right angles as the figure has sides. Therefore all the interior angles, together with all the exterior angles, are equal to all the...
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A practical treatise on ... land and engineering surveying, Volume 34

Henry S. Merrett - 1863
...sides. It has been proved by the foregoing corollary that all the interior angles, together with the four right angles, are equal to twice as many right angles as the figure has sides. Therefore all the interior angles, together with all the exterior angles, are equal to all the...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864
...Wherefore, if a side of any triangle be produced, &c. QED COR. 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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