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" ... 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. "
Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ... - Page 30
by Robert Potts - 1868 - 410 pages
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...which is the common vertex of the triangles; that is, (I. 15. Cor. 2.) together with four right angles. Therefore all the angles of the figure, together with...twice as many right angles as the figure has sides. COK. 2. — All the exterior angles of any rectilineal figure are together equal to four right angles....
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 176 pages
...internal angles, are equal to twice as many right angles as the figure has sides; but the internal angles, together with four right angles, are equal to twice as many right angles as the figure has sides (6); take away from both the internal angles, and the external angles remain, equal to four right angles...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...the angles of the polygon together with four right angles. But all the angles of the polygon GHKLM together with four right angles are equal to twice as many right angles as the polygon has sides (i. 32. Cor. i), that is, as there are plane angles constituting the solid angle...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...angles. Wherefore, if a side of a triangle, etc. QED COR. 1. All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many D right angles as the figure has sides. E.=^lT"\~~-^, \ 4C-\ For any rectilineal figure ABCDE can...
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The popular educator, Volumes 5-6; Volume 8

Popular educator - 1854 - 922 pages
...But it has been proved that nil the angles of these tiungles are equal to twice as many right anales as the figure has sides. Therefore all the angles...four right angles are equal to twice as many right ung'es as the figure has sides. Corollary 2. All the exterior angles of any rectilineal figure, made...
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A Manual for Practical Surveyors: Containing Methods Indispensably Necessary ...

E. W. Beans - Surveying - 1854 - 114 pages
...taken. If the entire survey has been made as above directed, the sum of all the internal angles will be equal to twice as many right angles as the figure has sides, diminished by four right angles. If this sum, as in practice will be likely to be the case, should...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...triangles in the figure ; that is, as many times as there are sides, less two. But this product is equal to twice as many right angles as the figure has sides, less four right angles. Cor. 1. The sum of the interior angles in a quadrilateral is equal to two right...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...of the figure together with four right angles. But it has been proved that all the angles of these triangles are equal to twice as many right angles...twice as many right angles as the figure has sides. СOR. 2. — All the exterior angles of any rectilineal figure, made by producing the sides successively...
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Scientific and practical geometry for self-instruction

Rolla Rouse - 1879 - 400 pages
...40 ... ... ... ... ... 103 The exterior and interior angles of an rectilineal figure, are together equal to twice as many right angles as the figure has sides, 41 ... 104 „ angles are together equal to four right angles, 42 ... ... ... ... „ The interior...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - Geometry - 1879 - 282 pages
...But ACD+ACB = 2R; BAC+ABC+ACB = 2R. Corollary 1.—All the interior angles of a polygon are together equal to' twice as many right angles as the figure has sides, minus four right angles. Let ABODE be a polygon, and let n represent the number of its sides. Draw...
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