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" 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. "
A Course of Mathematics: For the Use of Academies, as Well as Private ... - Page 292
by Charles Hutton - 1831
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1857 - 444 pages
...is equal to twice as many right angles as the polygon has sides. Again, the sum of all the interior angles is equal to twice as many right angles as the figure has sides, less four right angles (p. 26). Hence, the interior angles plus four right angles, is equal to twice...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1857 - 538 pages
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two ; since the figure can be divided into that number of triangles. Hence this common rule. "...
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The Practice of Engineering Field Work, Applied to Land, Hydrographic, and ...

W. Davis Haskoll - Civil engineering - 1858 - 324 pages
...and in an irregular polygon they may be all unequal. The interior angles of a polygon are together equal to twice as many right angles as the figure has sides, less four. On this is based the theory of the traverse, of which further explanation will be given...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...that is, together with four right angles (Prop. V., Cor. 2). Therefore the angles of the polygon are equal to twice as many right angles as the figure has sides, wanting four right angles. Cor. 1. The sum of the angles of a quadrilateral is four right angles ;...
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A Course of Mathematics: Composed for the Use of the Royal Military Academy

Charles Hutton - Mathematics - 1860 - 1022 pages
...outward angles, is equal Ui t »ice as many right angles as the figure has sides. But the sum of all tbr inward angles, with four right angles, is equal to twice as many right angles as ttx figure has sides (th. 19). Therefore the sum of all the inward and all the oetward angles, is equal...
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Elements of Geometry, and Plane and Spherical Trigonometry: With Numerous ...

Horatio Nelson Robinson - Geometry - 1860 - 453 pages
...triangles is equal to two right angles, (Th. 11) ; and the sum of the angles of all the triangles must be equal to twice as many right angles as the figure has sides. But the sum of these angles contains the sum of four right angles about the point p ; taking these...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860
...two right angles ; and 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. 6. The opposite sides and angles of parallelograms are equal to one another, and the diameter bisects...
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The Mathematical Monthly, Volume 2

1860 - 462 pages
...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 (2n — 4) right...
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A Treatise on Land-surveying: Comprising the Theory Developed from Five ...

William Mitchell Gillespie - Surveying - 1880 - 570 pages
...proposition of Geometry, that in any figure bounded by straight lines, the sum of all the interior angles is equal to twice as many right angles, as the figure has sides less two ; since the figure can be divided into that number of triangles. Hence this common rule. "...
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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...sides minus two. Let ABCDEF be the given polygon ; the sum of all the interior angles A, B, C, D, E, F, is equal to twice as many right angles as the figure has sides minus two. For if from any vertex A, diagonals AC, AD, AE, are drawn, the polygon will be divided into...
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