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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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing... "
Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 30
by Euclides - 1842
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Annual Report of the Chief Superintendent of Education

1885 - 608 pages
...that the sum of the interior angles of any rectilineal figure together witli four right angles, is equal to twice as many right angles as the figure has sides. 5. Prove that the opposite sides and angles of a parallelogram are equal to one another, and that the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1885 - 538 pages
...eight right angles, or $ of one right angle. Cor. 4. In any equiangular polygon, any interior angle is equal to twice as many right angles as the figure has sides, less four right angles, divided by the mimber of angles. PROPOSITION XXVII. THEOREM. The sum of the...
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Land and Marine Surveying in Reference to the Preparation of Plans for Roads ...

William Davis Haskoll - Hydrographic surveying - 1886 - 354 pages
...of the angles having been correctly measured, because all the interior angles of the polygon will be equal to twice as many right angles as the figure has sides, less four right angles, or 360, if the theodolite has been correctly used. There will, however, generally...
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The Elements of Geometry

Webster Wells - Geometry - 1886 - 392 pages
...angles is expressed by 2 R x (n — 2) , or 2 nR — 4 R. That is, the sum of the angles of a polygon is equal to twice as many right angles as the figure, has sides, less four right angles. PROPOSITION XLVII. THEOREM. 149. If the sides of a polygon are produced so...
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First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - Geometry - 1887 - 202 pages
...produced to meet, the angles formed by these lines, together with eight right angles, are together equal to twice as many right angles as the figure has sides. 139. AP, BP, and CP are the internal bisectors of the angles of the triangle ABC. AP is produced to...
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A Treatise on Mine-surveying

Bennett Hooper Brough - Mine surveying - 1888 - 366 pages
...accuracy of the survey, as the interior angles of the polygon together with four right angles should be equal to twice as many right angles as the figure has sides. The interior angles of a traverse may be found from the bearings or courses by the following rules...
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 354 pages
...the given line, shew how to draw the perpendicular without producing the given line. 1. Prove that all the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. There are two regular polygons, the number of sides of one is double the number of sides of the other,...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...ACB together=two rt. ^s; [I. 13. ... LS CBA, BAC, BCA together=two rt. ^s. [Ax. 1. COROLLARY I.— All the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. D For any rectl. figure, ABCDE, can be divided into as many As as the figure has sides by drawing st....
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Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - Geometry, Modern - 1890 - 252 pages
...one-third of two right angles, or to 60. 63. THEOE. 6. All the interior angles of any rectilinieal figure together with four right angles, are equal...twice as many right angles as the figure has sides (Euc. I. 32. Cor. 1). Hence the angles of a regular polygon are each equal to the quotient obtained...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - Geometry - 1890 - 420 pages
...2 rt. Zs (n — 2) = 2n rt. Zs — 4 rt. Zs. Therefore, the sum of the angles of a polygon is also equal to twice as many right angles as the figure has sides, less four right angles. 149. COR. 2. The sum of the angles of a quadrilateral is equal to two right...
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