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" F, which is the common vertex of the triangles: that is », together with four right angles. 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. "
The Elements of Euclid, the parts read in the University of Cambridge [book ... - Side 33
av Euclides - 1846
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The Elements of Geometry

Webster Wells - 1886 - 371 sider
...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 - 1887 - 180 sider
...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 - 1888 - 302 sider
...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 - 1889
...perpendicular without producing the given line. 1. Prove that all the interior angles of any rectilineal figure, together with four right angles, are equal...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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Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - 1890 - 172 sider
...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 Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...CBA, BAC, BCA together=two rt. ^s. [Ax. 1. COROLLARY I.— All the interior angles of any rectilineal figure, together with four right angles, are equal...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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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 393 sider
...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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A Text-book of Geometrical Deductions: Book I [-II] Corresponding to ..., Bok 1

James Andrew Blaikie, William Thomson - 1891
...angles are together equal to two right angles. Cor. i.— All the interior angles of any rectilineal figure together with four right angles are equal to...as many right angles as the figure has sides. Cor. ii.— All the exterior angles of any rectilineal figure are together equal to four right angles. 33....
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The Colliery Manager's Handbook: A Comprehensive Treatise on the Laying-out ...

Caleb Pamely - 1891 - 578 sider
...tested by Euclid, for, " The sum of all the interior angles of any rectilinear figure, together with 4 right angles, are equal to twice as many right angles as the figure has sides." This is not so thorough a test as the plotting, because it checks only the angles taken and not the...
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A Text-book of Geometrical Deductions: Book I [-II] Corresponding to ..., Bok 1

James Andrew Blaikie, William Thomson - 1891
...with four right angles are equal to twice as many right angles as the figure has sides. Cor. ii.— All the exterior angles of any rectilineal figure are together equal to four right angles. 33. The straight lines which join the ends of two equal and parallel straight lines; towards the same...
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