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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... "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 35
av Robert Simson - 1806 - 518 sider
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Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term ...

Cambridge University Examination Papers.Michaelmas Term,1884 to Easter Term,1885.Volume XIV - 1885
...equal to two right angles, these two straight lines shall be in one and the same straight line. 2. All the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. 3. Equal triangles on the same base, and on the same side of it, are between the same parallels. If...
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Annual Report of the Chief Superintendent of Education

1885
...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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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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Land and Marine Surveying in Reference to the Preparation of Plans for Roads ...

William Davis Haskoll - 1886 - 230 sider
...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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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
...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 - 515 sider
...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 - 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 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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