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" ... figure, together with four right angles, are equal to twice as many right angles as the figure has be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles. "
The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ... - Página 40
por Āryabhaṭa - 1878
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A Treatise on Mine-surveying

Bennett Hooper Brough - 1888 - 366 páginas
...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 - 356 páginas
...line. 1. Prove that 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. 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 - 252 páginas
...60°. 63. THEOE. 6. All the interior angles of any rectilinieal figure together with four right angles, are equal to 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 - 538 páginas
...COROLLARY I.— 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. 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 - 420 páginas
...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

James Andrew Blaikie, William Thomson - 1891 - 160 páginas
...angles. Cor. i.— 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. Cor. ii.— All the exterior angles of any rectilineal figure are together equal to four right angles....
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The Colliery Manager's Handbook: A Comprehensive Treatise on the Laying-out ...

Caleb Pamely - 1891 - 666 páginas
...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 Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - 1891 - 262 páginas
...taking the angles or measuring the lines. But since the sum of all the interior angles of a polygon is equal to twice as many right angles as the figure has sides, lessened by four right angles, and since the given figure has five sides, the sum of all its five interior...
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The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - 1892 - 188 páginas
...Corollary 1. All the interior angles of a closed rectilineal figwe together with four right angles are equal to twice as many right angles as the figure has sides. Let ABCDE... represent any rectilineal figure. Take a point P within the figure. Join P to each angular...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 460 páginas
...I. 15, (,'or. Therefore all tho interior angles of the figure, with four right angles, am together equal to twice as many right angles as the figure has sides, Q. u. U, COROLLARY 2. If the sides of a rectilineal JlJure, which has no re.entrant angle, are produced...
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