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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 ... - Seite 39
von Robert Simson - 1806 - 518 Seiten
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 393 Seiten
...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 Blaikie, William Thomson - 1891 - 160 Seiten
...interior opposite angles, and the three interior angles are together equal to two right angles. Cor. i.— All the interior angles of any rectilineal figure...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 - 664 Seiten
...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 Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - 1891 - 231 Seiten
...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 - 184 Seiten
...an isosceles triangle. LE 8 118. 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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Plane Trigonometry

Sidney Luxton Loney - 1893 - 480 Seiten
...regular decagon. The corollary to Eue. I. 32 states that all the interior angles of any rectilinear figure together with four right angles are equal to...twice as many right angles as the figure has sides. Let the angle of a decagon contain x right angles, so that all the angles are together equal to 10#...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1894 - 892 Seiten
...at right angles to AD and CE at right angles to BC ; show that AE is equal to AD. (12.) 9. Show that all the interior angles of any rectilineal figure,...twice as many right angles as the figure has sides. A five sided figure has four equal angles, and the fifth angle equals a half of one of the four ; find...
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1897
...the triangles are equal in all respects. 3. Show that all the interior angles of any rectilineal 7 figure, together with four right angles, are equal...twice as many right angles as the figure has sides. 4. Parallelograms on equal bases, and between the 18 same parallels, are equal in area. 5. The complements...
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Plane Geometry

George D. Pettee - 1896 - 272 Seiten
...[alt. int. A (||s)] POLYGONS PROPOSITION XXX 43 111. Theorem. 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. Appl. Cons. Dem. i> Prove A + B + C, etc. = (2 n — 4) rt. Draw diagonals...
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Report of the Council of Public Instruction of the North-West Territories of ...

Northwest Territories Council of Public Instruction - 1897
....Vttf* (\tn<thl«trs must obtain at Ittist 34 ;xr <rnf. on rack section. A. 1. (<*} Prove that nil the interior angles of any rectilineal figure, together with four right angles, are equal to twice us many right angle* as th<« figure has shies. Cor I. I 82. \ Show that proposition vii> applies to...
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