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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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A Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - 1891 - 231 sider
...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 - 167 sider
...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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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 sider
...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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Plane Trigonometry

S. L. Loney - 1893
...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
...to BC ; show that AE is equal to AD. (12.) 9. Show 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. 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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The American Mathematical Monthly: The Official Journal of the ..., Volum 3

1896
...have any number of sides, the proposition is demonstrated just as in the case of a triangle. Therefore all the exterior angles of any rectilineal figure are together equal to four right angles. Corollary 1. Hence, all the interior angles of any triangle are equal to two right angles. For all...
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Plane Geometry

George D. Pettee - 1896 - 253 sider
...[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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Plane and Solid Geometry

James Howard Gore - 1898 - 210 sider
...exterior angles is equal to twice as many right angles as the figure has sides. But by (125) the interior angles are equal to twice as many right angles as the figure has sides, less four right angles. Therefore the exterior angles alone are equal to four right angles. QED EXERCISES....
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Science Examination Papers

Great Britain. Education Department. Department of Science and Art - 1899
...interior and opposite angles ; and that the three interior angles are equal to two right angles. Show that the exterior angles of any rectilineal figure are together equal to four right angles. If each angle of a rectilineal figure equals seven-eighths of two right angles, find the number of...
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