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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 sides. "
Elements of Plane Geometry: For the Use of Schools - Page 81
by Nicholas Tillinghast - 1844 - 96 pages
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...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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A Rudimentary Treatise on Land and Engineering Surveying: For Students and ...

Thomas Baker - Railroads - 1891 - 264 pages
...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 Colliery Manager's Handbook: A Comprehensive Treatise on the Laying-out ...

Caleb Pamely - Coal mines and mining - 1891 - 664 pages
...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 ..., Book 1

James Andrew Blaikie, William Thomson - Geometry - 1891 - 154 pages
...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 First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - Euclid's Elements - 1892 - 184 pages
...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 - Plane trigonometry - 1893 - 534 pages
...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 pages
...9. Show 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. 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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Logic, Deductive and Inductive

Thomas Fowler - Logic - 1895 - 620 pages
...Generic Property. It is, for instance, a property of all rectilineal figures that the sum of their angles is equal to twice as many right angles as the figure has * F sides, minus four right angles. Thus the angles of a plane triangle are together equal to two right...
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Plane Geometry

George D. Pettee - Geometry, Plane - 1896 - 272 pages
...3 [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 from one vertex. Let 7'...
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Elements of Geometry: Plane geometry

Andrew Wheeler Phillips, Irving Fisher - Geometry - 1896 - 276 pages
...sides in more than two points. PROPOSITION XVI. THEOREM 66. The sum of all the angles of any polygon is twice as many right angles as the figure has sides, less four right angles. GIVEN ABCDE, any polygon, having n sides. To PROVE—the sum of its angles is 2 — 4 right angles....
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