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" Now the sum of the areas of the triangles is the area of the polygon, and the sum of the angles of the triangles is the sum of the angles of the polygon. "
An Elementary Treatise on Plane and Spherical Trigonometry: With Their ... - Page 99
by Benjamin Peirce - 1861 - 359 pages
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An Elementary Treatise on Plane Trigonometry: With Its Applications to ...

Benjamin Peirce - Plane trigonometry - 1835 - 110 pages
...between the angles ; but if the error was large, it would show the observations were inaccurate, and must be taken again. The area of each triangle is...of the preceding formulas, and the sum of the areas (405) of the triangles is the area of the Avhole field. This method of solution is general, and may...
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An Elementary Treatise on Plane & Spherical Trigonometry: With Their ...

Benjamin Peirce - Plane trigonometry - 1845 - 498 pages
...between the angles ; but if the error was large, it would show the observations were inaccurate, and must be taken again. The area of each triangle is...areas of the triangles is the area of the whole field. Rectangular surveying. is so small as not to be affected by the earth's curvature. Second Method of...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1899 - 246 pages
...expressed in spherical degrees is numerically equal to the sum of all their angles minus (n — 2) 180. Now the sum of the areas of the triangles is the area of the polygon, and the sum of the angles of the triangles is the sum of the angles of the polygon. 396 THE...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1899 - 496 pages
...expressed in spherical degrees is numerically equal to the sum of all their angles minus (n — 2)180. Now the sum of the areas of the triangles is the area of the polygon, and the sum of the angles of the triangles is the sum of the angles of the polygon. 396 THE...
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An Elementary Physics for Secondary Schools

Charles Burton Thwing - Physics - 1900 - 396 pages
...given surface into triangles by drawing diagonals. Measure the base and altitude of each triangle. The sum of the areas of the triangles is the area of the surface. On the other side of the surface draw different diagonals and make an independent determination...
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Solid Geometry, Volumes 6-9

George Albert Wentworth - Geometry, Solid - 1902 - 246 pages
...expressed in spherical degrees is numerically equal to the sum of all their angles minus (n — 2) 180. Now the sum of the areas of the triangles is the area of the polygon, and the sum of the angles of the triangles is the sum of the angles of the polygon. SPHERICAL...
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Plane and Solid Geometry

George Albert Wentworth - Geometry - 1904 - 496 pages
...expressed in spherical degrees is numerically equal to the sum of all their angles minus (n — 2) 180. Now the sum of the areas of the triangles is the area of the polygon, and the sum of the angles of the triangles is the sum of the angles of the polygon. 396 THE...
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Railway Signaling, Volume 1

School of Railway Signaling (Utica, N.Y.) - Railroads - 1910 - 446 pages
...base multiplied by the altitude. To find the area of any quadrilateral, divide it into two triangles and the sum of the areas of the triangles is the area required. The area of a regular polygon may be found as follows. Multiply the length of a side by the...
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Plane and Solid Geometry

Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...and one side of the polygon. § 189 Since the sum of all the bases is the perimeter p of the polygon, and the sum of the areas of the triangles is the area of the polygon, it follows that Area of ABCD -.. =pr/2. EXERCISES 1. If n represents the number of sides of...
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Plane Geometry

Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...and one side of the polygon. § 189 Since the sum of all the bases is the perimeter p of the polygon, and the sum of the areas of the triangles is the area of the polygon, it follows that Area of ABCD — =pr/2. EXERCISES 1. If n represents the number of sides of...
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