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" ... and the sum of the angles in all the triangles is evidently the same as that of all the angles of the polygon ; hence, the surface of the polygon is equal to the sum of all its angles, diminished by twice as many right angles as it has sides less... "
First Part of an Elementary Treatise on Spherical Trigonometry - Page 71
by Benjamin Peirce - 1836 - 71 pages
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Elements of Geometry: With, Practical Applications

George Roberts Perkins - Geometry - 1850 - 332 pages
...all the triangles is evidently the same as that of all the angles in the polygon: hence the surface of the polygon is equal to the sum of all its angles, diminished by twice as many right-angles as it has sides minus two. ScTiol. Let s be the sum of all the angles in...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...angles of all the triangles is the sattne as that of all the angles of the polygon ; hence, the surface of the polygon is equal to the sum of all its angles, diminished by twice as many right angles as it has Asides less two, into the tri-rectangular triangle. APPENDIX....
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...angles of all the triangles is the same as that of all the angles of the polygon ; hence, the surface of the polygon is equal to the sum of all its angles, diminished by twice as many right angles as it has sides less two, into the tri•rectangular triangle. Scholium....
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1856 - 460 pages
...all the triangles is evidently the same as that of all the angles in the polygon ; hence the surface of the polygon is equal to the sum of all its angles, diminished by twice as many right angles as it has sides minus two. Scholium. Let s be the sum of all the angles...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...triangles, etc. PROPOSITION XXI. THEOREM. Tfte surface, of a spherical polygon is measured by the sum of its angles, diminished by as many times two right angles as it has sides less two, multiplied by the quadrantal triangle. Let ABCDE be any spherical polygon. From the vertex...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

George Roberts Perkins - Geometry - 1860 - 472 pages
...all the triangles is evidently the same as that of all the angles in the polygon ; hence the surface of the polygon is equal to the sum of all its angles, dimir ished by twice as many right angles as it has sides minus two. Scliolium. Let s be the sum of...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...the sum of all the angles of the polygon ; hence the surface of the polygon is measured by the sum of its angles, diminished by as many times two right angles as it has sides less two, multiplied by the quadrantal triangle. Cor. If the polygon has five sides, and the sum of...
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The essentials of geometry, plane and solid, as taught in French and German ...

John Reynell Morell - Geometry - 1871 - 156 pages
...polygon, to all its vertices. (Fig. 68.) Pig. 68. 81. The sum of the angles of every polygon amounts to as many times two right angles as it has sides minus two. For the angles of the triangles of the first decomposition noticed above composed the angles of the...
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