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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 and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1822 - 367 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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First Part of an Elementary Treatise on Spherical Trigonometry

Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
.../ff AC, AD, which divide it into as |\. / -905, many. triangles as it has sides minus ,>-_\/ JS ' if two. By the preceding theorem (891), the sum of the...as it has sides minus two, which agrees with (903). PEIRCE'S JRSE OF INSTRUCTION IN PURE MATHEMATICS, FOR THE E OF STUDENTS Ш HARVARD UNIVERSITY. 1. ELEMENTS...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...their angles diminished by as many times two right angles as there are triangles ; that is, the surface of the polygon is equal to the sum of all its angles...times two right angles, as it has sides minus two. 470. Theorem. If a portion ABCD (fig. 192) of a regular polygon, situated entirely upon the same side...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...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 two, into the tri-rectangular triangle. Scholium. Let...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...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 two, into the tri-rectangular triangle. Scholium....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...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 two, into the tri-rectangular triangle. Scholium....
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...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 two, into the tri-rectangular triangle. Scholium....
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...their angles diminished by as many times two right angles as there are triangles ; that is, the surface of the polygon is equal to the sum of all its angles...times two right angles, as it has sides minus two. Surface described by t!ie revolution of a regular portion of a Polygon. 471. Theorem. If a portion...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 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. Schol. Let s be the sum of all the angles in...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 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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