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" THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle. "
A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and ... - Page 38
by Daniel Cresswell - 1816 - 294 pages
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...the equal sides of the polygon for its base, and the aggregate of the altitudes for its altitude : In the same manner it may be shewn that the aggregate of tlie triangles, into which the figure is divided by straight lines drawn from P, is equal to a right-angled...
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A System of Plane and Spherical Trigonometry: To which is Added a Treatise ...

Richard Wilson - Logarithms - 1831 - 372 pages
...a portion of the surface of a sphere contained by several arcs of great circles. 32. PROP. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Let a, , y, S, &c. be the sides of the polygon subtending plane angles at the centre of the sphere...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...BC; and, therefore, each of these arcs is less than the sum of the other two. 439. Theorem. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Polar Triangle. Demonstration. From the centre O (fig. ISO) of the sphere draw the radii OA, OB, OC,...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 150 pages
...BC ; and, therefore, each of these arcs is less than the sum of the other two. 439. Theorem. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Sum of the Sides of a Spherical Polygon. Proof. From the centre O (fig. 180) of the sphere draw the...
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A treatise on plane and spherical trigonometry

Thomas Grainger Hall - Trigonometry - 1848 - 194 pages
...triangle, is always less than the circumference of a great circle. COR. Hence it is obvious that the sum of the sides of a spherical polygon is less than the circumference of a great circle. The Polar TriangU. 12. Let ABC be a spherical triangle. With points, A, В, С, as poles, describe...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...the arc of a ijreat circle ADB. Therefore, the shortest path, &c. PROPOSITION IV. THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let ABCD be any spherical polygon; then will the sum of the sides AB, BC, CD, DA be less than the circumference...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...of the arc of a great circle ADB. Therefore, the shortest path, &c. PROPOSITION IV. THEOREM. The sum of the sides of a spherical polygon, is less than the circumference of a great circle. Let ABCD be any spherical polygon ; then will the sum of the sides AB, BC, CD, DA be less than the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...a spnere, is measured on the arc of a great circle joining them. PEOPOSITIOlSr II. THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle. 238 For, draw the radii OA, OB, 00, OD, and OE\ these radii form the edges of a polyedral angle whose...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...of a sphere, is measured on the arc of a great circle joining them. PROPOSITION II. THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle. For, draw the radii OA, OB, OC, OD, and OE\ these radii form the edges of a polyedral angle whose vertex...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 512 pages
...of a sphere, is measured on the arc of a great circle joining them. PROPOSITION II. THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Let ABCDE be a spherical polygon situated on a sphere whose centre is 0 : then will the sum of its...
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