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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 Geometry: Plane, Solid, and Spherical : with Numerous ...

William Frothingham Bradbury - Geometry - 1877 - 262 pages
...face angle (VI. 59) ACB<ACD-\-DC B But AB is the measure of the BOOK VIII. THEOREM IV. 16. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Let ABDE be a spherical polygon ; then AB + BD + DE + EA <^ circ. of a great circle. Let C be the corresponping...
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Elements of Plane and Solid Geometry

George Albert Wentworth - Geometry - 1877 - 416 pages
...to its bases. What is the altitude of each part 1 THE SPHERE. PROPOSITION XIV. THEOREM. 724. The mm of the sides of a spherical polygon is less than the circumference of a great circle. Let ABCDE be a spherical polygon. We are to prove AB + B С etc. less than the circumference of a great...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 458 pages
...be less than the sum of the other two. Therefore any side, etc. 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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An Elementary Geometry: Plane, Solid and Spherical

William Frothingham Bradbury - Geometry - 1880 - 260 pages
...triangle AB D. Now the face angle (VI. 59) DC B But AB is the measure of the THEOREM IV. 16i The sum of the sides of a spherical polygon is less than the circumference of a great circle. Let ABDE be a spherical polygon ; then AB + BD -\- DE + EA <^ circ. of a great circle. Let C be the...
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The Elements of Geometry

Henry W. Keigwin - Geometry - 1897 - 250 pages
...pole 0, 0' of each small circle. Then use the equations. Sph. A OAB = sph. A O'A'B", etc.] Ex. The sum of the sides of a spherical polygon is less than the circumference of a great circle. 543. DBF. The distance between two points on a sphere is the length of the minor arc (or the spherical...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 404 pages
...sides of the spherical polygon compare with the circumference of a great circle ? Theorem. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Data: Any spherical polygon, as ABCD, on the sphere whose center is O. To prove AB + BC + CD + DA <...
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Texas School Journal, Volumes 16-17

Education - 1898 - 458 pages
...altitude. Prove. 4. The edge of a cube is 5 1-2 inches. V\ nat are its volume and surface? 5. The sum of the sides of a spherical polygon is less than the circumference of a great circle. Prove. 1899. November, G. The lateral surface of a prism is equivalent to the rectangle formed by a...
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