 | Adrien Marie Legendre - Geometry - 1819 - 574 pages
...shall have AB+AC + BC< ABD + ACD, that is, less than the circumference of a great circle. THEOREM. 462. The sum of the sides of any spherical polygon is less than the circumference of a great circle. Demonstration. Let there be, for example, the pentagon ABCDE (Jig. 225); produce the sides AB, DC,... | |
 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...+ BC ^ ABD + ACD, that is to say, less than a circumference. PROPOSITION V. THEOREM. The sum of all the sides of any spherical polygon is less than the circumference of a great circle. Take the pentagon ABCDE, for example. Produce the sides AB, DC, till they meet in F ; then since BC... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
...we shall have AB + AC + BC< ABD + ACD, that is, less than the circumference of a great circle. 462. The sum of the sides of any spherical polygon is less than the circumference of a great circle. Demonstration. Let there be, for example, the pentagon ABODE (fig. 225) ; produce the sides AB, DC,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...have AB + AC + BC < ABD + ACD, that is, less than the circumference of a great circle. THEOREM. 462. The sum of the sides of any spherical polygon is less than the circumference of a great circle. . Demonstration. Let there be, for example, the pentagon ABCDE, (fig. 225) ; produce the sides AB,... | |
 | Richard Wilson - Logarithms - 1831 - 372 pages
...primary and polar polygons ; each of the sides of the primary polygon being less than a semicircle, since the sum of the sides of any spherical polygon is less than the circumference of a great circle, (art. 32.) 49. PROP. If two spherical triangles have two sides of the one equal to two sides of the... | |
 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...+ AC + BC<ABD + ACD, that istosay,!ess than acircumference. PROPOSITION IV. THEOREM The sum of all the sides of any spherical polygon is less than the circumference of a, great circle. Take . the pentagon ABCDE, for example. Produce the sides AB, DC, till they meet in F; then since BC... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...have AB + AC + BC<ABD + ACD, that is, less than the circumference of a great circle. THEOREM. • 462. The sum of the sides of any spherical polygon is less than the circumference of a great circle. Demonstration. Let there be, for example, the pentagon ABODE (fig. 225); produce the sides AB, DC,... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 pages
...AB+AC+BC<ABD+ACD :— that is to say, less than a circumference. PROPOSITION V. THEOREM. The sum of all the sides of any spherical polygon is less than the circumference of a great circle. Take the pentagon ABCDE, for example. Produce the sides AB, DC, till they meet in F ; then, since BC... | |
 | George Roberts Perkins - Geometry - 1847 - 326 pages
...say, less than a circumference. add AB+ AC to eacli ; we PROPOSITION xvirr. THEOREM. The sum of all the sides of any spherical polygon is less than the circumference of a great circle.. Let us take, for example, jr. _c the pentagon ABCDE. Produce the sides AB, DC till they meet in F ; then... | |
 | Charles Davies - Trigonometry - 1849 - 372 pages
...AB + AC + BC<ABD + ACD, thatistosay,lessthanacircumference. PROPOSITION IV. THEOREM The sum,of all the sides of any spherical polygon is less than the circumference of a great circle. Take the pentagon ABCDE, for example. Produce the sides AB, DC, till they meet in F; then since BC... | |
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The sum of the sides of any spherical polygon is less than the circumference of a great circle. 
