 | George Roberts Perkins - Geometry - 1850 - 332 pages
...we shall have AB +AC+ BC< ABD + ACD ; that is to say, less than a circumference. PROPOSITION XVIII. THEOREM. The sum of all the sides of any spherical...is less than the circumference of a great circle. Let us take, for example, the pentagon ABCDE. Produce the sides AB, DC till they meet in F; then since... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOEEM. The sum of all the sides of any spherical polygon is less than the circumference of a great circle. Lit ABCDE be any spherical polygon, and 0 the centre of the sphere. Conceive 0 to be the vertex of... | |
 | Charles Davies - Geometry - 1854 - 436 pages
...hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOREM. The sum of all the sides of any spherical polygon is less titan the circumference of a great c1rcle. ^ Let ABCDE be any spherical polygon, and O the centre of... | |
 | George Roberts Perkins - Geometry - 1856 - 460 pages
...each ; we shall have AB + AC + BC < ABD + ACD, that is to say, less than a circumference. THEOREM ni. The sum of all the sides of any spherical polygon is less than the circumference of a great circle. EIGHTH BOOK. than BF + OF, the perimeter of the pentagon ABCDE will be less than that of the quadrilateral... | |
 | Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 442 pages
...hence, any side of a spherical triangle is less than the sum of the two other sides. PROPOSITION II. THEOREM. The sum of all the sides of any spherical...is less than the circumference of a great circle. Let ABCDE be any spherical polygon, and 0 the centre of the sphere. Conceive 0 to be the vertex of... | |
 | George Roberts Perkins - Geometry - 1860 - 472 pages
...each ; we shall have AB + AC + BC < ABD + ACD, that is to say, less than a circumference. THEOREM HI. The sum of all the sides of any spherical polygon is less than the circumference of a great circle. EIGHTH BOOK. than BF + CF, the perimeter of the pentagon ABCDE will be less than that of the quadrilateral... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...measured by the arc of a great circle joining the two points. PROPOSITION IV. — THEOREM. 525. TIte sum of all the sides of any spherical polygon is less than the circumference of a great circle. Let ABCDE be a spherical polygon ; then the sum of the sides AB, BC, CD, Ac. is less than the circumference... | |
 | Benjamin Greenleaf - Geometry - 1862 - 532 pages
...measured by the arc of a great circle joining the two points. PROPOSITION IV. — THEOREM. 525. Tlie sum of all the sides of any spherical polygon is less than the circumference of a great circle. Let А В С DE l>ea spherical polygon ; then the sum of the sides AB, В С, CD, &c. is less than... | |
 | Henry Barnard - Military education - 1862 - 412 pages
...of a great circle which joins the two given points. The sum of the sides of a spherical triangle, or of any spherical polygon, is less than the circumference of a great circle. Poles of an arc of a great or small circle.—They serve to trace arcs of circles on the sphere. Every... | |
 | Education - 1862 - 752 pages
...of a great circle which joins the two given points. The sum of the sides of n spherical triangle, or of any spherical polygon, is less than the circumference of a great circle. Poles of an arc- of a great or small circle. — They serve to trace arcs of circles on the sphere.... | |
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The sum of all the sides of any spherical polygon is less than the circumference of a great circle. 
