| 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 - Geometry - 1857 - 444 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 - 470 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 - 520 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 - 514 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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