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" The sum of all the sides of any spherical polygon is less than the circumference of a great circle. "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 11
by Nathan Scholfield - 1845 - 232 pages
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Elements of Geometry: With, Practical Applications

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...
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Elements of Geometry and Trigonometry

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...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

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...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

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...
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Plane and Solid Geometry: To which is Added Plane and Spherical Trigonometry ...

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...
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Elements of Geometry and Trigonometry: With Practical Applications

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...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

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...
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Military Schools and Courses of Instruction in the Science and Art ..., Part 1

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...
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The American Journal of Education, Volume 12

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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