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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

Adrien Marie Legendre - Geometry - 1819 - 208 pages
...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,...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...+ 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,...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1825 - 280 pages
...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,...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...both ; we shall have AB+AC+BCZ. ABD + AC D, that is to say, less than a circumference. THEOREM. 462. The sum of all the sides of any spherical polygon is less than the circumference of a great circle. Tęke the pentagon ABODE, for example. Produce the sides AB, DC till they meet in F ; then since BC...
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A System of Plane and Spherical Trigonometry: To which is Added a Treatise ...

Richard Wilson - Logarithms - 1831 - 372 pages
...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...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 pages
...both; we shall have AB + AC + BC<ABD + ACD, that isto say,less than a circumference. PROPOSITION IV. THEOREM The sum of all the sides of any spherical...pentagon ABCDE, for example. Produce the sides AB, DC, D till they meet in F ; then since BC is less than BF + CF, the perimeter of the pentagon ABCDE will...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1839 - 372 pages
...to both; we shall have AB + AC + BC<ABD + ACD, thatistosay,lessthanacircumference. PROPOSITION IV. THEOREM The sum of all the sides of any spherical...circumference of a great circle. Take the pentagon ABCDE, for C_ example. Produce the sides AB, DC, till they meet in F; then since BC is less than BF + CF, the...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 235 pages
...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,...
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A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ...

Nathan Scholfield - Conic sections - 1845
...always bisect each other. But in the triangle BCD, we have (Prop. II.) the side BC<BD+CD ; add AB + AC to both ; we shall have AB+AC+BC<ABD+ACD :— that...The sum of all the sides of any spherical polygon is'Jess than the circumference of a great circle. Take the pentagon ABCDE, for example. Produce the...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...AB+AC+BC < ABD+ACD, that is to say, less than a circumference. add AB+ AC to eacli ; we PROPOSITION xvirr. THEOREM. The sum of all the sides of any spherical...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 ;...
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