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" If two lines are drawn through the same point across a circle, the products of the two distances on each line from this point to the circumference are equal to each other. "
First Principles of the Differential and Integral Calculus, Or, the ... - Page 3
by Etienne Bézout - 1824 - 195 pages
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...may be inscribed, within a circle, all the polygons that can be circumscribed about it. THEOREM. 280. The area of a regular polygon is equal to the product of its perimeter by half of the radius of the inscribed circle. Demonstration. Let there be, for example, the regular polygon GHIK...
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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
...may be inscribed, within a circle, all the polygons that can be circumscribed about it. THEOREM. 280. The area of a regular polygon is equal to the product of its perimeter by half of the radius of the inscribed circle. Demonstration. Let there be, for example, the regular polygon GHIK...
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Elements of Geometry...: Translated from the French for the Use of the ...

Adrien Marie Legendre, John Farrar - Geometry - 1825 - 294 pages
...inscribed, within a circle, all the polygons that can be circumscribed about it. V/ THEOREM. I 280. The area of a regular polygon is equal to the product of its perimeter by half of the radius of the inscribed circle. Demonstration. Let there be, for example, the regular polygon GHIK...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...circle is equal to the product of its circumference by half the radius. It was demonstrated, 280, that ' the area of a regular polygon is equal to the product of its perimeter by half the radius of the inscribed circle.' But the regular polygon of an infinite number of sides becomes...
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The North American Review, Volume 27

Jared Sparks, Edward Everett, James Russell Lowell, Henry Cabot Lodge - American fiction - 1828 - 598 pages
...circle is equal to the product of its circumference by half the radius. It was demonstrated, 280, that ' the area of a regular polygon is equal to the product of its perimeter by half the radius of the inscribed circle.' But the regular polygon of an infinite number of sides becomes...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 156 pages
...triangles, its area must be C EXhalf of A DjC EX half of BC, or C EXhalf of (A BfB C). 104. THEOREM. — The area of a regular polygon is equal to the product of its perimeter by half the radius F 64 of the inscribed circle. Let ABCDEF (fig. 64) be the polygon, and NP the radius of...
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1841 - 288 pages
...may be inscribed, within a circle, all the polygons that can be circumscribed about it. THEOBEM. 280. The area of a regular polygon is equal to the product of its perimeter by half of the radius of the inscribed circle. Demonstration. Let there be, for example, the regular polygon GHIK,...
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New Practical Arithmetic in which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1869 - 332 pages
...the trapezium WXYZ is equal to the triangle WXZ plus the triangle XYZ, made by the diagonal X Z. W 5. The area of a REGULAR POLYGON is equal to the product of the perimeter by half the perpendicular drawn from the center to any one of the sides. For, any regular...
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New Practical Arithmetic: In which the Science and Its Applications are ...

Henry Bartlett Maglathlin - Arithmetic - 1873 - 362 pages
...trapezium WXYZ is equal to the triangle WXZ plus the triangle XYZ, made by .„ the diagonal X Z. .X 5. The area of a REGULAR POLYGON is equal to the product of the perimeter by half the perpendicular drawn from the center to any one of the sides. For, any regular...
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Elements of Geometry with Exercises for Students: An an Introduction to ...

Aaron Schuyler - Geometry - 1876 - 384 pages
...also of 15, 30, GO, . . . sides, can be constructed bij 287. 295. Proposition XII.— Theorem. Tlie area of a regular polygon is equal to the product of its perimeter by one-half of its apothem. Let s denote one side of the polygon, n the number of sides, p the perimeter,...
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