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" The area of a zone is equal to the product of its altitude by the circumference of a great circle. "
Elements of Geometry - Page 434
by Andrew Wheeler Phillips, Irving Fisher - 1896 - 540 pages
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...content, by less than any the same given difference. PROP. 3. The convex surface of a right cylinder is equal, to the product of its altitude by the circumference of its bane. For, if this product be|not equal to the convex surface of the cylinder, it must either be...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...altitude the altitude of the cylinder; whence it follows, that the convex surface of a right cylinder is equal to the product of its altitude by the circumference of its base. In like manner the developed surface of a right cone will form a circular sector, the arc...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1837 - 216 pages
...sphere is the product of its diameter by the circumference of a great circle. And, the area of a zone is the product of its altitude by the circumference of a great circle. 473. Corollary. Since the area of the great circle is, by art. 279, half -the product of its radius...
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - Geometry - 1847 - 204 pages
...sphere is the product of its diameter by the circumference of a great circle. And, the area of a zone is the product of its altitude by the circumference of a great circle. 474. Corollary. Since the area of the great circle is, by 5; 279, half the product of its radius by...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...The surface of a sphere is equal to the convex surface of the circumscribed cylinder. For the latter is equal to the product of its altitude by the circumference of its base. But its base is equal to a great circle of the sphere, and its altitude to the diameter;...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1857 - 242 pages
...of a sphere is equal to the product of its diameter by the circumference of a great circle. Cor. 1. The area of a zone is equal to the product of its al titude by the circumference of a great circle. For the surface described by the lines BC, CD is...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...of a sphere is equal to the product of its diameter by the circumference of a great circle. Cor, 1. The area of a zone is equal to the product of its al titude by the circumference of a great circle. For the surface described by the lines BC, CD is...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1861 - 638 pages
...radius, or one fourth of the diameter (Prop. XV. Bk.YL). 590. Cor. 2. TJie surface of a zone or segment is equal to the product of its altitude by the circumference of a great circle. For the surface described by the sides BC, CD of the inscribed polygon is equal to the product of the...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 518 pages
...coincide with the arc BCD; consequently, the surface of the zone described by the revolution of BCD is equal to the product of its altitude by the circumference of a great circle. In like manner, the same may be proved true of a segment, or a zone having but one base. 591. Cor....
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...radius, or one fourth of the diameter (Prop. XV. Bk. VI.). 590. Cor. 2. The surface of a zone or segment is equal to the product of its altitude by the circumference of a great circle. For the surface described by the sides BC, CD of the inscribed polygon is equal to the product of the...
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