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" A circle may be considered as a regular polygon of an infinite number of sides, the circumference being equal to the perimeter, and the radius to the perpendicular. "
Mensuration, Mechanical Powers, and Machinery: The Principles of Mensuration ... - Page 67
by Daniel Adams - 1850 - 128 pages
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Mathematics: Compiled from the Best Authors, and Intended to be ..., Volume 1

Samuel Webber - Mathematics - 1808 - 466 pages
...circumference and diameter. RULE 2.f Multiply the square of the diameter by '7854. * DEM0NSTRATI0N. A circle may be considered as a regular polygon of an infinite number of sides, the circumference being equal to the perimeter, and the radius to the perpendicular. But the area of a...
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A Treatise on Practical Mensuration in Eight Parts ...

Anthony Nesbit - Surveying - 1824 - 476 pages
...the area of a circle b divided by .7s3*, the quotient will be the square of the diameter. ^ * 2. A circle may be considered as a regular polygon of an infinite number of sides, the perimeter of which being equal to the circumference, and the perpendicular equal to the radius ; consequently, bv...
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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
...xxvii. — No. 60. 27 For this purpose, we only require the admission of the following proposition. The circle may be considered as a regular polygon of an infinite number of sides. This may be made intelligible to the mind of any youth, in the following manner. Take a circle aiKi...
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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
...xxvii. — NO. 60. 27 For this purpose, we only require the admission of the following proposition. The circle may be considered as a regular polygon of an infinite number of sides. This may be made intelligible to the mind of any youth, in the following manner. Take a circle and...
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An Introduction to Mensuration and Practical Geometry

John Bonnycastle - Geometry - 1829 - 256 pages
...Multiply half the circumference by half the diameter, and the product will be the area. * Demon. A circle may be considered as a regular polygon of an infinite number of sides, the circumference being equal to the perimeter, and the radius to the perpendicular. But the area of a...
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Introductory Discourse, and the Lectures Delivered Before the ..., Volume 5

American Institute of Instruction - Education - 1835 - 318 pages
...the several parts of the demonstration. Now, if according to the method of indivisibles, the circle be considered as a regular polygon of an infinite number of sides, the truth would flash at once upon a mature mind, but to a youth, it would not seem rigidly proved. The...
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An Introduction to Mensuration and Practical Geometry

John Bonnycastle - Geometry - 1848 - 320 pages
...the circumference by half the diameter, and the product will be the area. * Demon. A circle may lx- considered as a regular polygon of an infinite number of sides, the circumference being equal to the perimeter, and the radius to the perpendicular. But the area of a...
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Mensuration, Mechanical Powers and Machinery: The Principles of Mensuration ...

Daniel Adams - Arithmetic - 1849 - 142 pages
...remaining part of the circle contains 342 ; what is the diameter of the circle ? Ans. 29 ft. 7 in. 5T 62, To find the area of a circle. ANALYSIS. Any circle...multiplying the perpendicular by one half the perimeter, (If 53, rule,) the area of a circle may be found by applying the same principles. Hence, To find the...
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A Treatise on Practical Mensuration

Anthony Nesbit - Measurement - 1859 - 494 pages
...If the area of a circle be divided by .7854, the quotient will be the square of the diameter. 2. A circle may be considered as a regular polygon of an infinite number of sides, the perimeter of which being equal to the circumference, and the perpendicular equal to the radius : consequently by...
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The industrial self-instructor and technical journal, Volume 4

Ward, Lock and co, ltd - 1884 - 570 pages
...a circle is equal to the circumference multiplied by the half of the radius ; for the circumference may be considered as a regular polygon, of an infinite number of sides ; it is then the perimeter of the circle which, multiplied by the half of the radius, will give its...
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