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" The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C... "
New Elementary Geometry: With Practical Applications ; a Shorter Course Upon ... - Page 100
by Benjamin Greenleaf - 1873 - 176 pages
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Elements of Geometry: On the Basis of Dr. Brewster's Legendre : to which is ...

James Bates Thomson - Geometry - 1844 - 268 pages
...polygons will ultimately become equal to the circle, and equal to each other. PROPOSITION X. THEOREM. The circumferences of circles are to each other as their radii ; and their areas are as the squares of their radii. Let the circumference whose radius is CA, be designated by circ. CA...
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Elements of Plane Geometry: For the Use of Schools

Nicholas Tillinghast - Geometry, Plane - 1844 - 110 pages
...other as BC2 : KL2 (BV Prop. 22), they will also be to each other as BO2 : KS2. PROP. VIII. THEOREM. The circumferences of circles are to each other as their radii ; and their surfaces as the squares of those radii. Let us designate the circumference of the circle whose radius...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 894 pages
...PROPOSTTION XIV. THEOREM, The circumferences of circles are to each other as their ra~ dii, and the areas are to each other as the squares of their radii. Let us designate the circumference of the circle whose radius is CA by clrc. CA; and its area, by area...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 326 pages
...expressed thus : AO' : ao> : : AO.iABCD : ao.iabcd ; whence, AO : ao : : % ABCD : £ abed. Consequently the circumferences of circles are to each other as their radii, and therefore their surfaces are as the squares of the circumferences. Cor. 2. It follows, also, that similar...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1849 - 252 pages
...of the sector ACB is equal to the product of its arc AEB by half of AC. PKOPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and their areas are as the squares of their radii. Let R and r denote the radii of two circles; C and c their circumferences...
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Elements of Geometry and Trigonometry Translated from the French of A.M ...

Charles Davies - Trigonometry - 1849 - 372 pages
...circumscribed circles, or as the squares of OD, od,the radii of the inscribed circles. PROPOSITION XI. THEOREM. The circumferences of circles are to each other as their radii and the areas are to each other as the squares of their radii. Let us designate the circumference of the...
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Arithmetic on the Productive System: Accompanied by a Key and ..., Volume 1

Roswell Chamberlain Smith - Arithmetic - 1850 - 314 pages
...diameters of the circles. The same is true of the arc* and chords of similar segments. 57. Circles, or their areas are to each other as the squares of their radii, diameters or circumferences. 58. To find the area of a regular polygon, or any regular figure : Multiply...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...PROPOSITION XIII. THEOEEM. Tfie circumferences of circles are to each other as their radii, and the areas are to each other as the squares of their radii. Let us designate the circumference of the circle whose radius is CA by tire. CA ; and its area, by area...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1854 - 436 pages
...Indeed, the circle is but a regular polygon of an infinite number of sides. PROPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and the areas are to each other as the squares of their radii. Let us designate the circumference of the...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...of the sector ACB is equal to the product of its arc AEB by half of AC. PROPOSITION XIII. THEOREM. The circumferences of circles are to each other as their radii, and their areas are as the squares of their radii. Let R and r denote the radii of two circles ; C and c their circumferences...
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