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" The circle contains a greater area than any other plane figure, bounded by an equal perimeter, or outline. 2. The areas of circles are to each other as the squares of their diameters ; any circle twice the diameter of another contains four times the area... "
The Artillerists̓ Manual, and British Soldiers̓ Compendium - Page 330
by Frederick Augustus Griffiths - 1859 - 354 pages
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Safety-valves: Their History, Antecedents, Invention and Calculation

William Barnet Le Van - Faucets - 1892 - 178 pages
...constructive reasons, a breadth very considerable in proportion to the diameter closed by the valve; and since the areas of circles are to each other as the squares of their diameters, the area of the circle circumscribed by the outer border of the valve sit is materially larger than...
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Irrigation Manual: Containing Useful Information and Tables, Appertaining to ...

Walter P. Butler - Irrigation - 1892 - 270 pages
..." circumference X .07958. " = Vz diameter X Yz circumference. " = square of radius X 3.1416. .i _1 areas of circles are to each other as the squares of their ~~ ( diameters. 153 MERSURATION, continued. Doubling the diameter of a circle increases the area 4 times. e= * »ide...
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Essentials of physics

Fred John Brockway - 1892 - 392 pages
...light, and AB at double this disFIG. 54. tance. The diameter of AB is twice that of CD, and the surfaces of circles are to each other as the squares of their diameters. AB has four times the area of CD — four times as large for twice the distance — or the intensity...
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New Practical Arithmetic: In which the Science and Its Applications are ...

Henry B. Maglathlin - 1894 - 370 pages
...surface, when the first hax ground off his portion, there will remain J of that surface. Tiien, since the areas of circles are to each other as the squares of their diameters (Art. 431), The whole stone : part remaining :: square of diameter of the whole stone : square of diameter...
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Paving and Municipal Engineering, Volume 7

Municipal engineering - 1894 - 518 pages
...inches and 6 inches. Or, AD=,/122+6a+82+4J=16.1245 inches. This is founded on the theorem that the area of circles are to each other as the squares of their diameters. FR Lockling, CE Hannibal, Mo., Sept. 3, 1894. THE WATER SUPPLY OF A NEBRASKA CITY. To the Editor of...
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The American Amateur Photographer, Volume 7

Photography - 1895 - 644 pages
...the light admitted through a lens varies as the area of the circular aperture or diaphragm, and as the areas of circles are to each other as the squares of their diameters, and as the diameters of diaphragms may be, and are expressed in fractions of the focal length, therefore...
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Concrete Geometry for Beginners

Adelia Roberts Hornbrook - Geometry - 1895 - 222 pages
...one being 5 times that of the other, and show the truth of the following principle: PRINCIPLE 50. — The areas of circles are to each other as the squares of their diameters, or as the squares of their radii, 97. How many times is the area of a circle whose radius is 2 inches...
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - Engineering - 1895 - 1234 pages
...-^. 7854 ;=~; Л = ; =0.«1881С; :=2V; =1.12838*^"; Л = £; = 0.159155C; = V '-; = 0.504189 »'л. Areas of circles are to each other as the squares of their diameters. To find the length of an arc or a. circle : BtruB 1. As 360 is to the number of decrees in iliu arc,...
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Elements of Geometry: Plane and Solid

John Macnie - Geometry - 1895 - 386 pages
...by S, since S = £ R . C, (397), and~ C = 2-n- . ft (396), S = T- RX 2 TT . ft = TT ft~. 399. COR. 2. The areas of circles are to each other as the squares of their radii. For S = TT • ft2, and S' = w ft'; (398) .-. S : S' = TT R- : TT ft'2 = ft2 : ft'2....
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Experimental Physics

William Abbott Stone - Physics - 1897 - 392 pages
...diameter. A wire 2mm in diameter has four times the area of cross-section of a wire lmm in diameter, since the areas of circles are to each other as the squares of their diameters ; consequently a wire lm long and lmm in diameter would have a resistance of — x 4 = x. But the 4...
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