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" The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R "
The Elements of Plane and Solid Geometry ... - Page 220
by Edward Albert Bowser - 1890 - 393 pages
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 138 pages
...-^T«jo similar polygons are to each other as the squares of their homologous sides — . r 2. — Two circles are to each other as the squares of their radii or diameters — . <t 3. — The surfaces of two spheres are to each other as the squares of their...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 264 pages
...ABD. 33. The areas of circles are to each other as the squares described on their diameters : that is, the areas of two circles are to each other as the squares described on the diametres AB and CD. 39. If from any point of the circumference of a circle, a line...
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An elementary course of practical mathematics. Key, Part 2

James Elliot - 1852 - 106 pages
...whole circle of which EGF forms a part, and c, that of the circle forming the base of the cone. Since the circumferences of two circles are to each other as their radii, C:c::CB:ED, and £ C:1<;::CB:AB. But C: arc EGF :: 360° : Z ECF (Euc. vi, 33). .-. £ C-:£arcEGF::90°:ZECG....
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A Treatise on Conic Sections: Containing an Account of Some of the Most ...

George Salmon - Conic sections - 1855 - 376 pages
...indefinitely near lines of equal length are at right angles to the line joining their extremities. Ex. 2. The circumferences of two circles are to each other as their radii. If polygons of the same number of sides be inscribed in the circles, it is evident, by similar triangles,...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...or as their radii. 3. The area of a circle is IT multiplied by the square of the radius. Hence, any two circles are to each other as the squares of their radii, or as the squares of their diameters, or generally as the squares of any two homologous lines. 4. The...
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A Treatise on Arithmetic, Combining Analysis and Synthesis: Adapted to the ...

James Stewart Eaton - Arithmetic - 1857 - 376 pages
...conversely, if the area is divided by .785398, the quotient will be the square of the diameter. 5. The areas of two circles are to each other as the squares of their radii, diameters or circumferences. FIG. 12. 6. The square described on the hypothenuse of a right-angled...
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The Progressive Practical Arithmetic: Containing the Theory of Numbers, in ...

Horatio Nelson Robinson - Arithmetic - 1859 - 352 pages
...hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. 2d. The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. 1. The two sides of a right-angled triangle are 3 and 4 feet; what is...
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The Mathematical Monthly, Volume 2

John Daniel Runkle - Mathematics - 1860 - 590 pages
...centre, and radius СЖ, describe a circle ; then, as is easily seen, (1) CAZ : CE* =2:1. But since the areas of two circles are to each other as the squares of their radii, it follows from (1) that the area of the circle С К is half the circle С A. In precisely the same...
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The Progressive Higher Arithmetic, for Schools, Academies, and Mercantile ...

Horatio Nelson Robinson - Arithmetic - 1860 - 444 pages
...examples of this class relating to circles, may be solved by means of the following property : — The areas of two circles are to each other as the squares of their radii, diameters, or circumferences. NOTE. — This property of the circle is only a particular case of a...
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Primary Elements of Plane and Solid Geometry: For Schools and Academies

Evan Wilhelm Evans - Geometry - 1862 - 116 pages
...multiplied by 3.14159. Cor. 2. The diameter is equal to the circumference divided by 3.14159. THEOREM XVI. The areas of two circles are to each other as the squares of their diameters. The same construction being used as in the last theorem, it may be shown as before,...
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