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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 "
Primary Elements of Plane and Solid Geometry: For Schools and Academies - Page 72
by Evan Wilhelm Evans - 1862 - 98 pages
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The Mathematical Questions Proposed in the Ladies' Diary: And ..., Volume 4

Thomas Leybourn - Mathematics - 1817
...the rectangle oc X AF : hence, since OF r: oc, we have OA := AF, or 2AF — OF — oc. Then, since circles are to each other as the squares of their diameters, the area of the circle of which oc is the diameter, is quadruple the area of the circle DBF : and consequently...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 252 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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Popular cyclopaedia of natural science (by W.B. Carpenter).

William Benjamin Carpenter - 1843
...convey no more blood than the single trunk. For, according to a simple rule in geometry, the ami* of circles are to each other as the squares of their diameters. The area of the trunk is expressed, therefore, by the square of 10^, which is almost exactly 102. The areas...
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Lectures on the Philosophy of Arithmetic and the Adaptation of that Science ...

Uriah Parke - Arithmetic - 1849 - 395 pages
..." Square the diameter of the given circle, and multiply by .7854 for the area." Yet admitting that circles are to each other as the squares of their diameters, the reason is obvious enough. The Permutation and Combination of quantities, and the doctrine of chances,...
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LECTURES ON THE PHILOSOPHY OF ARITHMETIC AND THE ADAPTATION OF THAT SCIENCE ...

URIAH PARKE - 1850
..." Square the diameter of the given circle, and multiply by .7854 for the area." Yet admitting that circles are to each other as the squares of their diameters, the reason is obvious enough. The Permutation and Combination of quantities, and the doctrine of chances,...
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Questions on Subjects Connected with the Marine Steam-engine: And ...

Thomas Main, Thomas Brown (of the Royal Naval College) - Marine engines - 1857 - 108 pages
...the cylinder ; find also, the capacity of the pump, supposing it to be similar to the cylinder. Since circles are to each other as the squares of their diameters, the area of the air-pump bucket is úth that of the piston. Hence its area = =1486 - 1675 square inches,...
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A Treatise on Arithmetic, Combining Analysis and Synthesis: Adapted to the ...

James Stewart Eaton - Arithmetic - 1857 - 355 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...
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Animal Physiology

William Benjamin Carpenter - Physiology, Comparative - 1859 - 604 pages
...convey no more blood than the single trunk. Fof, according to a simple rule in geometry, the areas of circles are to each other as the squares of their diameters. The area of the trunk is expressed, therefore, by the square of 1(H, which is almost exactly 102. The area...
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The Progressive Practical Arithmetic: Containing the Theory of Numbers, in ...

Horatio Nelson Robinson - Arithmetic - 1859 - 336 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...
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Key to Davies' University Arithmetic: Embracing the Answers, and a Full ...

Charles Davies - 1859
...other as their bases. As two similar figures are to each other as the squares of therr like dimensions, two circles are to each other as the squares of their diameters or radii ; that is, the square of the radius of the second circle will be two-thirds the square of...
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