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" S' denote the areas of two whose radii are R and R', and diameters D and D', respectively. Then, | = "* = = • <337> That is, the areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. "
New Plane and Solid Geometry - Page 168
by Webster Wells - 1908 - 298 pages
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Short, But Yet Plain Elements of Geometry: Shewing how by a Brief and Easie ...

Ignace Gaston Pardies - Geometry - 1734 - 192 pages
...been faid of Circles in the fourth Book. Wherefore all fimilar Figures, &c. COROLLARY I. •• I. Circles are to each other as the Squares of their Radii or Diameters .- forfuppofe a Circle whbfe Radius is r, and then another Circle greater/ or"'lfefs;' than...
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Hawney's Complete Measurer: Or, The Whole Art of Measuring: Being a Plain ...

William Hawney - Geometry - 1820 - 336 pages
...SA*xAB; ---- x -- = -- xAB, 3 5 )5 the sum of all the series of squares, ma", nc*, py2, Sfe. But as circles are to each other as the squares of their radii or diameters ; it evidently follows that -^ SA1 x.7854xAB will he the solidity of one-fourth of the spindle...
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Elements of Geometry: With Practical Applications, for the Use of Schools

Timothy Walker - Geometry - 1829 - 138 pages
...-^Tjo 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 radii...
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First Lessons in Geometry: With Practical Applications in Mensuration, and ...

Charles Davies - Geometrical drawing - 1840 - 262 pages
...circumference 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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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Electronic book - 1855 - 592 pages
...&c. For nais. MATHEMATICAL DICTIONARY AND [SPH , = 4ят = mi. The surfaces of two spheres are to each other as the squares of their radii, or as the squares of their diameters ; or in general, as the squares of any two homologous lines that can be drawn in the sphere. If a right...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...again subdivided into varieties, &c. For ' surface, , - 4;rr3 = The surfaces of two spheres are to each other as the squares of their radii, or as the squares as spherical angle, spherical triangle, spherical polygon, &c. SPHERICAL ANGLE. An angle included of...
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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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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1857 - 608 pages
...a, we have the following formulas for the surface. The surfaces of two spheres are to each other an the squares of their radii, or as the squares of their diameters ; or in general, as the squares of any two homologous lines that can be drawn in the sphere. If a right...
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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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Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1859 - 622 pages
...spherical angle, spherical triangle, spheri- . The sur?jccs of two spheres are to each other ea' polygon, as the squares of their radii, or as the squares of their diamctcre ; or in general, as the squares of any two homologous lines that can be drawn in the sphere....
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