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 168by Webster Wells - 1908 - 298 pagesFull view - About this book
| 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... | |
| 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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...-^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 radii... | |
| 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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...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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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