 | William Templeton (engineer.) - 1845 - 210 pages
...circle contains a greater area than any other plane figure bounded by the same 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 of the other. 3. The radius... | |
 | William Vogdes - Arithmetic - 1847 - 324 pages
...is a right line passing through the centre, and terminated on each side by the convex surface. 46. The areas of circles are to each other as the squares of their diameters, radii, or circumferences. The areas of similar figures are to each other, as the squares of their like sides. 47. The surfaces... | |
 | Mechanical engineering - 1847 - 190 pages
...circle contains a greater area than any other plane figure bounded by the same 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 of the other3 The radius of... | |
 | Charles William Hackley - Geometry - 1847 - 248 pages
...other as the ratio of the arcs which subtend them to their radii. THEOREM LXXII. The areas or spaces of circles are to each other as the squares of their diameters, or of their radii. Let A, a denote the areas or spaces of two circles, and D, d their diameters ; then... | |
 | John Bonnycastle - Geometry - 1848 - 320 pages
...respectively equal to the three angles of the other, are called equiangular triangles, or similar triangles. K 4. In similar triangles the like sides, or sides opposite...and the angles contained by those sides respectively qual. 8. The areas of similar figures are to each other as the squares of their like sides. OF THE... | |
 | American Academy of Arts and Sciences - Chimneys - 1848 - 32 pages
...mean diameter, that at the top being 15.5 inches, and at the bottom 14 inches, is 14.75 inches. As the areas of circles are to each other as the squares of their diameters, we have these areas in the proportion of 217.56 to 1. This number multiplied by the depth in inches,... | |
 | American Academy of Arts and Sciences - Humanities - 1848 - 390 pages
...mean diameter, that at the top being 15.5 inches, and at the bottom 14 inches, is 14.75 inches. As the areas of circles are to each other as the squares of their diameters, we have these areas in the proportion of 217.56 to 1. This number multiplied by the depth in inches,... | |
 | Daniel Adams - Arithmetic - 1848 - 330 pages
...each to grind down, the waste hole through which the spindle passes, being 5 niches square ? NOTE. — The areas of circles are to each other, as the squar.es of their diameters. Ans. 6'675949 in., A grinds ; 10'310898 in., B grinds ; 11'942086 in., C grinds. 7. What is the greatest... | |
 | American Academy of Arts and Sciences - Humanities - 1848 - 378 pages
...mean diameter, that at the top being 15.5 inches, and at the bottom 14 inches, is 14.75 inches. As the areas of circles are to each other as the squares of their diameters, we have these areas in the proportion of 217.56 to 1. This number multiplied by the depth in inches,... | |
 | Daniel Adams - Arithmetic - 1848 - 320 pages
...each to grind down, the waste hole through which the spindle passes, being 5 inches square ? NOTB. — The areas of circles are to each other, as the squares of their diameters. Ans. 6-675949 in., A grinds ; 10'310898 in., B grinds ; 11'942086 in., C grinds. 7. What is the greatest... | |
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The areas of circles are to each other as the squares of their diameters. 
