 | William Grier - Mechanical engineering - 1842 - 320 pages
...74. The circumferences of all circles are to each other as their diameters. 75. The areas or spaces of circles, are to each other as the squares of their diameters, or of their radii. 76. The area of any circle, is equal to the rectangle of half its circumference... | |
 | William Benjamin Carpenter - 1843 - 610 pages
...will 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... | |
 | William Templeton (engineer.) - 1845 - 210 pages
...definitions. 1 . The circle contains a greater area than any other plane figure bounded by the same perimeter or outline. 2. The areas of circles are...contains four times the area of the other. 3. The radius of a circle is a straight line drawn from the centre to the circumference, as OB. 4. The diameter... | |
 | William Templeton - Mathematics - 1846 - 518 pages
...large engine has less rubbing surface, or less friction, according to its power, than a small one. 3. The areas of circles are to each other as the squares of their diameters, or as .7854 to 1 : a circle twice the diameter contains four times the area. EXAMPLE 1. — Required... | |
 | Mechanical engineering - 1847 - 190 pages
...and Definitions1 The circle contains a greater area than any other plane figure bounded by the same perimeter or outline 2 The areas of circles are to...diameter of another contains four times the area of the other3 The radius of a circle is a straight line drawn from the centre to the circumference, as O B4... | |
 | 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... | |
 | 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
...5. The areas or spaces of similar triangles are to each other as the squares of their like sides. 6. The areas of circles are to each other as the squares of their diameters, radii, or circumferences. 7. Similar figures are such as have the same number of sides, and the angles... | |
 | 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 - 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,... | |
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The circle contains a greater area than any other plane figure, bounded by an equal 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... 
