 | Thomas Malton - 1774 - 484 pages
.... For, the Square of AC=AB D -)-BC D ; confequently, AC a is double EC, equal FH, a. But the Area's of Circles are, to each other, as the Squares of their Diameters, - - - - - - - - - C. i. i4. 6. therefore, the Circle ABCD is double FGHD. PRPOSiflON VIII. To make... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...other in the same ratio as the diameters of the circles. o-. ED THEOREM XCI1I. 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 3D, 4i their diameters ; then A : a : : D1... | |
 | Charles Hutton - Mathematics - 1812 - 620 pages
...other in the same ratio as the diameters of the circles, q. E. ». , THEOREM XCIII. 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, anJ •*, d, their diameters ; then A : a : :... | |
 | Charles Hutton - Arithmetic - 1818 - 646 pages
...same ratio as the diameters of the circles. QED THEOREM XCU1. The Areas or. Spacies of Circles, arc 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, tl their diameters ; then A : a : : oa... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...other in the same ratio as the diameters of the circles. <*. E. r>. THEOREM XCm. 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 0r spaces of two circles, and r> tl, their diameters ; then A : a :; D* :... | |
 | Charles Hutton - Mathematics - 1825 - 608 pages
...radius, of the said circular sections, is equal to the sum of the squares of the two ethers. And because circles are to each other as the squares of their diameters, or ef their radii, therefore the circle described by KL in equal to both the circle* described by KM and... | |
 | William Grier - Mechanical engineering - 1832 - 366 pages
...75. The circumferences of all circles are to each other as their diameters. 76. The areas or spaces of circles, are to each other as the squares of their diameters, or of their radii. PROBLEMS. 1. To bisect a line AB; that is, to divide it into equal parts. C From the two centres A... | |
 | William Templeton (engineer.) - 1833 - 224 pages
...the circle required. Some of the Properties of a Circle. 1. — It is the most capacious of all plain figures, or contains the greatest area within the...another contains four times the area of the other. 4. — The area of a circle is equal to the area of a triangle whose base is equal to the circumference,... | |
 | William Grier - Mechanical engineering - 1836 - 380 pages
...hence we find that, 2772 „ =: 77 inches, ou nearly equal to the area of the pump's bore; now the area of circles are to each other as the squares of their diameters, and the area of a circle whose diameter is 9, is 63-6; therefore, 63-6 : 77 : : 92 : 98 the square... | |
 | William Ruger - Arithmetic - 1836 - 274 pages
...stake, to give him the liberty of eating two acres of grass 1 . Ans. 55| yards. NOTE. — The area of circles are to each other, as the squares of their diameters. To find the area of a globe or ball. RULE. — Multiply the whole circumference by the whole diameter,... | |
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The areas of circles are to each other as the squares of their diameters, or of their radii. 
