.... 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...

...deducting the '05, theremainder T97 is the diameter of the powder cylinder within the bag: and because the areas of circles are to each other as the squares of their diameters, and the squares of these numbers, 1'97 and 2'02, being to each other as 308 to 408, or as 97 to 102;...

...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...

...the -05, the remainder 1-97 is !the diameter of the powder cylinder within the bag : and be-* >cause the areas of circles are to each other as the squares of their diameters, and the squares of these numbers, 1-97 and 2'02, being to each Other as 388 to 408, or as 97 to 102...

...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...

...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 ;...

...An angle in a semicircle is a right angle. 2. All angles in the same segment of a circle are equal. 4. In similar triangles the like sides, or sides opposite...and the angles contained by those sides respectively equal. 8. The areas of similar figures are to each other as the squares of their like sides. MENSURATION...

...engine whose piston is 80 inches in diameter, and that of the induction pipe only 10 ; then, since the areas of circles are to each other as the squares of their diameters, we have 80* = 6400, and f 6400 10 =100; therefore, -^ = 64, which is the number of times the area of...

...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...

...capacious of all plain figures, or contains the greatest area within the same perimeter or outline. 2. — The areas of circles are to each other as the squares of their diameters, or of their radii. 3. — Any circle whose diameter is double that of another contains four times the...