.... 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;...

...TtR1, or -\7lDt. For C=27tR. §342 Substituting in (1), S= | X %7tR XR, S=7tR*. Also 8 = 345. COR. 2. — The areas of circles are to each other as the squares of their radii or as the squares of their diameters. Let S and S' denote the areas of two circles,...

...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...

...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 : :...

...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...

...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...

...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* :...

...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...

...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...