Approximate graphic method of squaring the circle

Editorial.

88 effected,

fropl all of which

the

ore is extracted.

The

finding

of

this important metal in California may be regarded as the last crowning act which was required to place California in advance of Respectfully, all the world for mineral wealth. A.R. ROESSLER.

APPROXIMATE GRAPHIC METHOD OF SQUARING THE CIRCLE, Philadei&hia,

January

6, 1869.

.-The following geometrical construcProf. Morton.-Dear Sir d tion, though very simple and beautiful, may be new to your readers I owe it to the kindness of a Scotch professor. as it is to me. It enables us, lst, to graphically square any circle to within i2 part of its area (sufficiently near for most practical purposes.) 2d. To increase (exactly) any square, (and hence any rectilinear figure) 25 per cent. its area. 3d. To decrease the same 20 per cent,. let A B be the side of a square ,circumscribed about any circle o. Draw D c tu the middle of A B. Then the chord c E will be the side of the square approximately equal the circle, and will be exactly 2 the first square. The proof is based on the well-known principle “ the square of the tangent equals the product of the secant and its extreme segment.” That known

is fi*=~ quantity

Thence

?%‘is

c X D E, where

is D E, which found

radius

thence

being

equals

to be (3 to) R2, while

known

the only

un-

tif the

circle

is (3.14 +j

R2, and the square on A B (4) R'. Another curious and useful result is that the sides of the second square are divided at c, H and K into $, 4 and 8 parts respectively, which fact enables us to enlarge a square 4 its area without the use of the circle. c B and o is the middle of, we have the means ho as B K-4 of reducing a square + its area without the use of the circle. Yours,

truly,

D. D. WILLARD.