The Secret of the Circle And the Square

Cover The Secret of the Circle And the Square
The Secret of the Circle And the Square
J C Jeremy Carlisle Willmon
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^ circumference X 2 radius = area.
. *. A d X a c = area of circle a f c g. A b"-^ = a d X a c. (If from a point in the circumference a j^ be drawn to the diameter, and chords from the point to the extremities of the diameter, the j_ is a mean propor- tional between the segments of the diameter and each chord is a mean proportional between its adjacent seg- ments and the dian>eter. ) . *. A d: a b :: a b: a c. . -. A b- = a d X a c.
28 But a d X a c = area of circle a f c g as above, and a b'^
...= area of square.
. '. The square a b i h := circle a f c g which was to be constructed.
Note. — The angle bac Figure 3, when construct- ed, may be used for solving problems 2, 3, 4 and 5, and other allied problems, by constructing equal angles. (The nearest approximate to angle, b a c is 27*^*36' — and for convenience, for practical work, it may be marked on a protractor, or a triangle containing the essential angle constructed of wood metal or other ma- terial may be used. ) PROBLEM III To draw a circle = in area to a square.


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