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Earth and Her Moon

John Michell's famous construction

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Earth has a mean diameter of 7,920 miles, the Moon 2,160 miles (radius 1,080 miles). Start by drawing a horizontal line length 4. With compasses and ruler divide the line in half and then half the halves; now a vertical length of 3 can be swung up and so a 3-4-5 triangle made. From here progress as shown in the top part of the diagram. Circles representing the Earth and the Moon can now be drawn with over 99.9% accuracy. The circle represents Heaven, the square represents Earth. With π as 22/7 a heavenly circle passing through the centre of the Moon has a circumference of 44 - the same length as the perimeter of the earthly square around Earth. Thus the Earth squares the circle of Moon.