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4If there be an area or field, whose form is a square, and it is required to set out another field whose form is also to be a square, but double in area, as this cannot be accomplished by any numbers or multiplication, it may be found exactly by drawing lines for the purpose, and the demonstration is as follows. A square plot of ground ten feet long by ten feet wide, contains an hundred feet; if we have to double this, that is, to set out a plot also square, which shall contain two hundred feet, we must find the length of a side of this square, so that its area may be double, that is two hundred feet. By numbers this cannot be done; for if the sides are made fourteen feet, these multiplied into each other give one hundred and ninety-six feet; if fifteen feet, they give a product of two hundred and twenty-five.
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