Problem 2

To find the side of a square equal in area in any given
superficies whatever.

Initially,
the statement of the problem is vague. Without reading the notebook further, the
first thing I did was to look up in the *Oxford
English Dictionary* what “superficies” means. It turns out to be, with
respect to geometry, “a continuous extent having only two dimensions (length and
breadth, without thickness).” The question becomes perfectly clear when Macdonald
finally turns his problem into a numerical one. Later under this problem he
writes, “If the area of a circle be what is the side of a square equal in area
thereto?”

Solution:

or to three decimal places.