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that a young girl was capable of bringing sixty dozen eggs plus one to market all by
herself. Other examples invoke the conventions of courtly love, chivalric romance, and
biblical narrative. What are we to do with mathematics like this? There are at least two
avenues of approach (and here I am being deliberately ahistoricist): (1) the mathematics
and (2) everything else. I'll consider each in turn.
To make an informed conclusion about whether this mathematics is our math or their
math, and if the two are really the same or not, we have to do the math, so I make this
prescription: avoid the avoidance of math. We must read through the math itself, and
check it. A three-fold system seems to be the minimum effort necessary to make a
proper check. The first step is to solve a problem according to modern methods, if
possible. This will show if the problem is capable of any mathematical solution, though
we must be aware that we are situated in history as well and that our mathematical
techniques and standards of rigor are as fungible as any other. The second step is to
solve the problem according to the technique prescribed in the text's solution. Some-
times the technique is flawed (again, by our standards) so at this stage it is important
to determine if an answer, if correct, is perhaps the result of luck. If the prescribed
technique fails, then we move to the third step, which is to determine if some other
method taught in the same text would solve the problem. To see how this works, let's
return to the example of the drunkard and his beer. By the method generally taught for
such problems today, it is immediately obvious that that the problem is soluble, and that
the numerical answer provided in the text is correct.
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Problems arise, however, when
we try to apply the prescribed method of solution. The text invokes the golden rule.
This is another common name for the rule of three. Here's a modern example: “If a
gallon of milk costs four dollars, how much will I pay for seven gallons?” The premise
posits three known amounts and one unknown amount. The rule of three provides a
method to determine the unknown amount from the known amounts. Today this would
be an easy problem of basic algebra: four divided by one equals x divided by seven,
solve for x. The answer is $28. But since such algebraic manipulation was not yet avail-
able in the early sixteenth century, the rule of three explained how to use the gram-
matical arrangement of the problem to organize the data and find the solution. To return
to the drunkard, the first problem to face is that the golden rule has not yet been taught
under that name. It will be within a few pages, and the rule of three had been taught a
few pages earlier, but for the reader learning mathematics from scratch, there is no way
to know that the rule of three and the golden rule are the same thing. For such a reader,
this problem is to be solved by a method that does not yet exist. Next, there is no
