UPDATE: I worked through these last night, and my conclusion is that the early Medievals probably had a form of arithmetic similar to the Greek love for proportions. It's possible to do these problems using algebra, but it's clunky by comparison; we wouldn't even think of problems like "if only there were twice as many, plus half of half as many, plus half of that, plus two: then we'd have a hundred!" The fact that the problems take that form implies training in recognition of ratios, and probably an easy familiarity with common ones. Proposition 4, for example, seems easy for those who are used to recognizing that this is equivalent to the ratio of 4 to 5.
Early Medieval Math Problems
Medievalists.net have a short collection of ten math problems by Alcuin of York (who I assume needs no introduction here, but is introduced there anyway by his full name). Many of you will find them amusing, some of you because you like math, some because you like history, and some because they are inherently interesting.
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2 comments:
I'm sure the fact we have coins called "quarters" is related.
See: https://en.wikipedia.org/wiki/Carolingian_monetary_system
Also, I've always found it odd how the French number in scores, but I guess it makes sense given historical roots ( https://en.wikipedia.org/wiki/Vigesimal ), and how doing math in your head is easier for a lot of people if it's rooted in proportions rather than just numbers.
Also, TIL that Inches were once "ounces of a foot".
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