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Double Fellowship?

A and B hold a piece of ground in common, for which they are to pay $36. A put in 23 oxen for 27 days, and B 21 oxen for 35 days; what part of the rent ought each man to pay?


Solution: As a side note, the text uses this problem to illustrate the application of the rule of "double fellowship," which states:

  • Multiply each man's stock into the time of continuance, then say
  • As the total sum of all the products is to the whole gain or loss,
  • So is each man's particular product to his particular share of the gain or loss.
Any idea what this all means?

Source: Samuel Webber's Mathematics Compiled from the Best Authors, 1808, p. 123.