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Problems from Another Time

Individual problems from throughout mathematics history, as well as articles that include problem sets for students.

Two Equal Parts of a Triangle
The three sides of a triangular piece of land, taken in order, measure 15, 10, and 13 chains respectively.
Series of Circles
A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
Breaking Bread
Divide 100 loaves of bread among 10 men including a boatman, a foreman, and a doorkeeper, who each receives double portions. What is the share of each?
Peano on Wronskians: A Translation - Appendix 1: Student Tasks
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Animal Customs
A fox, a wild-cat, and a hound pass through customs and together pay 111 coins.
Sick Leave
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months' absence caused by sickness, he received only $409.50. What was his board worth per month?
Out to Pasture
Two men rent a pasture for 100 lire on the understanding that two cows are to be counted as being equivalent to three sheep. The first puts in 60 cows and 85 sheep; the second 80 cows and 100 sheep. How much should each pay?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Appendix A: The Land of 'Oc'
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Lucky Seven
There is a number which when divided by 2, or 3, or 4, or 5, or 6, always has a remainder of 1, and is truly divisible by 7. It is sought what is the number.
Hogsheads of Rum
Two merchants, A and B, loaded a ship with 500 hhds (hogsheads) of rum; A loaded 350 hhds, and B the rest; in a storm the seamen were obliged to throw overboard 100 hhds; how much must each sustain of the loss?

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