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Problems from Another Time

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

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 - Conclusion
How a translation of Peano's counterexample to the 'theorem' that a zero Wronskian implies linear dependence can help your differential equations students
Buying Wood
Three people buy timber together. One pays the merchant 5 coins, another 3 coins, and the last 2 coins.
Ladder Problem
If a ladder, placed 8 ft. from the base of a building 40 ft. high, just reached the top, how far must it be placed from the base of the building that it may reach a point 10 ft. from the top?
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?
Height of the Clouds
The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?

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