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Problems from Another Time

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

A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368.
A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received $150 for them. How many did he buy?
A barrel has various holes in it. The fist hole empties the barrel in three days...
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
A powerful, unvanquished, excellent black snake, 80 angulas in length, enters into a hole at the rate of 7 1/2 angulas in 5/14 of a day, and in the course of a day its tail grows 11/4 of an angula.
Determine the different values of x, when a certain function hits a minimum.
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
A series of circles have their centers on an equilateral hyperbola and pass through its center. Show that their envelope is a lemniscate.
Given a wooden log of diameter 2 feet 5 inches from which a 7 inch thick board is to be cut, what is the maximum possible width of the board?

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