# Problems from Another Time

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

Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
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.
Two men brought their fish through customs. Find how much the fish cost, and what is the customs fee.
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?
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...
A man agreed to pay for 13 valuable houses worth $5000 each, what the last would amount to, reckoning 7 cents for the first, 4 times 7 cents for the second, and so on, increasing the price 4 times on each to the last. A father left$20,000 to be divided among his four sons ages 6, 8, 10, and 12 years respectively so that each share placed at 4 1/2 compounded interest should amount to the same value when its possessor becomes the age 21.