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Problems from Another Time


Given: a circle with an inscribed equilateral triangle. The triangle has an area of 12 square units. What is the area of the circle?
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27.
If 80 dollars worth of provisions will serve 20 men for 25 days, what number of men will the same amount of provisions serve for 10 days?
Two persons sat down to play for a certain sum of money; and agree that the first who gets three games shall be the winner. After a few games they resolve to divide the stakes. How much should each person receive?
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
What is the sum of the reciprocals of the triangular numbers?
A certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?
Suppose the area of an equilateral triangle be 600. The sides are required.