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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 circles of radii 25 feet intersect so that the distance between their centers is 30 feet. What is the length of the side of the largest square inscribable within their intersecting arcs?
What will the diameter of a sphere be, when its volume and surface area are expressed by the same number?
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 circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?
Prove geometrically that the hypocycloid is a straight line when the radius of the rolling circle is one-half the radius of the fixed circle.
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.
Given the fraction ax/ (a-x ), convert it into an infinite series.