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Problems from Another Time

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

Given two circle tangent at the point P with parallel diameters AB, CD, prove that APD and BPC are straight lines.
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 mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot. The mouse decends 1/2 a braccia a day and at night it turns back 1/6 of a braccia.
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.
Seven men held equal shares in a grinding stone 5 feet in diameter. What part of the diameter should each grind away?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
Given a pyramid 300 cubits high, with a square base 500 cubits to a side, determine the distance from the center of any side to the apex.
Given the fraction ax/ (a-x ), convert it into an infinite series.
In a rectangle, having given the diagonal and perimeter, find the sides
A two door gate of unknown width is opened so that a 2 inch gap exists between the two doors.

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