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Problems from Another Time

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

There is a lion in a well whose depth is 50 palms. He climbs and slips back a certain amount each day. In how many days will he get out of the well?
What will the diameter of a sphere be, when its volume and surface area are expressed by the same number?
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.
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
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.
A horse, halving its speed each day, travels 700 miles in 7 days. How far does it travel each day?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
A rifle ball is fired through a three-inch plank, the resistance of which causes an unknown constant retardation of its velocity.
Given the fraction ax/ (a-x ), convert it into an infinite series.
As for a square piece of land that amounts to 100 square cubits, if it is said to you, "Cause it to make a piece of land that amounts to 100 square cubits that is round," what is the required diameter?