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Problems from Another Time

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

Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
A certain man says that he can weigh any amount from 1 to 40 pounds using only 4 weights. What size must they be?
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.
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?
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.
If an arc of 45 degrees on one circumference is equal to an arc of 60 degrees on another circle, what is the ratio of the areas of the circle?
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
Knowing the base, b, and the altitude, a, of a triangle. Find the expression for a side of the inscribed square.
Given the fraction ax/ (a-x ), convert it into an infinite series.
Now there are 100 deers [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.

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