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Problems from Another Time

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

Three circles of varying radius are mutually tangent. The area of the triangle connecting their centers is given. Find the radius of the third circle.
What is the perpendicular height of a cloud when it's angles of elevation were 35 degrees and 64 degrees as taken by two observers?
Two officers each have a company of men, the one has 40 less than the other.
How much does Landowner A give to each worker knowing Landowner B gives a certain amount more and has few workers.
A number is required; that the square shall be equal to twice the cube.
A leech invited a slug for a lunch a leuca away.
Find the height of a window.
A man entered an orchard through 7 gates, and there took a certain number of apples. When he left the orchard, he gave the first guard half the apples he had and 1 apple more.
Chuquet claimed that if given positive numbers a, b, c, d then (a + b) / (c + d) lies between a/c and b/d. Is he correct? Prove your answer
Determine a number having remainders 2, 3, 2 when divided by 3, 5, 7 respectively.