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Problems from Another Time

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

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?
How much does Landowner A give to each worker knowing Landowner B gives a certain amount more and has few workers.
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.
Two officers each have a company of men, the one has 40 less than the other.
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.
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.
Age
My age is a number consisting of two digits, 1/2 of this number is a mean proportional between these two digits, and two years hence, my age will be a third proportional to the same two digits, directly as they stand in my present age.
Thirty flasks-10 full, 10 half-empty, and 10 completely empty- are to be divided among 3 sons so that flasks and contents should be shared equally. How may this be done?

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