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Problems from Another Time

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

A merchant woman buys and sells apples and pears for Denaros. How much did she invest in apples; how much in pears?
A vessel is anchored in 3 fathoms of water and the cable passes over a sheave in the bowspirt which is 6 ft above the water.
What is the sum of the reciprocals of the triangular numbers?
Prove that if the sums of the square opposite sides of any quadrilateral are equal, its diagonals interect at right angles.
A powerful, unvanquished, excellent black snake, 80 angulas in length, enters into a hole at the rate of 7 1/2 angulas in 5/14 of a day, and in the course of a day its tail grows 11/4 of an angula.
On a day in spring a boy has gathered cherry blossoms under a cherry tree. Nearby a poet is reading some of his poems aloud. As he reads, the boy counts out the cherry blossoms, one blossom for each word of a poem.
Find two number with sum 20 and when squared their sum is 208.
A man hired a horse in London at 3 pence a mile. He rode 94 miles due West to Bristol then due north to Chester, whence he returned toward London for 66 miles, which put him in Coventry.
A tree is 20 feet tall and has a circumference of 3 feet. There is a vine that winds seven equally spaced times around the tree and reaches the top. What is the length of the vine?
In the figure at the left, if the radii of each inscribed circle is 1, what are the dimensions of the bounding rectangle?