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Problems from Another Time

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

Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.
I owe a man the following notes: one of $800 due May 16; one of $660 due on July 1; one of $940 due Sept. 29. He wishes to exchange them for two notes of $1200 each and wants one to fall due June 1. When should the other be due?
A certain man had in his trade four weights with which he could weigh integral pounds from one up to 40. How many pounds was each weight?
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
Given a semicircle, Prove that if O is the circle's center, DO=OE.
What is the value of X...
Of a collection of mango fruits, the king took 1/6; the queen 1/5 the remainder, and the three princes took 1/4, 1/3 and 1/2 (of the same remainder); and the youngest child took the remaining 3 mangoes.
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.
Three vertical posts along a straight canal, each rising to the same height above the surface of the water. By looking at the line of vision, determine, to the nearest mile, the radius of the earth.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?