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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 man died leaving 3 sons, to whom he bequeathed his estate in the following manner: to the eldest he gave 184 dollars; to the second 155 dollars and to the third 96 dollars;
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.
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 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 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?
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.
Given a semicircle, Prove that if O is the circle's center, DO=OE.
The third part of a necklace of pearls, broken in a lover's quarrel, fell to the ground...
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.
Given the fraction ax/ (a-x ), convert it into an infinite series.