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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 number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
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;
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
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 number is required; that the square shall be equal to twice the cube.
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

A leech invited a slug for a lunch a leuca away.
If 40 oranges are worth 60 apples, and 75 apples are worth 7 dozen peaches, and 100 peaches are worth 1 box of grapes and three boxes of grapes are worth 40 pounds of pecans, how many peaches can be bought for 100 oranges?
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
One hundred men besieged in a castle, have sufficient food to allow each one bread to the weight of 14 lot a day for ten months.