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Problems from Another Time

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

Dimensions of a Triangle
Determine the dimensions for a right-angled triangle, having been given the hypotenuse, and the side of the inscribed square.
University Payment Plan
A merchant gave a university 2,814 ducats on the understanding that he was to be paid back 618 ducats per year for 9 years, at the end of which the 2,814 ducats should be considered as paid.
Logarithms: The Early History of a Familiar Function - About the Authors and More Information on Sources
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.
Silver and Gold
There are two piles, one containing 9 gold coins, the other 11 silver coins.
Coins
A boy gives 11 coins of equal denomination to a man, and the man finds that their total value in yen is 4 less than his age.
Looking for Bargains
One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?
'He Advanced Him 200 Lambs of Gold': The Pamiers Manuscript - Proportionality Techniques
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
Log Stuck in a Wall
Now given a cylindrical log of unknown size buried in a wall...
Harvest Time
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now, supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?
Free Fertilizer
If 12 oxen eat up 3 1/3 acres of meadow in 4 weeks and 21 oxen eat up 10 acres of exactly similar meadow in 9 weeks, how many oxen shall eat up 36 acres in 18 weeks? (Hint: The grass continues to grow.)

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