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Problems from Another Time

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

In a right triangle, let the perpendicular be 5 and the sum of the base and hypotenuse 25. Find the lengths of the base and hypotenuse
A general formed his men into a square, that is, an equal number in rank and file, and he found that he had an excess of 59 men.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11 and a second side has length 19. Find the lengths of the sides of the second triangle.
A man went to a draper and bought a length of cloth 35 braccia long to make a suit of clothes.
Make of 10 three parts such that one part multiplied by 3 makes as much as the other multiplied by 4 and as the other multiplied by 5.
A water tub holds 73 gallons; the pipe which fills it usually admits 7 gallons in 5 minutes; and the tap discharges 20 gallons in 17 minutes.
One military horse cannot pull a load of 40 dan; neither can 2 ordinary horses, nor can three inferior horses...
Prove that if the sums of the squares of opposite sides of any quadrilateral are equal, its diagonals intersect at right angles.
A pond has two water reeds, where the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes every day half of that of the preceding day, while the other grows twice as much as on the day before.
The authors recount the 'great tale' of Napier's and Burgi's parallel development of logarithms and urge you to use it in class.

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