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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 certain lake, swarming with red geese, the tip of a lotus bud was seen to extend a span [9 inches] above the surface of the water.
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse.

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?
Determine by using algebra the number of degrees in the angle A where: cos A = tan A
What number which being increased by 1/2, 1/3, and 1/4 of itself, the sum shall be 75?
A certain slave fled from Milan to Naples going 1/10 of the whole journey each day. At the beginning of the third day, his master sent a slave after him and this slave went 1/7 of the whole journey each day.
A gentleman has bought a rectangular piece of land whose perimeter is to be 100 rods.
There is a round fish pond of certain dimensions, and into the pond is dropped a marble column. How high will the water rise?
A copper water tank in the form of a rectangular parallelopiped is to made. If its length is to be a times its breadth, how high should it be that for a given capacity it should cost as little as possible?
A ladder is placed perpendicular to the plane of the horizon, and in coincidence with the plane of an upright wall.