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Problems from Another Time

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

Find the area of the elliptical segment cut off parallel to the shorter axis;
A number of 3 digits in base 7 has the same three digits...
If two Post-boys, A and B at 59 miles distance from one another, set out in the morning in order to meet...
The purchase price for an apple and an orange is 100 yen. When n oranges and n + 3 apples are bought the price is 520 yen. Find the number n of oranges and the price of one orange.
Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
The square of a certain number multiplied by itself and by 200 is 446,976. What is the number?
Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
Given four numbers whose sum is 9900; the second exceeds the first by 1/7 of the first...
The cavity of our chimney is an upright parallelepiped, the diagonal of whose base is 60"; and the height of the lower side of the lintel above the plane of the floor is 40".