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Problems from Another Time

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

There is a four-sided field whose eastern side measures 35 paces, its western side 45 paces, its southern side 25 paces and its northern side 15 paces. Find the area of this field.
A cylindrical tin tomato can is to be made which shall have a given capacity. Find what should be the ratio of the height to the radius of the base that the smallest possible amount of tin shall be required.
A round pond sits in a rectangular garden. Its center is inaccessible; however, you know the distances from each corner of the garden to the center of the pond: 60, 52, 28, and 40 yards. What is the radius of the pond?
The sum of the two digits of a 2-digit number is 9. If 45 is subtracted from the number, the result will be expressed by the digits in reverse order. Find the number.
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
To find three quantities x.y, and z...
A carpenter has undertaken to build a house in 20 days. He takes on another man and says; "If we build the house together, we can accomplish the work in 8 days!" How long would it take this other man to build the house working alone?
There are two numbers which are to each other as 5 and 6 and the sum of their squares is 2196. What are the numbers?
A fellow said that when he counted his nuts by twos, threes, fours, fives and sixes, there was still one left over; but when he counted them by sevens they came out even. How many did he have?
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...

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