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Problems from Another Time

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

An Inscribed Ellipse
Given right triangle ABC where C is the right angle, ellipse O (a,b) is inscribed in it, with its major axis parallel to BC. Calculate the semi-major axis, a, in terms of AC, BC and b.
Viete: Triangle II
In a right triangle, the hypotenuse is 13 and the sum of the sides around the right angle is 17. Find the lengths of the sides around the right angle.
Travelling Steamers
The steamer, Katie, leaves the wharf at New Orleans and runs an average speed of 15 mph. When Katie had gone 25 miles, the steamer R.E. Lee leaves the wharf and runs the average speed of 18 mph. How far will the Lee go before she overtakes the Katie?
Reverse the Digits
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 Clothes Call
A man went to a draper and bought a length of cloth 35 braccia long to make a suit of clothes.
10 Into 3 Parts
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.
Long Time to Fill the Tub
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.
Horsing Around
One military horse cannot pull a load of 40 dan; neither can 2 ordinary horses, nor can three inferior horses...
Squared Proof
Prove that if the sums of the squares of opposite sides of any quadrilateral are equal, its diagonals intersect at right angles.
Water Reeds
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.

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