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Problems from Another Time

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

If a ladder, placed 8 ft. from the base of a building 40 ft. high, just reached the top, how far must it be placed from the base of the building that it may reach a point 10 ft. from the top?
An oracle ordered a prince to build a sacred building, whose space would be 400 cubits, the length being 6 cubits more than the width, and the width 3 cubits more than the height. Find the dimensions of the building.
Discussion of 15th century French manuscript, with translation of its problems, including one with negative solutions
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.
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.
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?
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 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.

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