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Problems from Another Time

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

Circle With a Chord
In a circle whose circumference is 60 units, a chord is drawn forming a segment whose sagitta is 2 units. What is the length of the chord?
Right Triangle
Given a right triangle where you know the length of the base and the sum of the perpendicular side and the hypotenuse...
 
Circle, Square, and Triangle
A circle, a square and an equilateral triangle all have the same perimeter equal to 1 meter. Compare their areas.
Still More Numbers
Find two numbers, x and y, such that their sum is 10 and x/y + y/x = 25
Storm's a' Brewin'
What is the perpendicular height of a cloud when its angles of elevation were 35 degrees and 64 degrees as taken by two observers?
Deer in the City
Now there are 100 deer [being distributed] in a city. If one household has one deer there is a remainder...Find the number of households in the city.
Perpendicular Curves
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
A Hole in One?
A barrel has various holes in it. The first hole empties the barrel in three days...
Out to Pasture 2
X, Y and Z hired a pasture for the season for $90.00. Each has a different number of mules and are on the pasture for a different number of days. How much is each to pay?
Fields of Grain
I have two fields of grain. From the first field I harvest 2/3 sila (a measurement of grain volume) per sar (a unit of area); from the second, 1/2 sila per sar.

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