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Problems from Another Time

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

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.
Gun metal of a certain grade is composed of 16% tin and 84% copper. How much tin must be added to 410 lbs. of this gun metal to make a composition of 18% tin?
Now there are six-headed four legged animals and four-headed two-legged birds. Find the total number of animals and birds.
The perimeters of two similar triangles are 45 and 135 respectively. One side of the first triangle has length 11″ and a second side, 19″. Find the lengths of the sides of the second triangle.
Suppose General [George] Washington had 800 men and was supplied with provisions to last 2 months but he needed to feed his army for 7 months.
A guest on horseback rides 300 li in a day. The guest leaves his clothes behind and the host rides off to catch up with the guest once he discovers the clothes. Assuming the host rides without stop tell how far he can go in a day?
I have two fields of grain. From the first field I harvest 2/3 a bushel of grain/unit area; from the second, 1/2 bushel/unit area.
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Two men have a certain amount of money. The first says to the second, "If you give me 5 denari, I will have 7 times what you have left."
Prove that the area of a regular polygon can be given by the product of its perimeter and half the radius of the inscribed circle.

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