# Convergence articles

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A merchant gave a university 2,814 ducats on the understanding that he was to be paid back 618 ducats per year for 9 years, at the end of which the 2,814 ducats should be considered as paid.
A teacher agreed to teach 9 months for $562.50 and his board. At the end of the term, on account of two months absence caused by sickness, he received only$409.50. What was his board worth per month?

Three images from Kepler's 1609 Astronomia Nova, the text in which he introduced his first two laws of planetary motion

There is a lion in a well whose depth is 50 palms. He climbs and slips back a certain amount each day. In how many days will he get out of the well?
Two men brought their fish through customs. Find how much the fish cost, and what is the customs fee.
Determine the dimensions of the least isosceles triangle ACD that can circumscribe a given circle.
One says that 10 garments were purchased by two men at a price of 72 dirhams. The garments varied in value. The price of each garment of one man is 3 dirhams more than the price for each garment of the other. How many garments did each man buy?
In a right triangle, the hypotenuse is 9.434 and the sum of the sides around the right angle is 13. Find the lengths of the sides around the right angle.
This conference takes place in 2006 at Pennsylvania State University, Erie.
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