# Convergence articles

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One says that 10 is divided into three parts and if the small part is multiplied by itself and added to the middle one multiplied by itself the result is the large one multiplied by itself...
This is from a letter of June, 1695 in which Leibniz is discussing differentiation with Johann Bernoulli. The work in which these letters appear is the Virorum Celeberr. Got. Gul. Leibnitii et Johann Bernoulli Commercium Philosophicum et Mathematica, originally published in 1740.
Suppose that for every 4 cows a farmer has, he should plow 1 acre of land, and allow 1 acre of pasture for every 3 cows; how many cows could he keep on 140 acres?
A man bought a number of sheep for $225; 10 of them having died, he sold 4/5 of the remainder for the same cost and received$150 for them. How many did he buy?
If in a circle ABDC, circumscribe an equilateral triangle ABC; the straight line AD is equal to the sum of the two straight lines BD and DC: required a demonstration.
Two travelers, starting at the same time from the same point, travel in opposite directions round a circular railway.
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.
Given four integers where if added together three at a time their sums are: 20, 22, 24, and 27. What are the integers?

The author shows how teachers can use Leonhard Euler's original works in the classroom to explore Euler's famous polyhedral formula,
V + F = E + 2.

Given a number, take 1/3 of the number away from itself and add 2. If this result is multiplied by itself, it equals the number plus 24. What is the number?