# Convergence articles

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A wooden beam is stood vertically against a wall. The length of the beam is 30 units.
Page 12: Dilworth to Doob
Find the two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27
Given a door and a measuring rod of unknown dimensions, the rod is used to measure the door.
This is the title page of the 1640 printing of Galileo's Operation of the Geometrical and Military Compass, originally published privately in 1606. Galileo had invented a version of this geometrical compass a few years earlier and evidently gave copies of this manual to those who bought the compass. The compass had many uses, from performing square root calculations to determining ranges of cannons to solving surveying problems.
Having been given the sum of two numbers,a, and the difference of their squares,b, find the numbers.
I found a stone but did not weigh it; after I added to it 1/7 of its weight and then 1/11 of this new weight, I weighed the total at 1 mina. What was the weight of the stone?
A circle is inscribed in an isosceles trapezoid. Find the relationship of the radius to the sides.
A fish sees a heron looking at him from across a pool, so he quickly swims towards the south. When he reaches the south side of the pool, he has the unwelcome surprise of meeting the heron.
When knowing the sum of their ages along with another equation, determine how old a father and son are.