# Convergence articles

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A mouse is at the top of a poplar tree 60 braccia high, and a cat is on the ground at its foot. The mouse decends 1/2 a braccia a day and at night it turns back 1/6 of a braccia.
Having been given the lengths, a and b, of two straight lines drawn from the acute angles of a right triangle to the middle of the opposite sides, determine the length of those sides.
A woodcutter starts to fell a tree 4 feet in diameter, and cuts half way through. One face of the cut is horizontal, and the other face is inclined to the horizontal at an angle of 45 degrees. Find the volume of the wood cut out.
This is an invited working conference as part of the ICMI Study Series.
The edge of a cloud is at an altitude of 20 degrees and the sun above it at 35 degrees. The shadow cast by the edge of the cloud fall on a object 2300 yards away, how high is the cloud?
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?

Our reviewer praises the selection of excerpts, the use of facsimiles rather than transcriptions, and the commentary and English translation in this collection.

The Arithmetic of Boethius (480-524) dates from the early sixth century. This page is from a mansucript (Plimpton MS 165) that dates from approximately 1294, written on vellum.
A barrel has various holes in it. The fist hole empties the barrel in three days...
A listing of the history sessions at the 2008 Joint Mathematics meetings in San Diego, January 4-9, 2008.