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Chaos umpire sits
And by decision more
embroils the fray
by which he reigns: next
him high arbiter
Chance governs all.

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# Mathematical Treasures

## Antichissimo di Algorismo

Two illustrations follow from the fourteenth century Italian codex, Antichissimo di Algorismo. This is one of many algorisms written at this time. They were arithmetics designed to introduce the Hindu-Arabic numerals and their operational algorithms and to demonstrate their use in problem solving. The majority of the problems considered in this codex are commercial in nature. A few might be categorized as “recreational problems.” The two shown here are of this nature and have remained favorites over the years. A special feature of this codex is that it contains 42 illustrations, many of which supplement problems. These two illustrations are of this kind.

The picture found on folio 59 depicts a situation where two men must divide an item equally. The two companions have eight ounces of balm in an eight ounce vase. At their disposal they have two other vases, one holding three ounces, and the other five ounces. How can they accomplish the equal division?

The illustration on folio 60 presents the situation in which three couples wish to cross a stream. The small boat they have will accommodate only two persons at a time. How can they all get to the other shore if no man is to cross with another’s wife? This is a variation of the puzzle-type "River Crossing Problem” that has been posed over the centuries in many guises.