Propositiones ad Acuendos Juvenes/Problems/9 - De Sago

by : Problem $9$

 * De Sago: A Cloak
 * I have a cloak, $100$ cubits long and $80$ cubits wide.
 * I wish to make small cloaks with it, each small cloak $5$ cubits long and $4$ cubits wide.


 * How many small cloaks can I make?

Solution

 * $400$.

Proof
It is assumed there is no cloth spent on hems, and the making of a small cloak consists of little more than cutting a piece of cloth to the required size.

We have that:
 * $5$ goes into $100$ a total of $20$ times
 * $4$ goes into $80$ also a total of $20$ times.

Thus the cloth can be cut into $20 \times 20 = 400$ pieces that are $5$ cubits long and $4$ cubits wide.