Propositiones ad Acuendos Juvenes/Problems/29 - De Civitate Rotunda

by : Problem $29$

 * De Civitate Rotunda: A Round Town
 * There is a round town, $8000$ feet in circumference.


 * I want to build houses there,
 * each house being $20$ feet long
 * and $10$ feet wide.


 * How many houses must it contain,
 * each house being $30$ feet long
 * and $20$ feet wide?

Solution
One circuit of the town is $8000$ feet.

Divided in proportion $3$ to $2$ gives $4800$ and $3200$.

These must contain the length and breadth of the houses.

So take from each one half and there remains:
 * of the larger $2400$
 * and of the smaller $1600$.

Divide $1600$ by $20$, and there are $80$ $20$s.

Again the greater, that is $2400$, divided into $30$s, gives $80$.

Take $80$ times $80$ and there are $6400$.

This is the number of houses which can be built in the town according to the above instructions.