Greek Anthology Book XIV: Metrodorus: 121

Arithmetical Epigram of Metrodorus

 * From Cadiz to the city of the seven hills
 * the sixth of the road is to the banks of Baetis, loud with the lowing of herds,
 * and hence a fifth to the Phocian soil of Pylades -- the land is Vaccaean, its name derived from the abundance of cows.
 * Thence to the precipitous Pyrenees is one-eighth and the twelfth part of one-tenth.
 * Between the Pyrenees and the lofty Alps lies one-fourth of the road.
 * Now begins Italy and straight after one-twelfth appears the amber of the Po.


 * O blessed am I who have accomplished two thousand and five hundred journeying thence!
 * For the Palace on the Tarpeian rock is my journey's object.

Solution
The city of the seven hills, and the location of the Palace on the Tarpeian rock, is of course Rome.

Let $n$ be the number of between Cadiz and Rome.


 * $\dfrac n 6$ is the distance from Cadiz to the Baetis


 * $\dfrac n 5$ is the distance from the Baetis to Pylades


 * $\dfrac n 8 + \dfrac n {120}$ is the distance from Pylades to the Pyrenees


 * $\dfrac n 4$ is the distance from the Pyrenees to the Alps


 * $\dfrac n {12}$ is the distance from the Alps to the Po


 * $2500$ is the distance from the Po to Rome itself.

So we have:

So it is $15 \, 000$ from Cadiz and Rome, of which:


 * $2500$ is the distance from Cadiz to the Baetis


 * $3000$ is the distance from the Baetis to Pylades


 * $2000$ is the distance from Pylades to the Pyrenees


 * $3750$ is the distance from the Pyrenees to the Alps


 * $1250$ is the distance from the Alps to the Po

and as we know:


 * $2500$ is the distance from the Po to Rome itself.