“I will not inquire,” says Polybius, “whether the statement concerning the 3000 stadia is correct or not, but 7000 stadia is not the correct measure [from the Strait of Messina to the Pillars of Hercules], whether taken along the sea-shore, or right across the sea. The coast closely resembles an obtuse angle, one side reaching to the Strait of Sicily, the other to the Pillars, the vertex being Narbonne. Now let a triangle be constructed, having for its base a right line drawn through the sea, and its sides forming the aforementioned angle. The side reaching from the Strait of Sicily to Narbonne is above 11,200 stadia, while the other is below 8000. Now the greatest distance from Europe to Libya, across the Tyrrhenian Sea,[670] is not above 3000 stadia, and across the Sea of Sardinia[671] it is less still. But supposing that it too is 3000 stadia, add to this 2000 stadia, the depth of the bay at Narbonne, as a perpendicular from the vertex to the base of the obtuse-angled triangle. It will, then, be clear even to the geometrical powers of a child, that the entire coast from the Strait of Sicily to the Pillars, does not exceed by more than 500 stadia the right line drawn across the sea; adding to these the 3000 stadia from the Peloponnesus to the Strait of Sicily, the whole taken together will give a straight line[672] above double the length assigned by Dicæarchus; and, according to his system, you must add in addition to these the stadia at the recess of the Adriatic.” 3. True, dear Polybius, (one might say,) this error [of Dicæarchus] is manifested by the proof which you yourself have given when you inform us that from the Peloponnesus to Leucas[673] there are 700 stadia; from thence to Corcyra[674] the same number; and the same number again from Corcyra to the Ceraunian Mountains;[675] and from the Ceraunian Mountains to Iapygia,[676] following the coast of Illyria on the right, 6150 stadia.[677] But the statement of Dicæarchus, that the distance from the Strait of Sicily to the Pillars is 7000 stadia, and also your view of the matter, are both of them equally incorrect. For almost every one is agreed that the distance measured straight across the sea is 12,000 stadia, and this coincides with the received calculation of the length of the inhabited earth, which is estimated at above 70,000 stadia; the western portion of this from the Gulf of Issus[678] to the extreme western point of Iberia is little less than 30,000 stadia, and is thus calculated: from the Gulf of Issus to Rhodes 5000 stadia; from thence to Cape Salmonium,[679] which forms the eastern extremity of Crete, 1000; the length of Crete to Criu-metopon[680] above 2000; thence to Cape Pachynus[681] in Sicily 4500, and from Pachynus to the Strait of Sicily above 1000 stadia; the run from the Strait to the Pillars 12,000; and lastly, from the Pillars to the extremity of the said promontory[682] of Iberia, about 3000 stadia.[683]