Pytheas sailed northward with the intent of locating the Arctic Circle and exploring the "frigid zone" to the north of it at the extreme of the Earth. He did not know the latitude of the circle in degrees. All he had to go by was the definition of the frigid zone as the latitudes north of the line where the celestial arctic circle was equal to the celestial Tropic of Cancer, the "tropikos kuklos" (refer to the next subsection). Strabo's angular report of this line as being at 24° may well be based on a tangent known to Pytheas, but he did not say that. In whatever mathematical form Pytheas knew the location, he could only have determined when he was there by taking periodic readings of the elevation of the pole ("eksarma tou polou" in Strabo and others).