And, with all this, we have not touched on his greatest work, which was in the sphere of geography. He wrote a Περίοδος γῆς, a _Journey Round the Earth_, accompanied with a map. He used for this map the greatly increased stores of knowledge gained by the Macedonian expeditions over all Asia as far as the Ganges. He also seems to have devised the method of denoting the position of a place by means of two co-ordinates, the method soon after developed by Eratosthenes into Latitude and Longitude. He attempted calculations of the measurements of large geographic distances, for which of course both his data and his instruments were inadequate. Nevertheless his measurements remained a well-known standard; we find them quoted and criticized by Strabo and Polybius. And, lastly, he published _Measurements of the Heights of Mountains in the Peloponnese_; but the title seems to have been unduly modest, for we find in the fragments statements about mountains far outside that area; about Pelion and Olympus in Thessaly and of Atabyrion in Rhodes. He had a subvention, Pliny tells us (N. H. ii. 162, 'regum cura permensus montes'), from the king of Macedon, probably either Cassander or, as one would like to believe, the philosophic Antigonus Gonatas. And he calculated the heights, so we are told, by trigonometry, using the δίοπτρα, an instrument of hollow reeds without lenses which served for his primitive theodolite. It is an extraordinary record, and illustrates the true Peripatetic spirit. FOOTNOTES: [79:1] _Hellen._ ii. 2, 3. [80:1] Cf. Tarn, _Antigonus Gonatas_, p. 52, and authorities there quoted. [81:1] Lysias, xxxiii. [82:1] Dem. _Crown_, 208. [83:1] 'Such-like trash', _Gorgias_, 519 A; dust-storm, _Rep._ vi. 496; clothes, _Gorg._ 523 E; 'democratic man', _Rep._ viii. 556 ff. [84:1] _Laws_, 709 E, cf. Letter VII. [85:1] Aulus Gellius, xiv. 3; Plato, _Laws_, p. 695; Xen. _Cyrop._ viii. 7, compared with _Hdt._ i. 214. [87:1] This is the impression left by Xenophon, especially in the Symposium. Cf. Dümmler, _Antisthenica_ (1882); _Akademika_ (1889). Cf. the _Life of Antisthenes_ in Diog. Laert. [87:2] Γέρων ὀψιμαθήϛ, Plato, _Soph._ 251 B, Isocr. _Helena_, i. 2. [87:3] e. g. no combination of subject and predicate can be true because one is different from the other. 'Man' is 'man' and 'good' is 'good'; but 'man' is not 'good'. Nor can 'a horse' possibly be 'running'; they are totally different conceptions. See Plutarch, _adv. Co._ 22, 1 (p. 1119); Plato, _Soph._ 251 B; Arist. _Metaph._ 1024{b} 33; Top. 104{b} 20; Plato, _Euthyd._ 285 E. For similar reasons no statement can ever contradict another; the statements are either the same or not the same; and if not the same they do not touch. Every object has one λόγος or thing to be said about it; if you say a different λόγος you are speaking of something else. See especially _Scholia Arist._, p. 732{a} 30 ff. on the passage in the _Metaphysics_, 1024{b} 33.