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
+dioptra+, 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. Duemmler, _Antisthenica_ (1882); _Akademika_ (1889). Cf.
the _Life of Antisthenes_ in Diog. Laert.

[87:2] +Geron opsimathes+, 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 +logos+ or
thing to be said about it; if you say a different +logos+ you are
speaking o