Anaximander, answered from the texts and cited to the page.
The map followed from the same reasoning that produced the cosmology. If the earth holds its position at the center of the world by being equidistant from all extremities — neither falling nor tilting, since there is no reason for it to move in one direction rather than another — then the inhabited surface of that earth is itself a bounded whole, capable of being surveyed and rendered in outline.1
The principle of sufficient reason that explains the earth's stability also implies that the earth has a determinate shape: the column-form, with two flat faces, one upon which we walk and one opposite.2 The inhabited surface is therefore a finite, mappable thing. Eratosthenes, reported by Strabo, credited me as the first to publish a map of the earth.3
Diogenes Laertius adds that I drew the outline of earth and sea and also constructed a celestial sphere.4 The two achievements belong together: the same geometrical thinking that allows one to plot the positions of the heavenly wheels at numerical distances from the earth's center allows one to project the known coastlines, rivers, and regions onto a flat surface.
The map is the terrestrial counterpart of the celestial model. What the map required was not measurement in the modern sense but the application of a structural principle: that the inhabited world has a center, edges, and proportional distances between its parts, just as the cosmos has a center — the earth itself — and rings at determinate distances.
Miletus, the greatest commercial port of Ionia, gave me the raw material: sailors' reports, merchant routes, the accounts of those who had traveled to Egypt, Persia, Scythia, and the Black Sea colonies. The colony at Apollonia on the Black Sea was founded under my leadership; I had practical knowledge of those routes. The map organized that knowledge according to the same demand for rational coherence that organized the cosmology: not myth, not poetic geography in the manner of Homer's Okeanos ringing the world, but a reasoned projection of the known surface.
The map and the cosmology are a single project. To know where you stand on the earth's surface is to know something about the earth's position in the cosmos; to know the cosmos is to know the shape of the world you inhabit.
For it is appropriate that what is located in the middle and maintains an equal relation to the extremities should not move at all more up than down or to the sides; and it is impossible to move in opposite directions at the same time. So of necessity it remains in place.Early Greek Philosophy Vol II, Anaximander chapter, pp. 31–33
The earth is suspended; it is not controlled by anything, but remains where it is because it is at the same distance from all things. Its form is moist, round, similar to a stone column; of its surfaces, one is that upon which we walk, the other is opposite to it.Early Greek Philosophy Vol II, Anaximander chapter, pp. 14–16
Eratosthenes says that the first two [scil. geographers] after Homer were Anaximander [...] and Hecataeus of Miletus; and that the former was the first to publish a map of the earth.Early Greek Philosophy Vol II, Anaximander chapter, pp. 13–14
And he was the first to draw the outline of the earth and sea, and he also constructed a [scil. celestial] sphere.Early Greek Philosophy Vol II, Anaximander chapter, pp. 13–14