The Geography

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...under one and the same meridian. Whence, observing through the instruments which we have mentioned the points which were above the vertex [the zenith] of each end of the given distance: from these signs, through the intercepted circumference of the meridian, they held the distance noted on the earth under an equal proportion. For as has been said, the signs through the planes were assumed in one plane, and the lines passing through the ends of the distance to the points which were above the vertex necessarily converged, and the point of this coincidence was the common center of their joints. Therefore, whatever part of the circle described through the poles seemed intercepted by both points assumed above the vertex was the whole circumference to the entire circuit of the earth.

But if a distance of this kind is not under a circle described through the poles, but under any other of the greatest circles, the same can be shown: by observing in a similar way the elevations of the pole at the terms of that distance and considering at the same time the position which the distance itself has to the other meridians. Which things we have clearly demonstrated through an instrument which we constructed for the observation of shadows: through which we may easily capture many other very useful things. And on any day or night, by the elevation of the northern pole, and at every hour, we have the meridian position of the given distance and its dimension; that is, what angles the greatest circle described through the line of distance makes with the meridian circle near the point which is above the vertex. From which we show both the quality of the circumference through the instrument itself and the circumference of the equinoctial intercepted by two meridians, if the parallels be other than the equinoctial.

Whence, according to this demonstration, if we measure a single and straight distance on earth, the number of stadia of the whole circuit of the earth can be found. By this means, however, it remains that the dimension of all other distances, even if they are not entirely straight, nor perceived from the same meridian or parallel, may be obtained, provided the elevation of the pole and the inclination of the distance to the meridian are diligently preserved. For on the contrary, according to the ratio of the circumference to the greatest circle, the number of stadia can easily be held from the known circulation of the entire earth.

[Term: That observations from higher things are to be preferred to the knowledge of travelers.]

[Initial I]
THESE THINGS being thus held, those who traveled through regions one by one, if they had used observations of this kind, could have made an entirely certain description of our habitable world. But since Hipparcus [Hipparchus] alone has handed down to us the elevations of the arctic pole for a few cities (in proportion to the abundance of those which are noted in cosmography), he noted places for very few situated under the same parallels. Some truly after him related a certain [distance] of opposite places: noting that they were equally distant from the equator; but they assumed them simply to be situated under the same meridians from navigations, or from journeys made with a favorable north or south wind. But most of the distances, especially those which tend toward the rising or the setting of the sun, were conceived from a certain general tradition: not from the laziness of the authors themselves, but because the use of more diligent mathematics was not yet available.

Furthermore, because not many lunar eclipses had been observed at the same time in different places, as that eclipse which was noted at Arbela at the fifth hour, but at Carthage at the second: from which it could be seen by how many equinoctial hours or by what spaces of time places differed between themselves toward the rising or setting of the sun. It is also fair that he who knows the description of cosmography should prefer those things noted by more diligent observation as the foundations of his work; but adapt other things handed down by others to these, until their positions relative to one another are found more certain with the first traditions, as much as can be done.

[Term: That newer histories are more to be believed on account of changes which happen in the world at different times.]

[Initial I]
THE BEGINNING of our description, these things having been tasted beforehand, can thus be held equally. But since one cannot [know] all places because of their infinite magnitude, or because they are not...

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