The Geography

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[Page 3]

...it is geometric, for through the pure measurement of distances it shows how places are situated among themselves. As it relates to the celestial bodies, it teaches the positions of those same places by means of the fixed stars, using astrolabe organs invented for capturing shadows. And this is indeed certain and in no way doubtful. But the other kind is both more imperfect and stands in need of the former. For first, since it is necessary in both modes to suppose in what direction the distance of two places tends. For it is not only necessary to know how far this place is from that one, but toward which region of the sky: that is, whether to the north, or, so to speak, to the rising of the sun [east], or other particular inclinations; it is impossible for this to be considered more diligently without the help of the said instruments. For from these, in every place and at every time, the meridian line can easily be found, through which knowledge of these traversed distances is gained.

Then, even given this measurement, the fact that it consists of a number of stadia does not provide us with certain knowledge on account of journeys which are rarely in a straight line; with many diversions made by land and sea, so that it is necessary to conjecture from the terrestrial journey, according to the quality and quantity of the oblique distances, that which is a straight path, and to reduce the sum of the stadia so that the straight way may be found. This also happens in navigations for that reason: and because the blowing of the winds is least preserved with equality throughout the entire journey. Furthermore, even if the distance of those places is diligently held, yet no account is held of the whole circuit of the earth: nor is the site of the same captured in relation to the equinoctial circle [the Equator] or to the position of the poles.

However, the distance which is acquired from the observation of the heavens diligently shows any of these things. Furthermore, it shows what arcs the parallel circles and meridians, which are described through those places, intercept in turn—that is, what arcs they intercept in the southern parallels and the equinoctial, and what meridians intercept in the parallels and the equinoctial. From there it is taught what part the two places occupy of the circumference of the greatest circle which is circumscribed through the same on the earth. Which dimension, obtained from the aforementioned enumeration of stadia, does not lack a ratio of the parts of the earth to the circuit of the whole description.

[Margin: In what way the state of the world can be measured]

For it is enough to suppose the circulation of the earth itself to be of as many parts as one pleases, and that these are contained by the distances noted in the greatest circles of the earth itself. But for dividing the whole circuit of the earth, or its parts, into distances known by our measurements of stadia, this alone is not sufficient. Wherefore for this reason alone it was necessary to adapt a certain straight distance on earth to some circumference of a certain greatest celestial circle; and having obtained the proportion of this to the whole circle from the fixed stars, and having perceived the number of stadia of that part (or of the given distance on earth), we shall be able to measure the circuit of the whole world by stadia.

For since it is granted from mathematical demonstrations that the whole surface of the earth and water is spherical and has the same center as the sphere of the heavens, and that any planes which are emitted through the center make greatest circles in the common sections of themselves and the surfaces of heaven and earth: because those angles of the same planes which are around the center make the intercepted circumferences of the circles themselves of one and the same ratio, it follows that the distances which we take on earth (in a quantity of stadia, provided the distances are straight from measurements) can be perceived. But by the ratio of those same stadia to the whole circuit of the earth, they are by no means found, because no proportion to the whole can be given from here. But from a similar arc of the celestial circle it is given. For the ratio of the celestial circumference is captured in the proper circulation of the whole earth: and the same ratio and a similar portion exists in the circle of the earth as to its greatest circle.

[Term: How from the dimension of stadia of any straight distance, even if it is not under the same meridian, the measure of the circuit of the earth is to be perceived, and vice versa.]

[Initial Q]
THE ANCIENTS sought not only the straight distance on earth so that they might capture the circumference of the greatest circle; but they held that sought distance in a plane...

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