Claudius Ptolemaeus; Giovanni Antonio Magini — Geographiae universae tum veteris, tum novae (1597)

such a region, and from the other the West. I will not omit to say that although Ptolemy says that in the Geometric way it is absolutely necessary to use meteoroscopic instruments to find the meridian line, and with its help afterwards the other parts of the world, nevertheless in our times it is sufficiently convenient, without any instrument, to have such a meridian line and the remaining parts of the world solely with a magnetic compass, as is known to those who know how to use a nautical compass. It must also be noted that Ptolemy here understands by particular inclinations the degrees or parts of the circle by which any place is removed from the line of one part or region of the world, because it is not enough to say this city faces toward the East, or toward the West, since there are few that face precisely these parts, but for the most part they decline either to one side or the other from the said lines. Hence it is more convenient to know how many parts or degrees the said places recede from the said principal parts; but it is appropriate for Geographers and Astronomers to know that it is customary to divide the entire circle into 360 degrees, and to count 90 degrees from any region to another. If, however, this consideration is to be made with respect to the eight principal winds, we will count 45 degrees from one wind to another. And so, when we wish to describe the true inclination of one place with respect to another, we will say, for example, that it recedes so many degrees from the North or from another region, or even from the North-West, or from the South-East, or from another wind, as it has been known from observation.

Where Ptolemy later adds that the Geometric measurement of places, which is by stadia, is quite unsafe for having the true distance of places from one another, he seems openly to conclude the Geometric way to be very imperfect. Since exact itineraries, whether terrestrial or maritime, can never be had through measurement due to their tortuosity and flexibility, therefore a certain correction is always necessary in them, which is done by adding or taking away, that is, by subtracting from such a measurement that quantity which the tortuosity and inequality of the journey can increase in the aforesaid distance. It is to be understood, however, that such a Geometric way is unsafe for having the true measure of distances which would be found from place to place when there is no impediment and one could proceed by a direct path, and also to know how much such a measurement is in proportion to the heaven. Truly, it serves quite conveniently for daily use, that is, for the knowledge of journeys and distances of places, so that one can know how much time is consumed by proceeding from place to place.

As far as navigation is concerned, although according to Ptolemy it is difficult by itself to investigate the length of a journey due to the unequal motion of the ship, which depends on the wind, which are at times weak and at times strong, nevertheless some ingenious men have been found who have known how to measure the journey that a ship completes at any time, even if it moves now faster, now slower. Furthermore, Vitruvius teaches a most beautiful method in the 14th chapter of the tenth book of his Architecture, with certain wheels which ought to be moved by the motion of the ship, by counting the revolutions of the wheels themselves, because these wheels show the quantity of the journey very well; nor does it matter whether the ship moves now quickly or slowly, because the wheels will move in the same way.

It remains to be said concerning this place, that Ptolemy here and elsewhere always uses stadia in the measure of the earth, which is the measure of the Greeks, and a stadium consists of 125 paces, as Columella says in the first chapter of the fifth book, that is, 600 feet, for a pace