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

On the Twentieth Chapter.

The description of the inhabited earth can be accomplished in two ways. The first is on a spherical surface, which properly retains the likeness of the earth, for it is established from spherical elements that this terrestrial world, or this aggregate of land and water, is of a spherical shape. The second way is on a flat surface, which is manifold.

The first method of describing the earth on a spherical surface, or globe, has its advantages and disadvantages. Unless such a globe is convenient and of a just size, such that all parts of the earth itself, and then also the islands, provinces, and principal cities can be inscribed upon its surface, it will have no use, or very little, except for having some arrangement of the parts of the earth. However, it will admit the positions of particular regions and provinces with difficulty, and it will contain even fewer principal cities, except for a few of the more prominent ones. Ptolemy attributes another disadvantage to the globe, because the description of the entire inhabited earth cannot be seen in a single moment on the surface of this globe; rather, one must turn the sight or the sphere. On the other hand, a description of the earth of this kind on a sphere or globe of some noble magnitude has many utilities and advantages. Besides the fact that the arrangement will be similar to the nature of the earth, the distances and dimensions of any places whatsoever can be obtained. For if one takes the distance between two places with a circle, and applies it to the terrestrial Equinoctial or another great circle divided into three hundred and sixty parts, it will give the degrees of the great circle by which those two places differ from one another. When these are converted into miles—by assigning, for instance, fifteen German miles or sixty-two and a half Italian miles to each degree—they will reveal the travel distance between those two places, to which distance a third, or fourth, or another part must be added for the obliquity and inequality of the journey, as that journey happens to be more or less oblique. Furthermore, on a globe of this kind, one can conveniently know the celestial position of any place—that is, in which climate it falls, under which parallel, and by how many degrees either pole is elevated above the horizon of that place—from which we know how great the length of the longest day of any place is. The meridian circle, correctly divided into its parts, will give all these things. Vertical stars can also be known for any place; for a star will be vertical to a city when the star’s declination from the Equator matches the city's latitude, so that both obtain the same distance from the Equator and toward the same region. Similarly, we will also know which stars rise and set in some position on earth, which are always seen above the earth, and which remain perpetually hidden below the horizon. The terrestrial globe also has other notable utilities, which there is no need to relate here, since the booklets of Gemma Frisius, Johannes Tasnier, Johannes Schoner, and others exist concerning its use. Indeed, the notable geographer Gerardus Mercator published both globes, the celestial and the terrestrial, at Duisburg in metal type a few years ago; they are most elegant and delineated with the greatest diligence, the diameter of each of which equals nearly three feet. Besides these, we have both globes, whose diameter is nearly a foot and a half, beautifully engraved and crafted by the diligent man Jacob Floris and published at Antwerp, who also published the terrestrial one alone separately in a larger form. There also exists a terrestrial globe, not to be neglected, described by the most learned man Livio Sanuto and engraved on copper by his brother and published at Venice, which is somewhat larger

continues from previous page: than the globe of Mercator, though far inferior to it in perfection. Besides these, other globes circulate which are very imperfect and not free from significant errors.

The second method of describing the world on a flat surface has this advantage, as Ptolemy says, that it offers all its parts to our view; and according to this method, many ways of describing the world itself on a plane are given. For some have a certain likeness and commensuration with the spherical surface, namely when the meridians have the same relation on the plane that they have on the sphere, whether they are straight or curved, and the parallels on the plane also preserve the same proportion to the Equinoctial that they observe on the sphere. There are other methods, however, in which such commensuration and likeness are not heeded.

Having premised these things, let us come to the explanation of the text. Therefore, since Ptolemy had affirmed that a twofold figuration of the world is given—one, namely, that which is on a spherical surface, and another, which is on a flat surface—he consequently criticizes Marinus because he handed down a description of the world on a plane in his commentaries, believing he was exhibiting it as similar and conformable to the spherical description. For, as Ptolemy says, he makes the distances not at all commensurated, substituting straight lines for the parallels and meridians, which are circular lines, and making the meridians nearly equal to the parallels. Only the parallel through Rhodes did he make correctly commensurated to the meridian, which preserves a sesquiquarter proportion a ratio of 1.25 to 1 to the Equator; the other parallels, however, he did not. For the parallels described by straight lines are not like the parallels that are written on a sphere; for with the sight fixed on the middle of the Northern quadrant of the sphere, in which the greatest part of the world is described—that is, between the North pole of the world and the Equator—all the parallels appear as curved lines, whose convexities are turned toward the South due to the height of the pole. He also criticizes the same Marinus because he did not make the sections of the parallels that fall between the meridians in due proportion with the similar sections of the Equinoctial, but instead made them equal there. Similarly, he extends the distances of the climates that are more Northern than the parallel through Rhodes more than is necessary, and contracts those that are more Southern than the said parallel less; whence it follows that such climates and parallels do not correspond by the number of degrees assigned by him, as is clear in the text.

Furthermore, since Ptolemy at the end of this chapter relates that the Rhodian parallel, which is distant 36 degrees from the Equator, has the same ratio to the Equinoctial that 93 has to 115, and that the parallel through Thule, which recedes from the Equator 63 degrees, has the same ratio to the same Equinoctial that 52 has to 115, we will therefore teach here the method of finding the ratios of all parallels to the Equinoctial, and at the same time, we will prove these two examples of Ptolemy.

A geometric diagram depicts a meridian circle. The main circle is labeled with points A (left), B (top), C (right), and D (bottom). A vertical diameter BD intersects a horizontal diameter AEC at the center E. A horizontal chord F-I-H represents a parallel of latitude above the equator AEC, where I is the intersection point with the vertical axis. An arc above this chord is labeled G. Geometric lines connect points A to D, D to B, and F to I.

Let the Meridian ABC be described on center D, and let the Equinoctial be AEC, whose pole is B. Let the parallel be FGH, whose ratio to the Equinoctial we must find, and let the center of the parallel be I. Let AD, DB, and FI be connected.