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

IO. ANT. MAGINI

Then the same Marinus is especially commended by Ptolemy because he assigns 500 stadia a unit of distance used in antiquity, roughly 185-200 meters to each celestial degree, whether on the equator or on another great circle, and also because, in the parallel drawn through Rhodes, which is 36 degrees distant from the equator, he assigns only 400 stadia to one degree, although there is a small difference from the truth in this.

Marinus is criticized by Ptolemy in the calculation of two distances enumerated by him. One of these, from the city already mentioned of Hierapolis to the Stone Tower, which is in the region of Saca, contains 876 funes ropes/cables; a unit of measurement for distance, or 26,280 stadia. The other, from the same tower to Sera Metropolim, the capital of the region of Serica, is a journey of seven months and comprises 36,200 stadia. Marinus was mistaken in these distances, as he did not observe an equal verification in them, as can be seen in the text, which is sufficiently easy to understand. Furthermore, it should be noted here that the measure of a funes includes 30 stadia according to Ptolemy and others.

On the twelfth chapter.

Firstly, in this chapter, Ptolemy examines the distance mentioned in the previous chapter, namely, from the Stone Tower in the Saca region under the Byzantine parallel to the Seres, under the Hellespontine parallel, collected from a seven-month journey, which is set by Marinus at 36,200 stadia. He concludes that it must be reduced by half, namely to 18,100 stadia, to which he assigns 45 and one-quarter degrees, by giving 400 stadia to one degree. This is despite the fact that such a number of stadia does not strictly fit under the parallel through Byzantium and the Hellespont as it does under the Rhodian parallel. For strictly under the parallel drawn between Byzantium and the Hellespont, which passes through 42 degrees, only 375 stadia correspond to one degree. Hence, by this reasoning, nearly 48 degrees would correspond to that number of stadia. Therefore, 45 and one-quarter degrees will give a smaller number of stadia for the aforementioned distance, namely 16,970 stadia.

Secondly, Ptolemy refutes the comparison by which Marinus likens the path from the Stone Tower to that which stretches from the Garamantes to the region of Agisymba; nor does he wish to concede that such a large reduction of stadia occurs in both. From the former path, he reduces the distance from the Euphrates to the Stone Tower, which is subjected to 876 funes, to only 800 funes, which makes 24,000 stadia, due to the detours of the particular roads, which Ptolemy enumerates one by one. He then converts these 24,000 stadia into degrees. Since 400 stadia correspond to one degree under the Rhodian parallel, he adds these to the 45 and one-quarter degrees congruent to the interval from the Euphrates to the Seres, and concludes that the longitude between the Euphrates and the Seres is 105 and one-quarter degrees.

Finally, having examined some intervals of particular places, he concludes that the longitude from the Fortunate Islands to the Euphrates is 72 degrees. From these, he concludes that the total longitude of the known earth is 177 and one-quarter degrees. This is established by adding the 72 degrees of the distance of the Fortunate Islands to the Euphrates to the 105 and one-quarter degrees of the distance between the Euphrates and the Seres.

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COMMENT. ET ANNOT.

On the thirteenth chapter.

Since in the previous chapter Ptolemy had concluded from certain terrestrial journeys that the longitude of the known world is 177 and one-quarter degrees, he now attempts to confirm the same in these two chapters from certain navigations. In this chapter, having examined five particular distances, he concludes that the longitude between the Cory promontory and the Golden Chersonese is 34 degrees and 48 minutes.

The first of these distances is between the Cory promontory and the city of Curura or Curula, at 3,040 stadia. From this distance, Ptolemy first subtracts a third part, which is 1,010 stadia according to Ptolemy, and from the remaining number of 2,030, he again takes away a third part, namely 680. Finally, he takes only half of this remaining number of 1,350, which is 675 stadia, and asserts that this is the distance between the two places measured on a parallel circle of the equator. And so that his reasoning may be more clearly revealed, let us present the following figure, in which A is understood as the Cory promontory, C as the city of Curura, ABC as the Argarian gulf approaching the form of a semicircle, AC as the direct distance between the two aforementioned locations, CD as the meridian drawn through Curura, and E as the meridian through Cory, with AD being the portion of the parallel entering through Cory falling between the two meridians, which it is necessary to know. For the sake of simplicity, we shall take all these arcs as straight lines, since each of them differs little from a straight line. A geometric diagram displays a right-angled triangle CAD. Point A is at the bottom left, D at the bottom right, and C is directly above D. A curved line ABC (labeled B in the middle) arcs from A to C. A vertical line AE extends upwards from point A. A diagonal line AC connects A and C. Labels include E, B, C, A, and D. It is therefore evident that the first distance between Cory and Curura along the path of the ABC gulf is 3,040 stadia. But since the aforementioned navigation was uneven, and not without certain intercepted delays due to the unevenness of the winds, a third part should deservedly be removed from this sum so that an equalized navigation of 2,030 stadia results, according to the journey of the aforementioned ABC gulf. When this gulf represents the form of a semicircle, the proportion of the curved line ABC to the straight line AC will be as 11 to 7, according to the reasoning of Archimedes, by which it is established that the circle has a triple sesquiseptimal proportion to the diameter, that is, as 22 to 7. Indeed, Ptolemy did not observe this ratio precisely, but he assumes a proportion of 12 to 8, namely sesquialter, for the aforementioned curved line ABC to the straight line AC, increasing each number by one, which differs little from the aforementioned proportion of a circle to its diameter. Therefore, with a third part taken away from the said sum, the corrected direct distance AC of 1,350 stadia between Cory and Curura remains. Having known this, we shall consider the triangle CAD, which is right-angled: for the meridian CD is at a right angle to the parallel AD, because it passes through its poles. Therefore, since the straight line AC deflects from the meridian AE of the Cory promontory toward the North, the angle FAC will be 30 degrees, that is, one-third of one right angle: for the North wind recedes 30 degrees from the meridian line from the northern part toward the East, according to the tradition of the ancients who posited 12 winds; wherefore...