Автор сообщения: Егермейстер
Дата и время сообщения: 19 May 2004 at 07:54:29:
В ответ на сообщение: Мир глазами Птолемея: Попытка решения задачи, ч. 4
Как было обещано, Птолемей, "География", Книга 8, Глава 2.
Chapter II. What adaptation on each map is necessary
Such things therefore being presupposed, let us begin the task of a division such as the following:
We will make ten maps for Europe; we will make four maps for Africa; for Asia we will make twelve maps to include the whole, and we will state to which continent each map belongs, and how many and how great are the regions or provinces in each, and we will further explain what ratio the parallel which passes through the middle of the region has to the meridian, stating also what is the circumference of the entire map, and giving throughout each region the assumed elevation (latitude and longitude) of the chief cities, and the greatest length of a day in each of them.
We shall take the measure of distances in longitude without traveling to each mentioned locality, but from the meridian of Alexandria, either at sunrise or sunset, and from the number of equinoctial hours between the places. Besides this we shall find in which of the constellations of the celestial circle is the longitude of the places, and in which of the constellations the sun is once or twice directly overhead, and the constellation's position with regard to the tropics themselves. We shall learn in addition what stars each may have directly overhead, if by observation the latitude should appear at the same equinoctial point, that is if the latitude were always measured on the same parallel.
We have shown in a mathematical work that the sphere of the fixed stars revolves as the revolution of the earth and of the equinoctial signs, not around the equinoctial poles, but around the pole of the circle through the middle of the zodiac, erratically, so to speak. The same stars are not at all times directly overhead in the same place, but of necessity are more northward at one time than at another, and others are more southward.
But it might be considered useless to add such an epilogue, since it is according to law in the celestial sphere, following this hypothesis in stated durations of time, that we fix the site of a place on a circle which extends from pole to pole, counting the whole distance on one meridian, and noting that the same is as many degrees from the equator as the parallel of the place to be determined is distant.
And this it also will be easy to perceive at both poles although the location of no place is determined by the constellations of the fixed stars whether many or few.
These things being settled beforehand we can now attend to that which remains.
2. Which things are appropriate to include in the caption for each map
Starting from such a basis for the division, we have made ten maps of Europe, four maps of Libye, and twelve maps of the whole of Asia. We have set out the captions for each, putting first the continent to which the map belongs, its ordinal number, what countries it contains, approximately what ratio the parallel through its middle has to the meridian, and what the boundary of the whole map is. We have put below [this information] the elevations [of the pole] for the pricipal cities in each country, converted into the lengths of the longest days [that occur] there; and their longitudinal positions [converted] approximately into intervals from the meridian through Alexandria, whether to the east or to the west, in units of equinoctial hours; and for those that the ecliptic stands over, [we have recorded] whether the sun passes through the zenith once or twice [in a year], and how [the sun] is situated [on the ecliptic] with respect to the tropic points [when this happens].
We would also have added which stars pass through the zenith [at each locality] if these actually kept constant latitudes with respect to the equator, that is, if they traveled always on the same [celestial] parallels. But we have shown in the Mathematical Compilation [i.e., the Almagest] that the sphere of the fixed stars shifts in the direction of the trailing [parts] of the heavens with respect to the tropic and equinoctial points, and [it does this] not about the poles of the equator, but about those of the ecliptic, just like the [spheres] of the planets. [Ptolemy demonstrates this in Almagest 7.3. According to Ptolemy, Hipparchus, the discoverer of precession, already suspected that the precessional motion took place about the poles of the ecliptic, and not the equatorial poles; but the consequence of this, that the declinations of the fixed stars change gradually over time, had apparently not been noticed by geographical writers before Ptolemy. For Ptolemy's neglect of this effect in his criticism of Marinos, see p.65 n. 23.] For this reason, the same stars cannot culminate always for the same localities, but must shift, some of them to more northerly positions than before, others to more southerly ones. Therefore it seemed to us superfluous to make such a supplement to the caption, since using the star globe that we made in accordance with this theory [of precession] we can establish the position [of the sphere of the fixed stars] at the times in question with respect to the circle through the poles of both [the equator and ecliptic], and, revolving the whole [globe] along the graduated edge of the fixed meridian [ring], [we can] determine what point on [the ring] is as many degrees from the equator as the parallel thrоugh the place in question is in the same direction, and [so we can] conveniently find out whether no star at all passes through that point, or if there are many, and, [if so,] which one or ones. [The construction of the star globe is described in Almagest 8.3.]
After these preliminary explanations, let us here begin the rest of what we have proposed.
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