Galilei, Galileo, De Motu Antiquiora

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refuted by Aristotle in book IV of his De Caelo, [308b-309b] asserted {3} - assuredly it was in accordance with reason that bodies that enclosed more matter in a narrower place, should also occupy narrower places, such as are those that come nearer the center.If, for example, we understand that nature, at the time of the original construction of the world, divided all the common matter of the elements into four equal {1} parts, and then assigned to the form of earth its own matter, and in the same way to the form of air its own matter, and that the form of earth caused its matter to be concentrated in a very narrow place, and that the form of air caused its matter to be placed in a very wide place, was it not fitting that nature should assign to air a grand space, and to earth a lesser one?Now, in a sphere, places are narrower the nearer we come to the center, and they are more ample the more we recede from it: hence, it is with both prudence and fairness that nature decreed that the place of earth was that which is narrower than the others, that is, near the center, and that for the remaining elements the places were more ample, the rarer was their matter.I would not say, however, that the quantity of the matter of water is as great as that of the matter of earth, and that for this reason water, since it is rarer than earth, occupies greater places; but only that, if we take a part of water which weighs the same as a part of earth, and for this reason there is as much aqueous matter as earth [under consideration], assuredly this part of earth will then occupy a smaller place than the water, for which reason, justly, it will have to be placed in a narrower space, that is nearer the center. {1} And thus, by proceeding in a similar fashion with the other elements, we will find a certain suitability, not to say a necessity, in such a distribution of the heavy and the light.
Since we have determined in the previous {1} chapter, and have presupposed it as very well known, that it has been established by nature that, indeed, heavier things remain under lighter ones, it must now be considered how the things that are carried downward are moved by heaviness, and how those that are carried upward are moved by lightness.For since heavy things, in virtue of their heaviness, are such as to remain under lighter ones (for inasmuch as they are heavy, they were placed by nature under the lighter things) {1}, in virtue of the same heaviness, they will be such as to be carried under lighter things, if they are placed over them, lest, contrary to the distribution of nature, lighter things should remain under heavier ones.And similarly, in virtue of their lightness, light things will be carried upward, when they are placed under heavier ones: for if in virtue of their lightness they are such as to remain above heavier things, in virtue of the same lightness they will be such as not to remain under heavier things, unless they are hindered.Now from this it is evident that, in the case of motion, consideration must be taken not only of the lightness or heaviness of the mobile, but also of the heaviness and lightness of the medium through which the motion takes place: for if water were not lighter than stone, then a stone would not go down in water.But since a difficulty could arise here concerning why a stone projected into the sea naturally proceeds downward, despite the fact that the water of the sea is heavier by far than the projected stone, it must be remembered what we have noticed in chapter [1]: in fact, the stone is indeed heavier than the water of the sea, if we take an amount of water as great in size as the size of the stone; and thus, the stone, inasmuch as it is heavier than the water, will be carried down in the water.But, again, a difficulty will arise concerning why what must be taken into consideration is the stone and an amount of water as great in size as is the proper size of the stone, and not the whole sea.In order that we may remove this difficulty, I have decided to adduce some demonstrations on which depends not only the solution to this difficulty, but also the whole of the present work.Although in truth the media through which motions occur are several, that is, fire, air, water, etc, and in all of them the same reckoning must be made, we will presuppose that the medium in which motion is to take place is water: and first of all we will demonstrate that those bodies that are equally as heavy as water itself, when they are let down into water, are completely submerged, but that then, however, they are no more carried downward than upward; and secondly, we will show that bodies that are lighter than water not only do not go down into the water, but even cannot be completely submerged; thirdly, we will demonstrate that bodies that are heavier than water are necessarily carried downward.

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