274 In which all the things that have been demonstrated above {1} are considered from a physical point of view, and natural mobiles are reduced to the weights of a balance.
When someone has obtained the truth about a certain matter, and has acquired it with very great labour, then, when he inspects his discoveries more carefully, he often recognizes how the things that he has found with great effort could have been grasped very easily. For truth has the property that it does not lie hidden to the extent that many people have believed; but its traces shine brightly in different places, and many are the paths by which one approaches it: yet it often happens that we do not notice things that are nearer and more clear. And we have a manifest example of this at hand: for all the things that have been demonstrated and made clear above in a rather laboroius way are exposed to us so openly and manifestly by nature that nothing could be clearer or more open.
That this may be apparent to anyone, let us consider, first, how and why things that are carried upward, are carried with a force as great as as the amount by which an amount of the medium, through which they are carried, that is as great in size as the size of the mobile, is heavier than the mobile itself. Thus let us consider a piece of wood which goes up in water and floats on water: now it is manifest that the piece of wood is carried upward with as much force, as is necessary to submerge it by force under water. Hence if we find how great a force is necessary to hold the wood under water, we will have what is sought: but if the wood were not lighter than water, that is, if it were as heavy as an amount of water equal to its own size, then surely it would be submerged, and would not be raised above the water: therefore, a force that is as great as the heaviness by which the heaviness of the wood is surpassed by the heaviness of the said amount of water, suffices to submerge the wood. Therefore, the amount of heaviness required to submerge the piece of wood has been found: but it has just been determined that the piece of wood is carried upward with as much force as is required to submerge it; now, what is required to submerge it is the heaviness just found: hence the piece of wood is carried upward with a force as great as the heaviness by which an amount of water, as great in size as the size of the wood, exceeds the heaviness of the wood: which is what was sought.