that the lead sphere is carried downward with as much force, as would be required to pull it upward: but if the lead sphere were of water, no force would be necessary to pull it upward, or certainly the least of forces: thus as much heaviness resists, that the sphere might not be pulled upward, as that by which a lead sphere exceeds a sphere of water equal to it. </s>
<s id="id.1.1.9.03.04">But the lead sphere is carried downward with the same force, as that with which it resists being pulled upward: hence the lead sphere is carried downward with a force as great as the heaviness by which it exceeds the heaviness of a sphere of water. </s>
<s id="id.1.1.9.03.05">Now it is possible to observe the same thing in the weights of a balance. </s>
<s id="id.1.1.9.03.06">Indeed if there are some equally ponderous weights, and something heavy is put on one of them, in this case it will be carried downward; but not according to its whole heaviness, but only according to the heaviness by which it exceeds the other weight: it is the same thing as if we said, this weight is carried downward with a force as great as the amount by which the other weight is lighter than it. </s>
<s id="id.1.1.9.03.07">And for the same reason the other weight will be carried upward with as much force, as the amount by which the other weight is heavier than it. </s>
</p>
<p>
<s id="id.1.1.9.04.00"/>
<s id="id.1.1.9.04.01">From the things that have been conveyed in this and in the preceding chapter, the general conclusion can be drawn that mobiles of different species observe in the swiftnesses of their motions the ratio that the heavinesses of these same mobiles have to one another, provided they are equal in size, and this not purely and simply, but weighed in the media in which motion is to take place. </s>
</p>
<p>
<s id="id.1.1.9.05.00.fig"/>
<s id="id.1.1.9.05.01">Like, for example, let there be two mobiles, a, b, equal in size, unequal in heaviness; and let the heaviness of a in air be 8, but let the heaviness of b in air be 6: the swiftnesses of these mobiles in water will not observe, as has already been said, the ratio which is 8 to 6. </s>
<s id="id.1.1.9.05.02">For if we take an amount of water c, which is equal to the size of one or the other mobile; let its heaviness be 4; therefore the swiftness of mobile a will be as 4, but the swiftness of b will be as 2; these swiftnesses will be to one another in a ratio of 2/1, and not in one of 4/3, as are the heavinesses of the mobiles weighed in air. </s>
<s id="id.1.1.9.05.03">However the heavinesses of these same mobiles in water also will be in a ratio of 2/1; for the heaviness of a in water is only of 4. </s>
<s id="id.1.1.9.05.04">Which is evident as follows. </s>
<s id="id.1.1.9.05.05">If the heaviness of a were as 4, in water it would be zero. </s>
<s id="id.1.1.9.05.06">For then a would be equally as heavy as water, since it has been assumed that the heaviness in air of an amount of water as great in size as the size of a, namely c, is 4; now the heaviness of c in water would be zero; </s>
