Compendium of All Natural Science

ratio, which is that of a third part to an ounce, cannot be the half of an octuple ratio. For the octuple ratio, which is that of a two-thirds part to an ounce, must necessarily be compounded of the proportion which is of a two-thirds part to a third part, and the proportion which is of a third part to an ounce. But the two-thirds part to the third part is double; and the third part to the ounce is quadruple. Wherefore, since they are unequal, the double ratio is indeed far less than half of the octuple, while the quadruple is greater. For this reason, the octuple ratio compared to the quadruple will be somewhat less than double. It also happens, to those observing more subtly, that although something, being double, moves a thing, it may yet move it with more than double velocity. As if examples are taken of a half part and a fourth part as movers, and a sixth part as the thing moved.

One might also wonder, as if it were not necessary that things which move separately should move equally when joined together; which, however, will be proven to occur by this example. For if a third part, which was moving an ounce in a quadruple proportion (as is very well known), is joined to a third part which was moving a sixth part in a double proportion, and the sixth part and the ounce are also joined: the third part joined to the third part will constitute a two-thirds part; while the ounce joined to the sixth part will constitute a fourth part. The proportion of the two-thirds part to the fourth part is double superbipartient thirds; in which proportion neither third part, when separate, was moving its object. Among these things, however, this principle is most widely applicable: that * whatever moves something, that which is half of the power will be able to move half of the moved thing with equal velocity.