Compendium of All Natural Science

...will have power over the matter; for it will be less impeded.

In this, it is most worthy of note that since any proportion which is composed of a greater and a lesser proportion is somewhat less than double the greater proportion, but greater than the lesser. Therefore, if someone moves a sixth part although he is capable of a two-thirds part, and also a hemina of a sixth part: the velocity of the moved sixth part relative to the velocity of the hemina will not be double. For since the proportion of a two-thirds part to an ounce, or of a sixth part to a hemina, is octuple: it is composed of two unequal proportions: namely, the quadruple proportion, which is that of the two-thirds part to the sixth part; and the double proportion, which is that of the sixth part to the ounce. Wherefore the octuple proportion will indeed be less than double compared to the quadruple, which is the greater; but greater than double compared to the double proportion. Wherefore it is concluded that the velocity of the ounce will not be doubled. Conversely, it can happen that one moves half of a thing with more than double the velocity of the whole: as if we apply to the same rule a fourth part, which moves an ounce and a sixth part. For the proportion of the fourth part to the sixth part is sesquialterate, and to the ounce, triple. That the triple is indeed greater than double the sesquialterate is demonstrated by arithmetic reasoning.

By the same observation it is gathered that if a third part moves an ounce, yet a two-thirds part (which is double the third part), if it moves the same ounce, will not move it with double velocity. For the quadruple proportion,