Hitherto Unpublished Works, Fascicle 4

and so one half will be of a heavy nature and the other of a light nature. But this cannot be the case for the same simple body according to its species species: here referring to the specific category or essence of a substance, whether we take "heavy" and "light" relatively or absolutely. Both heavy and light taken absolutely create a difference in species just as they do when taken relatively. Therefore, it is necessary that there are proportionate means means: intermediate values or steps in a sequence between them.

For this, there is the authority of Boethius An influential 6th-century philosopher and mathematician who bridged the gap between Classical and Medieval thought and the argument by analogy in physical numbers. Thus, in the third book of The Consolation of Philosophy 8 The Consolation of Philosophy Book 3, poem 9, line 10., he introduces Philosophy speaking and saying to God: "You bind the elements with numbers."

As he teaches in his Arithmetic 10 Arithmetic Book 2, chapter 46., between all solid mean numbers there are two proportionate means, while between surface numbers there is one. For example, between nine and four there is six. These are connected in a three to two ratio sesquialtera proporcione: a mathematical ratio where the larger number is one and a half times the smaller, such as 3:2 or 6:4.. But between 27 and 8 there are two means, namely 18 and 12, all of which are connected by that same three to two ratio.

For this reason, Boethius and all the ancient philosophers proposed, following the likeness of physical numbers, that there are two means between the extreme elements. There are, therefore, at least five bodies of the world: the four elements and a fifth body. This is called the quintessence, the heavens, and the ether ether: the celestial substance that was believed to fill the upper regions of the universe, distinct from the four earthly elements..

If it is argued to the contrary that there are only two motions that are straight according to their species, namely upward and downward motion, and therefore only two bodies, it must be said that the expositors and commentators were mistaken here. Averroes A 12th-century philosopher from Islamic Spain whose commentaries on Aristotle were central to medieval university education teaches this in his commentary on the first book of On the Heavens and the World 23 On the Heavens and the World Book 1, commentary 5 and commentary 90..

He clarifies this for us, maintaining that there are not only two motions in the most specific kind, but only in a subordinate category subordinate category: a logical classification that sits between a general genus and a specific species.. The locations of air and fire are different in species. If air were in the sphere of fire, it would descend. Therefore, upward motion is twofold in species, according to the diversity of the locations that differ in species. The same applies to water and earth.