MEDICINE AND PHILOSOPHY 11 TH AND 12TH CENTURIES 103 



with one of the two elements or the impossible combination, hot 

 and cold.*^ Of the six combinations of the four qualities, four 

 are possible and determine the four elements; and the remaining 

 two combinations, hot and cold, dry and wet, are impossible. 



** The demonstration of the harmony or unbreakable chain of elements binding 

 the universe together, dependent on the interposition between fire and earth of two 

 and only two elements, goes back to Plato, but the changes in the properties of the 

 elements on which the demonstration depends mark changes in the doctrine of 

 elements. Plato's argument depends on the nature of proportion and of numbers: 

 if the universe had been a plane surface, one middle would have sufficed; since it is 

 solid two middle terms are required. Macrobius gives a rough translation of this 

 passage, omitting the references to proportions and square and cubic numbers; 

 instead he discusses hot and cold, dry and moist. (Commentarii in Somnium 

 Scipionis, VI, 23-33) . The Medieval tradition, finally, presents the Platonic analysis 

 of elements as permutation of sets of three qualities, elaborated and systematized 

 from his account of the properties of elements resulting from the geometric forms 

 assigned to them (Timaeus, 55C-56B) . The systematic account of the six qualities 

 of the elements is known as early as Nemesius, and scholars have argued that his 

 source is a lost commentary of Posidonius on the Timaeus or a lost commentary of 

 Porphyry. If the problem is treated in terms of three qualities, the two extreme 

 elements of the universe are opposed by sets of contrary qualities — subtle, mobile, 

 acute (fire) vs. corporeal, immobile, obtuse (earth) , whereas if it is treated in 

 terms of two qualities, the contraries separate the elements in groups of threes, but 

 the two extreme elements are not opposed by contrary qualities — hot, dry (fire) 

 vs. cold, dry (earth) — and therefore, according to Nemesius (V, 11, p. 64). the 

 sequence of elements is not merely an ascent and a descent but a circle, since fire 

 shares with earth the quality dry. ^Miatever the origin of the analysis in which each 

 element is characterized by three qualities, the Latin writers of the Middle Ages 

 learned the distinctions it employs from the Commentary of Chalcidius on the 

 Timaeus. The sequence of elements between the two extremes, fire and earth, as 

 set forth by Chalcidius, may be schematized as follows — 



Ignis — acutus subtilis mobilis 



Aer — obtunsus subtilis mobilis 



Aqua — obtunsa corpulenta mobilis 



Terra — obtunsa corpulenta immobilis 



The two extreme pairs — fire-air and water-earth — share two qualities and are 

 opposed in one; the sequence consists in the change of one quality at each step; 

 the two extremes are opposed in all three contrary qualities. Chalcidius' translation 

 and commentary (in the manuscripts that have come to us) are incomplete. The 

 translation breaks off at 53C, immediately before the analysis of the mathematical 

 forms which constitute the elements and of the sequence of the elements relative to 

 each other. The Commentary is also incomplete: the list of topics enumerated is 

 not completed; nonetheless the treatment of the elements is complete and it runs 

 through all three forms of analysis. The theory of the elements as mathematical 



