ON MUSIC 
445 
points ont that the extract given by Porphyry shows some 
differences from our text and contains some things quite 
unworthy of Euclid; hence he is inclined to think that the 
work as we have it is not actually by Euclid, but was ex 
tracted by some other author of less ability from the genuine 
‘ Elements of Music ’ by Euclid. 
(5) Works on mechanics attributed to Euclid. 
The Arabian list of Euclid’s works further includes among 
those held to be genuine ‘ the book of the Heavy and Light ’. 
This is apparently the tract Be levi et ponderoso included by 
Hervagius in the Basel Latin translation of 1537 and by 
Gregory in his edition. That it comes from the Greek is 
made clear by the lettering of the figures; and this is con 
firmed by the fact that another, very slightly different, version 
exists at Dresden (Cod. Dresdensis Db. 86), which is evidently 
a version of an Arabic translation from the Greek, since the 
lettering of the figures follows the order characteristic of such 
Arabic translations, a, h, g, d, e, z, h, t. The tract consists of 
nine definitions or axioms and five propositions. Among the 
definitions are these : Bodies are equal, different, or greater in 
size according as they occupy equal, different, or greater spaces 
(1-3). Bodies-are equal in power or in virtue which move 
over equal distances in the same medium of air or water in 
equal times (4), while the power or virtue is greater if the 
motion takes less time, and less if it takes more (6). Bodies 
are of the same kind if, being equal in size, they are also equal 
in power when the medium is the same; they are different in 
kind when, being equal in size, they are not equal in power or 
virtue (7, 8). Of bodies different in kind, that has more power 
which is more dense (solidius) (9). With these hypotheses, the 
author attempts to prove (Props. 1, 3, 5) that, of bodies which 
traverse unequal spaces in equal times, that which traverses 
the greater space has the greater power and that, of bodies of 
tire same kind, the poiver is proportional to the size, and con 
versely, if tire power is proportional to the size, the bodies are 
of the same kind. We recognize in the potentia or virtue 
the same tiling as the Svrafjus and ia-\vs of Aristotle. 1 The 
1 Aristotle, Physics, Z. 5.