310 Dr DONALDSON, ON PLATO'S COSMICAL SYSTEM 



to be irotKtXos, that is, spangled, or, as Shakspere expresses it, in the passage which will 

 be quoted by and bye, " thick inlaid with patines of bright gold ;" and in another passage 

 (Hamlet, Act ii. Sc. 2), " fretted with golden fires." The translators miss the force of the 

 epithet when they render it by bunt, or " exhibiting a variety of colours," for ttoik/Xos, as 

 distinguished from ajoXos, which denotes stripes or bands of alternate colours, always implies 

 variation by way of spots — distincius maculis — and the epithet -n-oiKiXavtos (Find Pyth. 

 II, 8) is explained by the -^pvaovwTo^ ^via of Sophocles (4/. 847), i. e. the I'im adorned on 

 the upper side with little patines or plates of gold (see Lobeck's note on the passage). 



The only other remark which I have to make on the Greek text is that in 6l7 b. I pre- 

 fer the common reading dvarovov, or dvd tovov, which is found in many of the MSS. and 

 is approved by Wyttenbach (ad Plut. de anim. procreat. p. 189), to the reading eva tovov, 

 which most of the modern editors have adopted on very good authority, but which appears 

 to me unintelligible. Plato obviously says that each of the Sirens uttered one note accord- 

 ing to the scale, that is, as Cicero expresses it (Somn. Scip. c. 5): illi octo cursus septem 

 efficiunt distinctos intervallis sonos, qui numerus rerum omnium fere nodus est. 



(s) The next step is to indicate the philosopher's object in giving this fanciful picture 

 of the universe. 



It appears to me that here, as at the beginning of the eighth book, Plato's design was to give 

 due prominence to the mysterious properties of the sacred numbers'. In common with the 

 Pythagoreans he laid much stress on the numerical coincidences between the results of astro- 

 nomy and music as they were then known. And an additional coincidence had been fur- 

 nished by the moral and political theory propounded in the Republic. At every turn he was 

 met by the sacred number seven and its cpnstituent parts. If he began with geometry, he 

 had the yaf/L^Xiov Sidypanfia (Plut. Is. et Os. p. 373 e), or the right-angled triangle with the 

 commensurable sides 3, 4, 5, and as 3* + 4^ = 5% so 3' + 4* + 5' = 6^. Then six again, the 

 number of sides in the cube, is the first perfect number. And when he passed on to music 

 he found that the number 6, as the combination of the first odd and even, played a prominent 

 part in the theory of harmonics. It was called 'Atppol'irri, from the goddess of love, who was the 

 mother of Harmonia. And while the two ratios with which the Greeks were best acquainted 

 in their musical scale were |- and |, representing the 4th and 5th, which, when multiplied 

 together, gave the number 2 as the representative of their diapason, so the cube itself implied 

 all the harmonic numbers, for it consists of 12 sides, 8 angles and 6 planes, and these num- 

 bers stand related to one another in harmonic proportion. Passing on to cosmogony he recog- 

 nised the same numerical harmonies in the order of the universe. The system of the heavenly 

 bodies was represented by the intervals of the musical scale according to the Platonic tetractys, 

 as it is called, which branches from unity on one side by three successive doublings, and on 

 the other by three successive treblings: thus 1, 2, 4, 8, and 1, 3, 9, 27, — the product of the last 

 terms, which are the cubes of 2 and 3, being equal to the cube of 6, or the sum of the cubes of 



' All the learning on this subject was collected by Cornelius Agrippa in his second book De Occulta Philosophia, 



chaps. Ill— XII. 



