168 PROCEEDINGS OP THE AMERICAN ACADEMY. 



and nine make thirteen, eight and twenty-seven make thirty-five. Of 

 all which numbers, the Pythagoreans called five the uourisher — that is 

 to say, the breeder or fosterer — of sound, believing a fifth to be the first 

 of all the intervals of tones which could be sounded. But as for thirteen, 

 they called it the remainder ; despairing, as Plato himself did, of being 

 ever able to divide a tone into equal parts. Then, five and thirty they 

 named ' harmony,' as consisting of the two cubes eight and twenty -seven, 

 the first that rise from an even and from an odd number ; and as also 

 being composed of the four numbers — sis, eight, nine, and twelve * — 

 comprehending both harmonical and arithmetical proportions." t 



This comprehensive nature of thirty-five and the various proportional 

 relations of its main factors, admitting of their application to every 

 dimension in a symmetrical system, seem to have induced the archi- 

 tect of the Temple of Zeus to adopt it as the fundamental number for 

 the determination of the dimensions and proportions of the building. 

 For, upon closer investigation, it will be seen that it is not only the 

 chief factor of the measure of the diameter of the column, but that 

 it enters intimately into the determination of the size of every 2>art of 

 the building. For the minute of the diameter, which serves as the 

 universal common measure, is one-sixtieth of 7.35, or .1225; and what 

 is 1225 but 35 X 35 ? For example of the application of the num- 

 ber to the building, let us take the measure of the breadth in minutes : — 



.1225 X 735, that is, as we have just seen, 35 times 35 multiplied 

 by 21 times 35. The abacus is 70' in breadth, that is 35 X 2 ; and 

 35 X 2 X 10^ = 735, or, as above, 35 X 21 = 735. 



If we take the length in minutes, a similar result appears : — 



.1225 X 1680 = the length; that is, 35 times 35 multiplied by 48 

 times 35 = the length. 



It is further to be noticed that 21, the factor with 35 of the breadth, 

 is the multiple of three times 7 ; and that 48, the factor with 35 of the 

 length, is composed of 35 and 13, — the latter number holding, accord- 

 ing to Plutarch, an important place as " the remainder " in the Pytha- 

 gorean scale. 



* lu the Pythagorean musical scale, 6 denoted the octave, 8 the fifth, 9 the 

 fourth, and 12 unison. See Westphal, p. 133; and Boeckh, § 10, p. 146. 



t Macrobius (Somn. Scip. I. vi.), commenting on the passage in "Timaeus," 

 gives a similar scheme of the numbers. He says, " Duos esse priraos omnium 

 numerorum cubos, id est, a pari octo, ab imparl viginti septem ; et esse impareni 

 marem, parem feminam superius expressimus. . . . Coeant enim numeri, mas 

 ille qui memoratur et femina, octo scilicet et viginti septem ; pariunt ex se 

 quinque et triginta." 



