OF ARTS AND SCIENCES. 169 



But tills is not all : 35 being not only the measure of the minutes, 

 but also of the number of the minutes, of which each of the principal 

 dimensions of the building is composed, is consequently the measure 

 of those dimensions. But here a new subtlety appears. The main 

 dimensions are not simply multiples of 35 ; but they are multiples of 

 the cube of 35 by the same factor as 35 is of the minutes by which 

 they are measured ; * for, the number of minutes which measures each 

 principal dimension being a multiple of 35, and the minute itself being 

 35^, the number of feet and decimals of a foot in the dimension equals 

 35^, multiplied by the same factor as, multiplied with 35, gives the 

 number of minutes. 



Taking the breadth, for an example, again, we have seen that it is 

 stated in 



Minutes, thus . . . . 35 X 21 = 735'. 

 Now its measure in feet is 



to be stated, thus . . 35^ x 21 = 90,0375 



And so with the length . 35 X 48 = 1680'. 



„ „ . 35'^ X 48 = 205.8000 



It would seem that the architect, having determined to base his 

 design upon 35, the number called harmony itself, had exercised his 

 ingenuity in devising such dimensions for his Temple as should form a 

 complete and most complex composition of harmonic relations. 



He may in this manner have secured that satisfaction for his inven- 

 tive faculty, and that freedom of independent conception, of which he 

 was deprived, so far as concerned the general character of the build- 

 ing, by the prescribed scheme of the Greek Temple. 



* Cube and square numbers were most liighly esteemed by the Pythagoreans. 

 They had discovered that cubes were composed of a regular sequence of odd 

 numbers : — 



The first cube, 8 of 3 + 5. 

 „ second „ 27 of 7 + 9 + 11. 

 „ third „ 64 of 13 + 15 + 17 + 19, and so on. 



In like manner squares, by adding the odd numbers in sequence to unity : — 

 The first square 4 = 1 + 3. 

 „ second „ 9 = 1 -J- 3 + 5. 

 „ third „ 16 = 1 + 3 + 5 + 7. 



„ fourth „ 25 = 1 + 3 + 5 + 7 + 9, and so on. See Theo- 

 nis Smymaei, Expositio eorum quss in Arithmeticis ad Platonis Lectionem utllia 

 sunt. Ed. Gelder, Leyden, 1827, c. xv. (p. 43) ; c. xxv. (p. 63). 



