PRINCIPLES OF THINGS. 25 



upon their diiferent systems, and are perpetually in danger of drowning 

 them. Pythagoras compared the existence of matter, in its primary and 

 amorphous state, to pure arithmetical numbers, before they are rendered 

 visible by arithmetical figures, " ZJmV^/," says he, " and one (the former 

 of which he denominated mondd) are to be distinguished from each other : 

 unity is an abstract conception, resembling primary or incorporeal matter 

 in its general aggregate ; one appertains to things capable of being num- 

 bered, and may be compared to matter rendered visible under a particular 

 form." So again, -^Number is not infinite anymore than matter ; but it 

 is nevertheless the source of that infinite divisibility into equal parts which 

 is the property of all bodies."* 



Numbers, however, were not more generally had recourse to by Pytha- 

 goras, to typify elementary matter under different modifications, than they 

 are in the present day by the most elaborate chemists, to express its par- 

 ticular combinations: "As in all well-known compounds," observes Sir 

 Humphrey Davy, " the proportions of the elements are in certain definite 

 ratios to each other, it is evident that these ratios may be expressed by 

 numbers."! In consequence of which they are so expressed in various 

 places by himself, and by many French, Swedish, and English chemists, 

 the hint having been first suggested, I believe, by Higgins or Dalton. 

 And hence the doctrine of numbers is well known to have been very largely 

 and very repeatedly had recourse to under the Pythagorean system, and to 

 have been used in explanation, not only of the endowment of different 

 portions of matter with different forms, but of the harmony with which the 

 different natures of matter and mind unite in identic substances. Numbers 

 and forms are, in consequence, not unfrequently contemplated as the same 

 thing — as the models or archetypes after which the world in all its parts 

 is framed — as the cause of entity to visible beings : rovi oc^iGfMvq etinov^ 

 etveit TJJ5 et;e*/<j45.| 



And hence, again, under the term monad, or unity, Pythagoras is ge- 

 nerally conceived to have symbohzed God, or the active principle in 

 nature ; under duad, the passive principle, or matter ; and under triad, 

 the visible world, produced by the union of the two former. 



Pythagoras, however, was as much attached to music as to numbers, 

 regarding it as a mere branch of the science of numbers applied to a defi- 

 nite object. He has, indeed, the credit of having invented the monochord, 

 and of having applied the principles of music, as well as those of numbers, 

 to the study of physics. He conceived that the celestial spheres, in which 

 the planets move, striking upon the elastic ether through which they pass, 

 must produce a sound, and a sound that must vary according to the diversity 

 of their magnitude, velocity, and relative distance ; and as the adjustment 

 of the heavenly bodies to each other 'is perfect in every respect, he farther 

 conjectured, that the harmony produced by their revolutions must also be 

 the most perfect imaginable ; and hence the origin of a notion, which is 

 now, however,, <mly entertained in a figurative sense, a sense frequently 

 laid hold of by our. own poets, and thus exquisitely enlarged on by Dry- 

 den : — 



* Anon. Photii, lib. c. Nicomac. apud Phot. Themist. in Phys. lib. iii. sect. 25. p. 67. 

 See also Enfield's Brucker, i. b. ii. ch. 12. p. 383. 

 t Davy, Elem. i. p. 112. 



X Arist. Met. lib. i. c. 6. Plut. Plac. Phil, lib. i. cap. 3. Athenag. Apol. 49. 



4 



