Chap. VIII. ANTIENT METAPHYSICS. 449 



reans conceived to be in the Divinity. And the principle of Divinity, 

 as well as of Number, is unity perfedly indivlfible *. 



L 1 1 Plato, 



* It is a ftrange fancy of Dr Barrow, in his Mithematical Le(flures, p'. 29. that geo- 

 metry is, in the order of nature an I indignity, prior to arithmetic; mignitude being;, 

 according to him, the primary idea, of which number is only an aifeclion, ferving for 

 no other purpofe but to number the parts of magnitude. In this, as in other things, 

 the Do<Slor h.td done better to have followed his guides, the antients. It is a crude 

 thought of the DoQ;or*s, which he has endeavoured to fupport by reafons that I think 

 are not intelligible ; for magnitude is, as I have obferved, not fo fimple an idea as 

 number, including, befidea exiftence, fpace, and pofition in that fpace. And, /econdfyy 

 number, and its principle, the monade, are fo much primary ideas, that, without them, 

 we have no idea of any thing elfe. As to magnitude, if we were to confider it as infi- 

 nite, we mud conceive it as one thing, and we mufl: alfo confider it as confifting of a 

 multitude of parts contiguous to one another : So that the moft fimple conception we 

 can have of magnitude involves both the one and the many^ befides fpace and fitua- 

 tion. But, when we confider magnitude as bounded, the cafe is ftill clearer ; for we 

 can have no idea of the fimpleft rexSlilineal figure, viz. a triangle, without firft having 

 the idea of the number three. The Do£lor, in his reafoning upon the fubjedl, feems 

 to confound meafure with number ; for meafure is certainly an afFe£bion of magnitude 

 only, and therefore belongs to geometry only. But, when the parts meafured come to 

 be numbered, then there is the application of another fcience to geometry. 



It is to be obferved, that the antients not only diflinguiflied betwixt the monade and 

 number, but would not allow the duad to be number ; for, they faid, it was no more 

 than a flep of progreflTion from the monade to number ; therefore was betwixt the two, 

 and neither the one nor the other. It was quite different from the monade,inthis refpe<St, 

 that the monade is'not increafed by being multiplied into itfelf, but only by being added 

 to itfelf ; whereas, the duad is increafed by multiplication, as well as by addition ; 

 and it differs from number in this rcfpeft, that number is more increafed by being 

 multiplied, than by being added to itfelf; whereas, the duad is juft as much increafed 

 by being added to itfelf, as'j^ being multiplied by itfelf; fo that it is plainly betwixt 

 the two, and participating fomething of each. This is an obfervation of Prcclus, in 

 his fecond book of his Commentary upon Euclid, page 45. iSee alfo Jamblichus's 

 Commentary upon the Arithmetic of Nicomachus. Such obfervations upon theprinciples 

 of number are little attended to in modern times. But this diftindion betwixt the 



duad 



