450 ANTIENT METAPHYSICS. Book V. 



Plato, in his feventh book De Republican has obferved, with great 

 juflice, that there is no fcience which abftra(fts the mind fo much from 

 matter and fenfe, as arithmetic. It does fo, he fays, much more than 

 geometry, the fubjedl of which, viz. lines and figures, have pofition, 

 and are reprefented to the mind by material fymbols ; whereas num- 

 bers are (o much abRradlied from matter, that they cannot be exprefled 

 by any material form j fo that the mind, in the ftudy of them, is obli- 

 ged 



duad and number appears to have been known even to the grammarians, who, 

 in antient times, formed a language according to the rules of art. And, accordingly, 

 we find the Greek language, and other antient languages, which were the work of men 

 of fcience, had a dual number. See what I have further faid on this fubje£l in the 

 Origin and Progrefs of Language, vol. 2. book i. cap. 8. p. 88. 



Proclus, in the paflage above quoted, obferves, that the fcience of magnitude, as de- 

 livered by Euclid, proceeds in the fame manner as the fcience of number j for Euclid 

 begins his definitions of figures with the circle, which is the fimplefl of all figures, 

 being contained under one line, and therefore like to the monade of the arithmetician. 

 Then he proceeds to the femicircle, which may be called the duad of magnitude, as it 

 Is contained by two lines, the one a flraight line, and the other a curve. And 

 from thence he goes on to the triangle, which may be called the firft numerical figure. 

 In this manner, the antients compared things together ; and, by difcovering refem^ 

 blances between things feemingly moft different, fuch as figures aiui numbers, formed 

 fyftems of fcience, of much greater extent and comprehenfion than what is to be found 

 among us. Proclus, in this work, not only carries on the analogy betwixt numbers 

 and figures, but he finds out wonderful refemblances betwixt the (\iii philofophy and 

 both geometry and arithmetic ; explaining, after the manner of the Pythagoreans, by 

 figures and numbers, the prpceflion of Divinity, and the progrefs of mind in gene^ 

 ration and produclion. This he may have carried too far ; iior do I think the metar 

 phyfical part of this work the mafl: valuable part of it : But the geometrical part 

 I think admirable ; for he has explained the principles of geometry, and fbown the 

 method of reafoning in that fcience, compared with that in other fciences, better than 

 any body. This he was able to do by being a philofopber, and a man of univerfal 

 knowledge, as well as a very good geometer ; whereas, the mere geometer, though 

 he may improve feveral of the arts of life, and m vy be alfo ufeful to the philofopber, 

 yet he himfelf does not underftand even the pr'nciples of his own fcience, nor what 

 lank it holds in the Ericyclopediey or fyftcm of univerfal learning. 



