PREFACE. vil 



Sciences it is ImpofTible that Men can ever afcend to Philofophy*. 

 As to the Weftern and Northern Nations of Europe, it is to me evi- 

 dent that they never would have invented either Science or hberal 

 Art, if they had not been firft taught by the Greeks or Romans ; for, 

 as to the Arts, it is evident that, at this day, we pradife none of them 

 in the leaft degree of perfection, but in imitation of the Antients, 

 without whom we have no Painting, Sculpture, Architeaure, 

 Poetry, or Writing of any kind of any value. And as to Sciences, 

 though our Genius be more fitted for them, I think, by Nature, 

 than for the fine Arts, yet we have invented none, unlefs it be Sir 

 Ifaac Newton's Aftronomy, of which I have faid a great deal al- 

 ready, and (hall fay fomething more in this Preface. 



But 



* In a book of Nicomachus, a Pythagorean Philofopher, entitled,- ra G£cXcycu/^£^a 

 rn? AfiGjufTOt^;?, which is a very rare book, not to be found, I believe, in Britain, 

 but of which I had the ufe from the French King's Library, it is faid that there are 

 four fteps, or B^i(^x6oxi, as they called them, by which we afcend to Philofophy, viz. 

 Jrithmctic, Mufic (by which the Pythagoreans meant the dodrines of Ratios and Pro- 

 portions), Geometry, and, laftly, Sphccrics, the name which they gave to the Science 

 of Body in Motion, or, as we call it, Mechanics. I am afraid that moft of thofc 

 who call themfelve Philofophcrs at prefent, have done no more than get up thofe 

 fteps ; and I fufpeft that but few of them have fixed their feet, even upon the loweft 

 ftep, 'l mean Arithmetic, fo well as the Pythagoreans did, who ftudied the na- 

 tare and properties of Numbers, as much as they did thofe of Lines and Figures, di- 

 viding them as they did Figures into Triangles, Squares, Rcaangles, Cubes, and 

 ftiewhig how they were produced from one another. In this way they treated of 

 Numbers, confidered as abfolute and in themfclvcs ; then they confidercd them as 

 they ftood in relation to one another. This is the dodrine of Ratios and Propor- 

 tions, to which, as I have faid, they gave the name of Mufic ; and of this part of 

 the Science they treated in the fame fcientifical way, dividing the Ratios into their 

 fcveral Speciefes, and {hewing the wonderful proceffion and generation of the one 

 from the other. In this way. Arithmetic Is treated, and made a Science of, by Ni- 

 comachus in his Book of Arithmetic, and by Theon Smyrnxus, in what he has writ- 

 ten upon the fame fubjc6l. 7 



