c 1P5 > 
* his own. But it was not yet fo fimple as Mr. Barrow after- 
4 wards made it, by confidering more nearly the nature of Po- 
4 lygons, which offers naturally to the Mind a little Triangle, 
e compos’d of a Particle of the Curve lying between two Or- 
4 dinates infinitely near one another, and of the Difference of 
4 thefe two Ordinates, and of that of the two correfpondent 
4 Abfcijfds, And this Triangle is like that which ought to be 
‘madeby the Tangent, the Ordinate, and the Sub tangent: 
4 To that by one fimple Analogy, this laft Method faves all 
4 the Calculation which was requisite either in the Method of 
4 Des Cartes, or in this fame Method before. Mr. Barrow 
4 ftopt not here, he invented alfo a fort of Calculation proper 
4 for this Method. But it was neceffary in this as well as in 
‘that of DesCartes , to take away Fractions and Radicals for 
4 making it ufeful. Upon the Defedt of this Calculus, that of 
4 the celebrated Mr. Leibnitz. wSs introduced, and this learned 
4 Geometer began where Mr. Barrow and others left offi This 
4 his Calculus led into Regions hitherto unknown, and there 
‘madeDifcoveries which aftonilhed the mod able Mathema- 
4 ticians of Europe, ’ &c. Thus far theMarquils. He had not 
feenMr. Newtons Analyfis, nor his Letters of Decern. Io. 1672. 
June 13. 1676, and Ottob. 24. 1676 : and fo not knowing that 
Mr. Newton had done all this and fignified it to Mr. Leibnitz , 
he reckoned that Mr. Leibnitz, began where Mr. Barrow left 
off, and bp teaching how to apply Mr. Barrow’s Method 
without flicking at Fractions and Surds, had enlarged the 
Method wonderfully. And Mr. James Bernoulli, inth esAtta. 
Eruditorum of January 1691 pag. 14. Writes thus: ffui calcu- 
lum Barrovianum ( quern in hettionibus fuis Geometric is adum- 
Iravit Auttor, cujujque Sped min a Junt tota ilia Propcfttionum 
inibi content arum farrago,) intellexerit , [calculum] altertm a 
Domino Leibnitio inventum, ignorare vix poterit $ utpote qui 
in priori illo fundatus efl, & nifi forte in Differentialium notations 
dr operationis aliquo compendio ab eo non diffcrt. 
Now 
