( ' 76 ) 
fall applicatam ftttffe : ltd ut ejus ope, in qudvis Vi gun Curvilinea 
pfopojita, qttauna vel pluribus proprietatibus defi nit ur, Quadrat ur a 
vel Area dift# four#, accurata ft poffibile fit , (in minus infinite ve- 
rb propinqna, Evolutio vel longttudo Lined Curv£, Centrum gra- 
vitatis figure, Solida ejus rotatione genita & eorum (uperficres ; fine 
ulla radicum extrattione obtineri queant. Poflquam intellexerdt 
D. Gregorius banc methodum a D. Mercatore in Logarithmotech - 
niatifurpaUm & LdjperboU quadrandx adhibit am, quamque adaux - 
erat ipfe Gregorius, jam univerfalem redditam e(fe, omnibufque 
fguris applicatam ; acri fiudio eandem acquifivit multumque in ea 
enodanda defudavit. Vterque D. Newtonus & Gregorius in 
artimo hibet banc methodum exornare : D. Gregorius autem 
D. Newtoaum primum ejus iuventorem anticipare baud integrum 
duett. And in another Letter written to Mr. Oldenburgh to be 
communicated to Mr. Leibnitz, and dated June 14 167 6 . 
Mr. Collins adds : Hujus autem methodi ea e(l prdflantia utXum 
tarn late pat eat ad nullarn h&reat difficult atem. Gregorium autem 
aliofque in ea fuiffe opinione arbitror, ut quicquid ufpiam antea de 
hac re innotuit , quafi dubia diluculi lux fuit fi cum meridiana 
claritate conferatur. 
ThisTrad was firft printed by Mr William Jones, being found 
by him among the Papers and in the Hand-writing of Mr. John 
Collins, and collated with the Original which he afterwards 
borrowed of Mr. Newton- ft contains the above-mention’d 
general Method of Analyfis, teaching how to refolve finite 
Equations into infinite ones, and how by the method of 
Moments to apply Equations both finite and infinite to 
the Solution of all Problems. It begins where Dr. Wallis left 
off, and founds the method of Quadratures upon three Rules. 
Dr. Wallis publifhed his Arithmetica infinitorum in the 
Year 1655 , and by the 59th Propofition of that Book, if the 
Abfciffa of any curvilinear Figure be called x, and m and n be 
Numbers, and the Ordinates ereded at right Angles be x~»* 
m + n 
the Area of the Figure fhall be^ x T - * And this is aflumid 
