[730] 
Exercitatio Geometrica de DIMENSIONE FIGV- 
RARVM, Authore Davide Gregorio, in Acade- 
mia 'Kd'mhmgenfi Mathefeos Profe/fore. Edinbur- 
gi/«4°. 1684. 
IN this Treati(e,the Author firft takes notice of a Trea- 
tdQ of his XJnclt Mr. James Gregory printed at Padua^ 
in the year 1 66 7, entituled P^era Circuit & Hyper boh 
dratura, &c. Wherein he fliewi, that any Sedor of the 
Circle, Hyperbola, or Ellipfe, is, the termination of a 
certain Coaverging Series; whofetwofirft Termsare A 
and B ; whereof A is a Triangle, which, as to the Circle or 
Ellipfe, is Infcribed; but, as to the Hyperbola, Circum- 
Icribed, to the faid Sector: and B, a Trapezium, which 
("contrarywife) as to the Circle or Ellipfe, is Circum- 
fcribed 5 but as to the Hyperbola, Infcribed, to the faid 
Sedori The two fecond terms, /AB and ^—^^: the two 
thirds, in like manner derived from the feconds, as thefe 
are from the firft. And fo infinitely, with other things 
appertaining to the fame, and to other fuch like ap- 
proximations. 
He then mentioneth another method, ( different 
from that former) publilhed at London, the year fol- 
lowing, by Mr. Nicolaus Mercator, in his Logarithmotech^ 
nia, for fquaring the Hyperbola, by the htX^ oi Infinite 
Series. Approved alfo, and demonftrated, afterwards, by 
Mr. James Gregory, Apagogically. But, that a Gene- 
ral method, for fuch cafes was yet war-ting. 
That about the beginning of the year i<^7o.he under- 
ftpod from Mr. that Mr. Ifaac Newton ("Pro- 
feffor of Mathematicks at Ca?nbridge) had, before that 
time, a General method for, fuch Quadratures^ and. other 
like. 
