[731] 
like cafes. Whereof (as an Inftaiice)-Mr. Collins fent 
him an example, of fuch an Infinite Senei ,a€commodat« 
ed to a Circular Zone; namely, if the Radius be R, 
and the breadth of the Zone B ; the Zone is equal to 
3R 2-R3 5:^'R^ i'7^R^ 
That Mr. James Gregory was in purfait of like me- 
thods of Infinite Series , but was prevented by Death i 
and (belide fome particular examples) left nothing in 
his Papers (yet come to his hands) that might declare 
his method and way of finding fuch examples. 
Thathimfelfe {Mt, David Gregorie) doth fin this trea- 
tife make it his bufinefs to explain a method, which may 
iuit fuch examples of h s Uncle. 
And he doth here ajQTume (chough in other wordsj the 
DocStrine of liidivifibles, and the A 'ithmetick oi Infi- 
nites, as already known J and received by Geometers as 
fufficiently Demonftrated. And applies this to particu» 
lar cafes, in this manner; Suppofing a ftreight line or 
Axis, which he calls X, cut into parts infinitly fmall, and 
the refpediive values of each L ("which he calls £/^;?2^;2- 
tum,) or fmall part ofthe Curve, Plain, or Solid which is 
to be meafured ; anfwering to each oi thofe particles of 
X; (ox: at leaft fomewhat fo near the values of Lj as that 
the difference may be neg.edted; as when a ftiort Sub- 
tenfe or Tangent, is taken as coincident with a Curve;) 
he doth (according to the Dodrine of Infinites) colledt 
the Aggregates of all fuchL; which Aggregate is the 
Magnitude fought. 
Of this he gives diverfe examples in ParaboIa'SjHyper- 
bola's, Elliples, Spirals, Cycloids, Conchoids, Ciffoids^ 
and forae other Curves, or Curve-lined Figures j as to 
their Area's, and Curve»lines,with the Solids, and, Curve- 
furfaces, made by converfion of them, ^or otherwife de- 
rived from them, , 
Together 
