( 8ii ) 
fumendo SN mediam proportionalem inter SB & SL.' 
Curv^ qux ex Hyperbola methodo inverfa conftrui 
, pofTunc progrediuntur in hac Serie, 
■ : ■ . ' -2 2 
Hyperbola i. s : y :: r : a 
• • . . * i 
a. s : j :: 
• • 2 a 
. 5. s : y : : ri : 
' Ubi CtirvK quarum Jndicum denominatores funt in pro- 
.greffione i, 5, 9, 13, (^^c. exprimi polTunc in reiJtis & 
arcubns Hypeibolicis; reliqua; vero in redis & arcubus 
Curv^e modo explfcacx. 
Si ali;2 Curvae defiderentur quce alias exhiberent Se- 
ries, id facillime fieri potefl ope vel Circuli vel Redsc : 
h n 
ex eamm aliqua omnes, in quibus s : y'l a : r, 
conftrui poflunr, fumendo, fi o- 
pe Circuli Problema fit folven- 
dum, BSR ad BSL uc i ad 
»— r 1 
&SNinipraSR=^ ” xSL”; 
quippe Curvae pet omnia pun- 
• • n n 
^ua N dudiE ^quatio eric s : y : : a : r . Similiter ope 
• . n n 
Redse conftrui poflunt quarum icquatio s : y :: r : a-. 
Duas exhibuimus Series infinitas Curvarum redis 
commenfurabilium ; aliam arcubus circularibus, aliam 
Parabolicis, .aliam Hyperbolicis una cum redis menfu- 
rabiles demonftravimus : ex vero ad redarum menfu- 
ram arte fola infinica reduci pofTe videntur, ficut X- 
-^quatione fola infinica in redis exprimuntur. 
Cl. Author hrevitati fiudms paucis tradit, tlltm 
'tern fknius rem pro dignitate ejus iUuflraturum fperamus, 
IV. ^mar^s 
