f 94 ) 
f<px = A n , adeoque ab —fax eft ut quantitas P n ~A*. 
Defcribat corpus Curvam VK, vi centripcta tendente ad C, 
deturque circulus V XT, centro C intervallo quovis C V defcrip- 
tus. 2/it quantitas conftans, atque ~ = z. Sitque K1 elemen- 
tum Curvsej IN vel D E elementum altitudinis, AfTelemen- 
tum arcus : demonftrat Newtonus Elementum arcus feu XT 
exprimi pofte per hanc formulam 
Q*IN*CX 0 . , 
WF^ s,m,liKC 
A A 4/ A 
ex prremiftisDominus Bernoullius,pofito Arcu UX=z, & altitu- 
dine (eu diftantia=:.Y, elementum arcus ad hancreducit formu- 
• OCX 
lam fcil. z = — ^-7 — : ~ - A-. Ec P rimo quidem af- 
V ab. y 4 — x 4 /tpx — a c x 
pedu videbatur formula Newtoniana quodammodo fimplicior 
Bernoullian^, eo quod paucioribus conftat terminis ; at re di- 
Ifgentius exploratS, vidi Bernoullianam formulam omnino cum 
Newtoniarta coincidere 5 nec nifi in notatione quantitatum ab 
ea differre. Nam fi pro ab — f<px ponatur A EG E, pro a c 
ponatur & x pro A, a pro C X, & x pro IN, fit 
a 1 c x 2L* CX x I N 
4 / abx' — x*f<px — a z c z x z ^ A ^ * A BG E~ 21. A r — 
A 1 
OxCXxlN 
jgj 
- feu ponendo z z loco — , (quod facie 
AAVABGE-X 1 ‘ A 2 
Newtonus commodioris notationis gratia,) Formula Bernoulli- 
Q*CXx IN 
anaevadit 
AW~XBGE-z z 
unde conftat formulam illam 
non magis a Newtoniana diferepare, quam verba Latinis lite- 
ris exprefta difterunt ab iifdem verbis feriptis in Gracis cha- 
raefteribus. 
Poft traditam generalem formulam ; defeendit Dominus 
Bernoullius ad cafum particularem, ubi vis centripeta eft reci- 
proce 
