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# Title: [Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductae] Bernhardi Nieuwentiit Analysis Infinitorum, Seu Curvilineorum Proprietates Ex Polygonorum Natura Deductæ (shelfmark Leibn. Marg. 149)
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278 Analysis Infinitorum.
Cap. VIII.
infinitesimae per vocales a _ e, XC. LITTerAS,
compendii gratia, designentu, OrituE tangeN
tium inrentioni inserriens Cl. Barovii metho.
dus. Videatur C ap. I. 5. 3. Schol. II. _ 5. 43
536,738.
5. 4. Si vero exdem quantitares infinitesimae
rocalium ex litterarum loco, per indetermina-
tarum, quas respiciune, differentias (quae in-
finitesimarum naturam nihilo secius retinent)
exprimantur, deducitur hinc ecteberr. Leibnitit
calculus, differentalis nomine vocatUS, Cujus
specialem demonstrationem, cum inter praece
dentia, Luperiorum ad inctar, expresenon at
ringatue, hic adjunso. Sint quantitates inde-
terminaca quotcunque, X, y, 2, f, carumq.
infinirelimae respectira, en a, un 2, Quae juxta
D. Leibnitii placita per indeterminatarum difse-
rentias, Teu d x, dy, dZ, df, denOTCnEUT.
I. Ouaritur iptus x L. y, seu quantitatum
ad se mutuo additarum vel a se inricem Cb.
Aractarum, differentiale:
FiaE X F y = Z, quae requatio redacta ad in-
finitelimas (politis nimirum x Fe lOcO X, y + a
loco p, 2 F W loco2, (quod ec in sequentibus,
semper obserratum relim) dabie, x +e f Y + a
Z F w, ec deletis aequalibus, e F a = W; CCu
celumtis (ymbolis Lcibnitianis d X = d y = d 2.
Il. Quaeritur ipsius xy, seu indeterminata-
FUI.