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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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29C
Analisis Infinitorum.
C AP. X.
. 5. 6. Sit aequatio quaelibet infinitesimalis.
rXC = yy e= 3yy a; quae collectire Cumta, 
altCFA PaTS 3 y y a Cx 5. 2. HujuS reduCaTUE, 2
bic in collectire mixtam (vid 5. 5. exempl. I.)
omnia rx e = omnia yy c = y Quaruntur hinc
termini infinitesimales collectire sumti, qui valo.
rem ipsius y per quaslibet indeterminatas verb.
sc. F mulciplicati au dirisi, seu ipsum y’f F
adaequent. Ouod quomodo obtineatur in
calu mulriplicationis, sequens docebit theorema:
terminis expositis infinitelimalibus rx e- yve.
per f. Ccu quantitates indeterminatas prius
multiplicatis, pars aquationis expolx absoluta
perterminum infinitesimalem 3 ffi ex f30-
riundum multiplicata, cum suo signo legitimo
addotur; e Cumma haec infinitesimalium co-
lectire sumta xquabitur quaelito valori absolu
10 yf
Sic, ut in eodem mancamus exemplo; ex
inrenta aequatione omnia rx e omnia y y e=
y sequitur omnia rx f. e- omnia y y f et
omnia 3y ffi Fore aequalia ralori abloluto
Demonstratio. Cum enim (ex C ap. II. 5. 73)
sIF y
 omnia 3 yy f a + omnia 3 pf
omniarx f’e-omnia ryf’e + omnia 3y ffis
E collectira lixec ad insinitesimalem deprimarue
ACrI