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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)
# Folio 295, page id 1032977698:0317
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CAP. Z.
Analysis Infinitorum.
nia 2 X c; & juxra prxecedenria reducta exhibebit yy = X X y
ac extractaradice y= x; undeprimmo haec aequario insinite-
limalis FiG. LXX XIV. ad criansulum verb. BF. RPNV (iN
quo H
X, e 05: y,) reducieur.
Si vero invencae aequationi yy = XX, determinata quau-
cItaS er sub quolibet signo addatur, Crit, Cx. Br. yy=
XX = rr ad hyperbolam, ad quam eadem haec infinicesima-
sissecundo referri porest, politis enim in eadem sBurZ R A: Y.
Re: X, DD: y, OP: C, FFF: 4, SIECUEVa AD F. AyperbO-
la, undeiphus aequario x x = rr = yy, qua reducta ad in
siniresimasdabit 2X C= 274.
Onde POStiS RP in PH, RC in OS REC, EUM FF
 L F AC DQ in HK deC. erIL F P F criangulum = Om
Ma ya
yy; cum craperium AGWP = omnia xe, 2.
deoquehicreductio omnium xe ad : xx locumnon habet.
trac quidem de caut2, quod RP seu x non in torum, sed
Parre Colummodo sui AP ex infinicesimis P8, OL, ZC,
ec. Ceus Componatur; readua nimirum porrIOn
R a determinata Mahente, quare hoc incasu omnia re leu
crapertum AGW L Xquatur LXX = Lrr.
tertio, Sit jam LP: X, eaque (IIPPONAEIT CreFCCRE Per
LL. _C. Teu e; 2C D:y decrescereper DZ: a; expona-
curq. Quadrantis cireali aequacio rr = X X = yy, dabichaec
intinccalem - 241- + =- 27 a _. mucaris IgNIS, 2XC=
2γa3 AHREaurem Pa O P in OX Rc. omnia XO =
triangulo FL V. ac ns aqualia omnia ya (si quidem 
perpethio in L. F, HIL, VO PONatuT) ConstiLVCMEELaPe-
ude patet quanssiber aquationem insinicesimalem,
simplicirer sine restrictone propolicam, unam determina-
tam curram non lespreere. cum manente eadem insiniceli-
mali, post reduecten quancirates quaelibet decerminaex
multismodis xquac ac BI queaME, quorum eractario.
nem maxis accuratalr, cs plusrequirat remporis, quam
mihimea impraesenctarum permirtume nes ocia, aliorum iu
Z l. 34 sCl L pr - 197.
dapini ulteriori relinquo, hocaddo:
6. Sit