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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 294, page id 1032977698:0316
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294
Analysis Infinitorum.
C AP. X.
tis, sIE PerpetuO p: g.: f: y. unde qf = p9 =
qu gr; ec ductis omnibus in a, erie py a =
qu a -g+ a: dClocoF a POlITO y e, Crit p y a =
qu’aqye; e additoutrinque 2 9y e, aCOm
nibus collectire sumtis, emerget post transposi
eionem omnia 2 9y e = omnia qx a t omnid
gye omnia pya; adeoque (cum altera hu-
jus aequationis pars sit reducibilis per hujus 5. 2.
e 4. 2d 9y X
2PγY) tandem, juxta C ap. Il.
5. T3. Cradet; X y-
4q= omniay e= trilineum
AF P, unde _ hujus quadratura innorescit.
Potuisset ipsa alio modo inveniri: si enim in
venta aequationi pya = 9 X a - qy e addatuE
utrinque qX a, erit py a + 9y e + gX a =: 2 9 X 43
quibus collectire lumtis, ac juxta 8. 2. ex 4. hujus
reductis orietur ex Cap. II. 5. 13.
e omnnia x a = trilincum R AF.
P97 + 972
Scholium Noretur reductionem hane supponere indeter
minatas x e ) ec. nulla sui parre dererminaras esse, sed
meris infinicelimis ab inirio ad finem per roram Cui longiru-
dinem componi, de eodem quidem modo, quod circa
Cap. L. 5. 12. exprese monnimus; cum es requariones exre
ductione resulcances cerminum nullum omnino derermina-
rum admirrere. Si enim infiniresimae sinculla ad inderer-
minatas suas limicarione accipianeur, una eademque infi-
niresimalis aequario varias quandoque curvarum speciesret
piciet.
Ouod ur breviter ostendam, sic aequatio insiniresimalis
29A= 2 X C, quxe collectire sumra dabic omnia 2y a = om-
nia