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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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1
Analysis Infinitorum.
C AP. II
currarum proprietates, quae omnes Punt (pa-
tiomensurabiles, ut factis b. I xech= Ir exit X L: Y::
Y + X: yD.
Schet. Ouanta vero hinc cheoremarum, ac menturabi.
lium currilineorum copia enascatur, nullinon manifectum
esse porest; qui ex aliis cum porestacum, cum reliquarum
quanciracum, hypochelibus alias in infinicum oriri Curvas;
cum _ pro singulis, in aequatione generali, Fractionum
numeratoribus, quorlibec terminorum, simplicirer x cum
decerminaris continencium, aspregara curo astumi posse
perspexeric. modo haec sequentia observentur; I. ne plures
uno rerminosips Fractionum denominatores contincane II.
ne porestas pere detienara, nis per numerum attremori-
rum aut inceorum explicetur; caererisd, m, 5, ecc. Tup-
ponentisbene placitorelictis.
Duod, si secustrxc Pesehabeane, ac deveniatur igitur ad
r
hanc aur similem equarionem y = p. Fr aUILy = V rY  X X;
nulla adhuc hie recula eradica est (nis Forre incex subpor-
males reperrae ex 5. 18. menturam invenirene) quaom-
nium ye valorem absolurum indapare possimus; nisi adti-
bica priusreductione, quam per divisiones Mercator, PeF ex-
tractiones inclucus Nemcon ad optacam metam perduxerune.
ucraquehaec, cum dirisioniscum extractionis operatio po-
teltatum in Binomiis desienatione perticirur; urimox sub-
nectendarheoremare parehie.
2T. EH autem cheorema hujusmodi: (it bi-
nomium quodcunque z + ferehendum ad pore-
statem quamcunque delisnatam p: erit (pOlIto
termino hujus porestatis in ordine primo = L27
cuins genitura = 1) haec, Quae sequitur, gene-
ralis pro terminorum reliquorum senituris con-
BruIs