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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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CAD. II. nalysis Infinitorum.
respectira Ciroidali portione AR P, erit X
quale bis SUMEO reCtangUIO PX 1O Teu AP
in PF: est enim exnatura CiROidiS rZ = X Z
= X y.
Lum e alia ratione ex aequatione inventa
3d.
f= 2 p totius Cirsoidis ad circulum ratio
Cornolcitur; est enim rectansulum P K M,O
 p = rZ = X Z; Undc FactO X = r, Cu A d
=AO, pertincbit ipla f ad intesram Cirtoi-
dem, ac d ad tocum semicriculum, ec p era-
det aequalis nihilos quarc 3 d - f = 0, ecf =
3 d, seu cirsois ad semicirculum ut 3 ad 1.
Timilia hic porsene circa cirsoidem ex hyperbola
senitam aliasque curras adjungi.
5. 45. Sic Conchois ABC FIK XFV vet
tice A, normâ D e ac Polo M descripta:
VOCeNtITg. AG: X, GB: Z, GD: f, G M: l,
AD: Y, D MI: p, tum radio AD ducto circu
li quadrante ADZ, appelletE HG: Y, Tan
dem dicantur intinitelIa, 62: c, 4, 5: a 3
N 3: 0.
Notum est aequationem conchoidis propeie
tatem exprimentem esse ly = f2, haec redacta
ad terminos infinitesimales dabic f0 -2c=
la =ye, quae, si ducatur in l, dC l0c0 ly
Ponatur f2, exhibebic fl0 - l la = l Z e = fZ e:
unde (cum (Ic I - f = P, AC ex HatuEd CONChOI
dis l: Z:: f: y.) omnibus pei sdirilis fic
0