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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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CAP. VII. Analysis Infinitorum.
DetuE Per r Z + 5f; quae omnium minima hoc in
calu experitur. Sit erso rZ ts f= py aequatio
repexsentans virium Cummam; in quodcunque
etiam superficiei AF. punctum radius ex B in-
ciderit; in qua, ut p minima reperiatur, (FIs.
LXXZI. N, II.) ad interceptam communem
AC: X OrdinatX CONCIPIANEUEECS CUEVX AD
AB, AF; quarum applicatae dicantE C B: Z,
ejusque SUDEaNSCNS C K: l; CD in CaTU Le-
Hectionis, CF incalu refractionis vocentur: f,
carumque Cubtangentes CL _ C MI peoraria
intentione appellentur n; tandem in CurVa POHL
lit applicata HIC: v. ejusque (ubtangens CT: 1,
erit POSica Currarum inceF SC relationc r2 + 5)
yy, aequatio Tubtansentialis carum omnium
ex C aP. L. 5. 35. rZ + n + 5flF = 2 yγl n, in qua;
si y ad extremum sit determinanda, seu ad li-
ReaM ON, crit t infinita; unde ex SchOl.
Gencralis, N. XIT. rejecto 2γyln, ac divi
sione per instituta remancer Ln F 5fl = O, PiO
aequatione determinata.
Cum aurem hic ad omnimodam problemaris
determinationem aequationes neceslariae ex dato-
rum natura reperiri possine; ac (IT I. in triangu-
10 B AC in A rectanoulo, (vide FIC. L X XXI.
N. 2. eC 2.) d d Y X N = 2Z, Quae ett ad locum
CUEVX B A, erit ejus subtansentialis l = X