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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 251, page id 1032977698:0273
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1b
C AP. V.
Analysis Infinitorum.
crit BF = 5 + u - a, unde tangentium TD de
BF differentia continua cA: 1  2; (I VerO
Cxdem tangeNtCS TD, de B F ContanteE PFO.
ducantur in F _ F, ita UE T F appellat B,
linea BF SE perpetuo B F 2; Ceit D F = 5 + h
aC FT = B F + BF = 5 + 1 = a + B + a = 5 + B + 1
quare lincarum D F X YF differentia erit =
OF = W, lincaeque F F d F L aequales; unde
clauso per FF triangulo F FY, CxIF F Z utrique
Derpendicularis, ex lemmati 33, de Parallela
intiniresiX C B, AC ex T ducta T s itidem
X ip(I CB requidistans Faciet B S = CF = 2;
remanebitq. SY = T F = B: CUIL AUFEM F Z CIE
quoque intancelima, quoniam CB talis el,
continuata, ut in 5. 6. tansentium seric, eII-
TuS OmNTa FE abibune in curraI AFI, cui
omnes rectae cueram AD F tangentesnormales
crunt; unde, I1ambx ha curra in eodem punc.
tO A delIanE, Semper recta DF aquabituE
CUIEVA AD, FUMLjuXta S. 7. Tum etiam, quia
F. F aquatur ominibus u, Quonia BF XG1I2-
tur omnibus, i - , ec BI omnibus a, uti
tangentes continuando apparebit.
Ouare, SIdatA CVEVE AD F. relatione, adeo-
que omnibus eam tangentibus, inveniri posser
CurVA A FL natura, seu respectus ad axem AO
InVenta Toret hac unica opera omniu ecome
tricarum currarum longitudo.
Coroll.