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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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268
Analysis Insinitorum.
CAP. VII.
Fx qua extremi e linearum, quae curras in respectiris
punctiscanpune, proprierare sequens in maximi de mnimi
decerminatione emerxie Fundamentalis canon.
5. I. Si curra cujusdam ACD F H Z sub.
tangens BZ sic omni assisnabili maior aut in-
finita; erunt applicatae BC _ TD (OuXe me.
diante tansenti ZC ad subtansentem expo-
sitam ZB relatira, seu per ips coincidentem
currae intinitesimam DC, COnjUnGUNELIE) sibi
mumuo requales, adeoque inter reliquas currX
applicatas maximae aue minimae.
Demonstratio (IE BZ: t, BC: y applicata,
CR: C infinicesima, D R: a applicacarum incee-
mentum aut decrementum; erit, juxta pro-
prcetacem omnibus cueris communem, a 
S POSt vero + infinita = le m e e intini-
celuna explicata per in crit a = km m, quod
per lemm. 10. nihilo aequiralet.
Ouare, cum hoc in casu differentia applica-
carum nullasC, Coiplonec crescumenec decrel
cunt. Sed sibi mutuo requantur, adeoque juxta
modo praemissa maxima lunt, aut minima. 9. c. d.
5. 2. nde tandem manifectum eA; sI ex-
policae aequationis indeterminata quaelibet ad
maximum aut minimum determinando veniat,
RGUATIONEM MaEC, TANGUA Ex CUIVX COnre.
MenEiS