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# Title: [Bernhardi Nieuwentiit Considerationes Circa Analyseos ad quantitates infinitè parvas applicatae] Bernhardi Nieuwentiit Considerationes Circa Analyseos ad quantitates infinitè parvas applicatæ (shelfmark Leibn. Marg. 150)
# Folio 42, page id 1032704993:0048
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1032704993&page=48
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 32 lines, status machine
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42
Considerationes.
applicata RT sit ad subtangentem R NI, ut linea
data e ad porcionem applicatae IL. interceptam in-
eer curvam AI es rectam AL anculum semirectum
faciente cum axe AR. Ouam leguenti modo
solric rir Clar: ad afymFOcon AB perpendi
cutarem ad AIE, construatur logarithmica
vulsaris DC, cujus subtangens A L sE aequa
lis datae linea, r; a puncto quolibet locarith
micae C ducatur C I parallela axi AK, ex C C
ad eundem perpendicularis secans tangentem
Logarithmicae DF in puncto II; Cumeaque
BL aequali ips C EI; punctum Y crit ad cur
ram Guaesitam AJ.
Vocentur jam (ductis lineis ut apparene in
Schemate) IE I: y, ILM: L, CB: Z, AD:
s AK: ~, TL: y - ~, CTMIIE CXD: ANEHOrIS
constructione, AE ∞ QB ∞ r, eE CII ∞
BJ ∞ AKE ∞ x, unde _ HICF ∞ y - ∞ 8C
DCF ∞ b - Z, cum lit, PO D NIB D RS
∞ dy, 70 ∞ da, C5 ∞ dz.
Lst igitur ex problematis conditione y :
D= +r: y  x:: dy: du, unde vay ∞ yay - rdx
adeoque sumtis inceoralibus, omnia xay ∞ Z qu
ex ∞ crilineo B) a, quod cum CI: Au
thoris ouacratura convenit; (srnetur A.)
Sed ex Constructione problematis; DA:
AF:: DC: CH TCu R: 1:: k = 2
y 36
Onde Ky = Rx D tr = rZ, dc ductis
Omnibus