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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 21, page id 1032704993:0027
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Considerationes.
S. VIII. NC, autem CUEraS IN GOnCrCCON
cemplati, circa parcicularia hunc calculum cuto
adhiberi credamus; exemplum addo in circu
lo, ut currae hujus omnibuscoonita proprictas
rerum, insuetis alias latis intricatarum, disti
cultacem (ublevet.
Sit (F1g, 2.) DP: V, Cinuscirculi, cujus ra
diusr; lagieta A P: X, erit hujus proprictas,
Uti nOTUMI, 2 r X  X ∞ ∞ yY; cujus ditteren
cialis cA rd ~ =- ∞ d ∞ ∞ y d y; Qua, POlicis dy
xqualibus, denuo difterentiaca dabit, rddx
∞ d d X = dx d X ∞ ay dy (haec lignetur L)
quae si rurlum certio differentietur habebitur.
rd3 X d X a d ∞ - ∞ d3 X = 2 a ∞ d d X ∞ 9, (CI
rd X = d∞ adx = x d X ∞ 2 d ∞ d d∞ (TIGNCELIE
P) sedrelumta jam aequatione IL erit posterans
Politionem dxdx + dydy ∞ rddx - x ddX
∞ as as ex hujus s. VI; haec differentietur
denuo, Aetgue rd3x = d∞ a dx = X d3 V D
2d5dd5 ∞ 2 d x adx juxta aequationem littera
P designataM.
haec autem ultima in summatricem ver (a de
juxta lemma s reducta exhibebit post extractam
radicem quadratam ds∞ a x, jam ex hujus s. IIL
CAF: K:: d x: ds, adlcogne propter harum aequa
licatem, k D F, leutangens TD aequalis lubtan-
senti circulis Ccu ipsiLl.
Si rero inrenta xquario circuli disterentialis