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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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282
Analysis Infinitorum.
CAP. VIII.
BuS, nON EaMEN DE, FC, CI, Fore aequalia, adeoque
differentiam quandam incerillas intercedere. Dux quidem
differentiationum continuario num exiidem, quibus dit
ferentiario prima, tundamentis deduci gneat, sequen
rimodoinguisivi.
Sic (FiS. LXXXLTII.) curvilineum AZX, sumeaque
AO INTCTCCPTA: X, DO applICaLZ: y, AD CurVa: 63
subtanBeHEI FO: P, TangenEI FD: S; IN aXC AZ accipIaNEUI
se ULVOINSEqUENEESINETCCDEX AP, AR, AS, quarum
differentix sun infiniresimae seu omni daca minores, OP: es
PR: O, RS: N, CI. Leibnitio dx vocicacae; deinde 2d Giro1-
laaxis divisionum puncta h elerentur appliCaCR, PF, RC,
SI, erunc applicatarum differentix HIF: a, JC: pu TI: Z:
currarumque respectirarum, DF: U3 F. C: d, C L: E; que
rum illae D. Leibnitio, dy, Hxe de nOMIMaNEUE; qux Cyr
varum disterentiae insiniresimxe versus axem in F, F, C,
productae generabune infinicesias, FF: L. GF: ∞; ac duc-
EIS FK TB5, D23, F. 4, Tangences ad angulOS rectOS
secantibus alix rurtum orieneur infiniresimae, GR: 2,
FB = R5: 2, 34. = 2 L= DF: 13 4C= F C = d
Jam ob criansulorum F OD e D EI F Similicudi-
nem, eAt.
I. 1: y:: c: 43 TCW FO: OD:: DF: HTF; unde 2a = ve.
II. 5: 7: : 21: 4, Teu TD: DO:: DF: F. FL, undC 5u= 9a
NII. 1: 5: : c: 1. Teu FO: FD:: DFT: DF. UndC se = eH
Tum ob triangulorum F P P. _ F. gC similicudinem est.
IV. 12 C + 1: y. F a:: O: p TCH F P: PL:: F. G: JC, unde
perlemm. 10.) 30= rpu
V. 14 C F 1: 5. = 1 + d:: 0: d. Teu F P: F L:: F (J: FC,
unde (Per lemm. 10.) 50:+ 7d
VI. 5 + 1. + X: y + a:: d: 10. seH F F: P. P:: F. C: C 7, unde
(Perlemm. 10.) yd: 5pu.
Tremoberiangulorum GRC _ CLL similitudinem est.
VII. 5. + Y F a F H .F d: y + a + p:: Z: E. TeH GC: CR:
CI: TL. Unde (per lemma 10.) 36= 5E.
VITI. 5. 4. 2t . 2 +. 4 +. d: 1 + ∞ +1. + e + 0:: C: X. Teu CC:
GR:: C T: C L. Unde (ex lemm. 10.) tE= 5N
12. 1+i + D + e .+ 0: y . F a F p: : r: E seu GR: RC:: C L.:
E.L. unde (per lemm. 10.) 1E Y5.
110