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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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Analvsis Infinitorum.
CAP. V.
te ex hoc calculo prosuat. Sit FIZ. LXXV, CUI-
ra ADFF, cademque, gua in 5. L, linca
rum Crmbola, Crat p: k: : r: Z:: C: W, ande Z0
=ru quaeritur jaM (A Z POnatuEin C ad
e
spatium Currae BC NC ex typothes quadea-
bile) CurVA ADFF, qua idcirco, Cx S. T. in
rectam est mutabilis, proprietas; aur applicata
D 9 Ceu y ad A 9 seu x relatio; cum itq
que sC y: k: : r: Z, Crit d yγ: k k = yy:: pr:
2Z = pr _, TacOZZ = p r - ff
S. erit quo-
que y: l:: r: f:: e: a, unde fe = r a; positis ergo
fin OX, _ rin LM, eA curvilineum A X XO
= omnia fe, _c rectangulum F KFO = Om
nia ra, quae aequantur rectangulo dicto ry;
quare DO seu y =
omnia fe spat. AX XO
Unde Ctatim apparet sequens theorema; data
Figura quadtabili ABC0, cujus applicataC
seu 2, ad cundem arem applicetur secunda Fi-
sura AX XO, cujus applicata OX seu f; ita
TaCM, UE SIE PerDetLO ZZ = p r = f
deallumatur tertia Figura AFO, cujus applica-
ta DO seu y, ejus natuex, ut ducta determi-
natarin applicatam quamlibet DO Ccu p, sIE
continuo rectangulum ry aequale spatio curri-
lineo adiacenti. AX X scu omnibus fe, erit
CUIIVA AD F F in rectam convertibilis, e
Xqua