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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 5v, page id 00067993:0010
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Ego cum (aete sed quomam hac methodus ad eas tantum curvas specto
quarum ordinatae sunt frationalis absissis positis rationalibus, i quod in circulo
aiti
non fit, ided sitata a me est curva rationalis circul cujus area crculo
ordinatae aequipollet.Ejus
nde logar illumo termiam, dugit perelegantem Ego recisrocam excogitavi rationem
ex dato logarithmo inveniendi numerum; et Sed qu
Jacobus Gregorius scotus elegantem modum dedit, quo series convergentes ut
ille vocat, quales sunt polygonorum extra et intra curvam possunt terminari,
et locus mn convergenti non nunquam Geometrice, semper mechanice
terminari, id est inveniri quantites in qua una serres alteri occurrit
quod etiam ad quadraturas nonnunquam uile est. Quoniam an
ptrimus appovunquandi xexemplum dedit Archimides  magnitudine circuli,
quod nostr tempe adiu vestigus institit Ludolphus, sed posteriores Geometrae
vieta, suellius inprimis, Hugcuius et Grego Lucobus Gregorius preclara in eam rem
compendia reperere. Wallisius elegantem didit modum appropinguandi in numeris
rationalibus; sed illa toti tantum circulo non vero et partibus aptatum. Gregorius
serierum convergentium, utum ad quadraturas ostendit. Nam Selygono serem
duas unam polygonorum inscriptorum crescentem, alteram polyponorum circumscri-
plorum decrescentem, vocat convengentes, quarum concursus est in ipso circulo; ubi
modumque tradit qua series istae sallem per appropinquationem terminum
sed alia restabat via per series infinitas quantitati
quaesitae perfecte aequales, quae tantum praestant appropingoationibus, quantum
possint.
aequalo deleminationi Nam cum circulum ajo aequari huoc quonttiseriei i infinte
infinilae
1+ 1 + 4 - = + -  ec. posito quadratum circoniscriplum esse +
utique plus aliquid dico, quam gi modum appropinquandi exhiberem. Oanis eumt series continet
approx inquatonem quantum licet ecta exuctam, sid proterea veram quandm exactamque aequalitotus