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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 2
# Folio 7r, page id 00068204:0013
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non dubitabitur, credo, de binomialibus longé facilioribus quae
in his continentur, et prodeunt ponendo tantum litteram aliquam
E vel f vel g = 0, et n = 1 vel 2: et si series, in quas ista resoluant,
non posuerim in epistola priori, intentus non in omnia particu
laria enumeranda, sed in illustrandam methodum per unam et
alteram in singulis rerum generibus instantiam, quae ad osten
dendam ejus gneralitatem sufficere videbatur.
caterum, hac Theoremata dant series plusquam uno modo
nam premum si ponatur f = 0 Et n = 1, cuadit 2+977, onde
d
prodit serces nobis communicata. Sed si ponatur 2cg -s; et
n = 1, inde tandem oblinemus hanc sercem 1+  -  -  + 3 + + 2 1
 +_C. pro longitudine quadrantalis arcus cujus chorda est onilas
vel, quodperinde est, hanc 2+ 1
53 3 rec pro lonositudine.
dimidii ejus- et has forte, quia aequé simplices sunt ac atteroe
et magis convergunt, non repudiaebitis. Sed ego rem aliter
aestimo. Illud enira melius, quod vecliss M, et Problema.
minori labore. Soluit. Sic quamuis haec aqualit X’-X -.
appareat simplicior hacce, yy - 2y1= - 120 = Y20, tamen
in confesso est, posteriorem revera simpliciorem esse, proptere
quod radicem ejus y Geometra facilius ervit. Et ob Ranc ratione
series pro oblinendis arcubus circuli, vel (quod eodem recudit
pro obtinendis sectoribus conccarum sectionum pro optimis
habeo, quae componuntur ex potescatibus sinuum. nam siquis
vellet per simplex computum huy us Serrei 1+ 5 -  - 7 + + Xc
colligere longitudinem quadrantis ad viginti figuraru loca
decimalia, opus etlet 5000000000 terminis serice circiter,
adquorum calculum milleni anni requererentur; et res
tardius obtineretur pertangentem 45 grad. Sed adhibito sinu
recto 45 grad. quinquaginta quinque vel sexaginsa termini
hujus seriei V= X 11t +150 + 89 c sufficerent, quorum
computalio tribus vt opinor vel quatuor diebus absolui posset
Et tamen hic non est optinous modus computanditotam
peripkeriam: nam series ex sinu recto triginta graduum
vel ex sinu verso. Sexaginta graduum conflata, multo ctius
dabit areum suum cujus sexsuplum vel duodecuplum est
tota peripheriae. neque minori labore oruitur area totius
circuli en segmenso cujus sagitta est quadrant diametri. ejus
computi specimen, siquidem ad manus est, visum fuit apponem
et ona adjungere aream Hypertola quae eodem culculo
prodit
Posito ane transverso aequali 1 et sinu versa seu segmenti