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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 157r, page id 00068195:0313
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Approximatio ad Mensuram circularem Geometrica: Circulo eato inscrite
polygonum quodlibet, utoco tetragonum segmetitorum assume unum
saguttam produc extria C. continue subsegmenta bisccando. Pimum Trian–
culum (abscissis segmentis octogom) est ipsum Triangului altitudine sagibta bas
chorda tetragoni. Uet hnic Triangulo addas oa duo segmenta Triangula
duo octogoni, ex puncto qua sagitta  exit circulos  erige perpendientare
ad chordame octogoni, t aequale ragitte octogoni, et duc rectam
per extremitater ex extremitatibus aloguai tetrago chordae tetragoni
per Etjus perpendiularis finem, donec occurrat su sagittae productae. Tuan
gulum compreheusum sub hac recta, sub sagitta productuad chorda crogoni
aequale Triangulis octosoni Triangula sedecagoni adde primum ad
Friangulom octogoni produrtum ad Triangulum Tetragoni. Ita
info semper proredendo ticansulum istud semper aequabitiis omnibus
isstis Liangulis, et subsigmentorum, et si posset invendi hminas
Si scilicet poscessio
seu modus progcessionis, hhaberemus, quadraturam
ista reperiretu seometricac aut aliter summabilis
Ud si pona
necesse est differentias differentiarum c sine evanescere
Quod ita demonstro, C est finitum (=. K + f finitis).
Jam e = f+ f+ f... necesse est ergo numeram
nedum de scenden
une derescentem
et P ex non est
tium esse finitum. Mira est haec demonstratio
Hnc illud quoque demonstratur omnis seriei finitae pates
Caetrum easum esse possibilem ino utitem, infinitis mods ta
Hinc sequitur si destur quantitas ipsius e. vel X.
estro: cum f. invenire posse nmnerm possibilem serierumdum Aestadim
p et
fiat jam aliter etea alicusic. af
rteta
ata
s a
etc
ea
da
Ca
etc
b
m.
t
ete
ba
ba