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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 49v, page id 00067993:0098
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32+ 12+ 2C
irZ
sit calio de caeberis ti id genus rectangulis omnibus quam exignis omnibus
patet summam houam tuiam infinitarum quantitatum, quaum (differentias
infinite parvas  habentium) quarum una est  daturam esseraream
PaF
ipsius a
asse aream circuli, quare posito B esse et ut dixit dis intinte simam ipsius
Z, seu ipsas  et ipsas Z esse aritimetice propartionales seu differentiam
lequ.
dubentes cnstantem B, ideo pro B inifinti pumi ros comstante, subus sinit   5  35 48 6 80 99 1o e. aequ.
stitmendo a vn Ad. fui  Ea + Et si dutalur curib culu N erdina ti
hae
1 a1 Z 3 a. cussit ordinatae proprntiouales
abscissis positis Z nil ordinatae 
B1a +Z
ugae nons
his exiguis rectangulis B E(E), et portiones cue erunt sirationtus seu smmae
ordinatarum ejus (positis Z. anithmeticis) erent summae inquam omni 
sint Z. Ordinatae vero
erae
2Z. a sosituram esse circulo quipollentem,  quomam
sut
 () a +Z  da
eum ordinatae ejus recta lis AX) ciit circuli elementuribus apripallent
etiam ejus ordinntorum in β ductae, infer portionem abscissa differentiam ipsarum q)
Z2)  aulrctae hs rectangulis circuli elemen teribus CF A E (E) aequantur,
ergo tamma harum ordinatarum in corstantem B dustarum se seu area figuiae
curvilineae novae, portimim cirm suamae omnium horm rectangulorum, seu areae
circuli nons cuculi aequabitur portioni circulari respondenti aequabitur:
sufficit ergo in veniri summam ommium 85 a.   fiet seu
1) a
aiquom fractionem methodo Mercaloris in infinstem
p2 Pavaboloidum ordinutas resolvendo earumque summas ipsis subscribendo
(nO+ 538 +62424
+92
1 
ocnium 
a +3aZ+ 14eZ+
habebitud series rationalis infinita, exprimens magnitudinem sept niscgmenti
a
sn pornonia circularis et HER. sit ZBe a aequ.  8Z agu. b. 
(33223G
baae qu. . frer 
a __ aqu 
 aa it
aqu. b = bc+ bc eb 8c. et rurtus valores subslicuiendo fier.
a +t
ver  c
seu  bd aju. b - bc + bc - b c3 dc.
aequ
132+ Z6 adom et C 1t
et si tribus primis terminis, e contenti simus, ipsasque b. et E. varsus explicemus
est
ang2
fiet  caequo
vel ordiiendo L 
b
2424 2125 -928 474Z 41 8, B7 + 18, 2, V n
C -bc
Ga n equ.
s
111+Z
+ bc2
8- 14 a 48 36. 172 + 1d. 2
13, 915
+482682
13 15
area spatu im AEB, p AEBA, posito AE aequ.  et
2za  aAque haec est modu methodus generalis quae omnibus
DEB, aequ qix
 e
= egu. 8Z - 247 r48 Z + 17 Z + 15,8, 2 + 1827 52
e
3ei
1+ et summe omniom 
aeso
ommitio venivis malyticis (et suo modo etiam trans scendentibus)
dua res re adpuram analysin reducta: tantum enim suffic opus est inveniri
dutaa
diophanteo more solvatur: quod verio on semper fieri potest secus ac
 problematibus nmmericis, quoniam hic possunit irrationales etiam salulum
modam quo equativa curvae naturam explicans rationaliter atque indefinae vel ut cum sentono loquarus juamres eodem redit,) snus versus.a
ner applicaci potest, ulcunque aequationes earum sint implicatae, aut affectae