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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 18
# Folio 1r, page id 00068267:0001
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Inter omnes vias perveniendi ad quadraturas
speciales aut demonstrandi impossibilitatem nulla
nunc succurrit facilior, quam si serierum mearum
aliqua assumatur, et seriei ejus quaeratur quaerendo
summam investigetur seriei summatricis proprietas
replicata. Scinde investigari poterit an possibile
sit inveniri ejus seriei termmationem, seu coanditatem
narametrum totius seriei. Mnro id facile non fC, quando
differentiales seriemus datot tantum
serres mea pro circulo est:  - 1 + 1 - 1 + 1 ec
 seu
25
5+3
2 +
Numeri autem impares sunt 2X +1 ergo sevies t 3 generaliter
-L vel  etc. erit 
et fiet
2X + 2 + 1 = 2X +1
2X + 1. 2X + 3
2X + 1
en 2
a cujusterminus, 1
quaerenda ergo summa seriei y+r
a
vv-A
EV Ergo VV aequ
m-n aequ
a.
in in
vet
at + 44
l.M
eodem modo v + 2a aequ 2 aa + a: m - n
aa +a: l. m + 2a aequ Va1 + a: m - n
et
2X+2 + 1
ubi sunt X ovel
2
seu aXx + 6 + 3
2X + l. 2X + 1 + 2
et 2X + 1 appellando y. fiet: 0 +2y
sit series summanda
summaliix
sit a unitas
lum aequ a aequ
l- maeqo
+2X
posito y esse, veel 3 vet 5
vel si faciamus aux-3x+4-, seu
et ponamus _ vaego 2X - 2. fiet
f 9
vo-1 et differentiae
b
niter
V sunt 2
a
4, 35, 63
L t L. +
15
m n 
.Ergo fiet:
(aa, + a: (n + 4aa (= aa) - a: m-n aequaa aa + a: l m
seu a: quadr. Jum (+ 8a: l=  - 2a al m. m. n (+ 164 - Ba : m. n +a quda mon en at (B. 1. 
et sublatis fractionibus, si omnia multiptcentur per quadr. Jm in min fiet
a quod  a. quaer. M -n - 2a l.m. Mma n +  a. quadr la m aequ. P. P. M. A . n l n
seu a b = 2abc + a cc aequ 8 bc brC posito b aego l.m et eaego m -n. net
unde b +c aequ 1 - n
sed quia series l. m. n. decrescit decrescente serie b. C. d. sumanus
aliam progressionem p quae crescit p9. Y.  quae deciescit crescente
serre  b. c. d. idem erit bm rg seu bogo _ r.g idem idem
c. d
L
+7. ++
a
15
+ ia
plane palculus, faciendo r-q aequ d seu a: vervata-a
et q- p 4 seu c aequ a: v- aa
Et scribetur aequ. D. per omnia similis aequationi C pr
ploliteris l. M. n ponendo r. 9. p. Et quidem
conjumgere possernus aequationes C et t et in casu
terminitiones pontre laeqapier et Maego q et Magul