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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 18r, page id 00068022:0035
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chediasinatis de serierum summis pars VIII.
30 42
Quare si inveniretur separatim
jam
30 9d
90 110
ex. habentur absolute  1.
ex quad Hyperbolae.
90. etc. exhibent differentiam circuli
Hyperbobae seu residiun
circulescentes in unitatu quadrantis, detractu
spatio hyperbolico dimidiato
tunc data quad. Hyperbolo
daretur circuli quad ratura.
etc. resolvemus in = - - . +== + L - 1 etc.
Cujus seriei quadratricis quaeratur figura. Quaeramus primum
figuram seriei quadratricis; 
9 ea sive
 + bd + b + etc. quae tex summis omniam. 1 + y + yd + y ete.
quarum quaelibet aequalis huic ordinatae:
es
Eodem modo Series quadratrix L.
5
1y
 exoriginem habet  +  +  erc.
quae est summa ordinatarum V + y + yd et C. f
Figura cujus serits quadratrix est..
30  ex erit
1y
1 = V
1V+
sed 1- g dividi potest per 1 y, et provenit 1- y, 1. 7, et 147
et 1-y
112027
7 1+2y (177 (7)
1.7, 1+y. cub
sice 2
1-7, 1y4
1; et 1 - y, dividi potest per 1- y, et fit 1 + y. ergo ducendo 1 +7 in 147
fit: 1-  y f3
A tt. e V
sed misa faguia. Lvideauus tiguam airu.
+y y
Emr
1 11g Citg1 (, ars. 2)
uae momentum, est 9  ex 1-y, est q cujus habetur
ad nt porginae
1+Y, 2
dimensio cum sit Hyperbola  cubica.. Ejus momentum ex  1+ y
est
Compto
2s horum duorum momentorum summa aequatur figurae cylindio
Habetur ergo hujus figurae dimensio, ex data divensione hujus figurae
Opus est ergo ut hujus figurae dimensionem quaeramus, quod
eadem methodo egregie fiet:, nam momentum ejus ex 14y
dabit
147
qud quod est  cylinder spatii hyperbolici. Ejusdem
momentum ex r dabit 1- y dabit , qui est alics
cylinder spatii hyperbolici, horum duorum momentorum summa, dabit
duplum cylindrum ipsius figurae g.
unum colligamus
Cylindesi Hyperbolicio un
Cylindio Hyperbolae Cubicae a
 aee
a+ 2ay +y
Ergo ut omnii in
a alter a aucti
a - y
a +y
dant summani figurae cylindiumfi
cujus area aequatur sumnae
30 90 etc. Ergo
r D cylindium figurae
loy Crrye tyrG
(B. tam pqu +y4 Y pendet) ex circuto et Hup. sumil aodendo
 t 41e 615ae. 122 ro.
Tar 1+V 190  1 13 1, 1-y B ty  1