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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 32r, page id 00068194:0063
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octrina de le riebus infinitis Arithmetias, intervalla ninctum assignabilia
habentibus scapte natura intractabilis; non s ope Geometriae provehi potest.
Ope autend Geometricarur demonstrationum innumerae in ea detegi possunt
novac aequationes etharmoniae, eaeque forte inductione notis multa admorandir
adscriptae
Cum dentr  pometrice dentur multorum arenum circumferentiae sygnot
isio daturae.
ideo atque inter se; exprimantur duo sectores curque seriebus istis infinitis.
Cumque detui ratio sectorum dabitur et ratio senerum V una alterus
dupla sripla; etsi hoc ex ipsis forte nemo mortalum sit agnituru
Ex Tamgenleserniarus invenitur tangensarius ipsius resula bieni a pellio
tradita
3a 343, ra ga
tc
105
250
10g
1000, 00d, 30d, ,  1009, 00V, 0v0, ory, 00o,  ens 104, 009, 0ri, ory cv0, orvva
14. 2a 2 a - 2a n a  1a mer
= u5a - 1894 + 135a - 105
945a
1
iis
1000, 114
aa
EE
et bit bde
bd3
Ego a , b - am + bl F C = amn + blr + CIm etc.
Imn
Im
Atque ita semper quilibet terminus in caeteros omnes ductus
intelligetur, demto qui e ubscriphus est. Atque hoc est
Eompendiosa ratio reducendi quotcunque fractiones ad eundem denomina.
torem, nimirum termini omnes ducantur in, se, H Inde ai quot sunt
termini tobies ad hibeatur productus, aliquo termino minatus  dmupa q
u
nat
et i resituum in eum numtatorem ducatur, qui est subtracti noraloris
I. ita praectera habetur ralio, eaque universalissina
91
3)
lmnp
lun
imap = pa
Factus Nominatorum ducatur vi summas numeratorum.
inveniendi fractionum summas:
a poducto anferatur summa factorum ex quolibet numeratore in suntu
nomindorem.
vel fiet
e. g.
lmnp 4)
lmnp b divisu prlmap.
lmmpa
linmp 2x.
Ergo nihit an
ducu
am
p
dumn
720
220 -
at b.
n
 42 +34
at b+
in
marh. A