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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 21r, page id 00068200:0041
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ecembis. 1679
Ummum
calculi analytici
fastigium. per Calculum Alyorithmicum
diuallem
exprimi potest per infit numerum decadicum sive
finitum, sive in infinitum productum
Hanc seriem
necesse est habere certam quandam periodum. Et quidem
si numeri sint rationales fracti, periodus erit regula
series periodica, id est iidem semper characteres deadici
decimales redibunt. Si series sit irrationalis, non erit pure
periodica habebit tamen utique regulam quandam
quam in vestinse
Eodem modo licebit investi
series radicis
regula characeee
periolum (quam habet radix alicujus aequationis affectae 
denique quomiam nulla est quantitas transcendens quae
non possit exprimi ver numeros, necesse est modum
he appropinquando in infinitum; utique semper
regula progressionis aliqua poterit inveniri
porro ut in algebra sumimus  literas pro quantita
tibus, ita hoc loco seriem literarum vel aliorum
hharacterum infinitam pro illa quantitate sumemus.
Et  loco progressionis decimalis, sumemus bimalem
rerum
seu ayadicam, quam ipsa natura praescripsit
alia enim omnes albitrariae. Habet autem la
bimalis hoc sane mirabile q magni momenti, quod omnes
ejus characteres sunt vel 1. vel 0. ideo et
potentiae literarum assumtarum, nempe a b et
item a. b etc sunt iidem qui cum radicibus, nempe
itaque ut cunque alte
a aequ. a. et b. aequ. b.
assurgant in aequationibus hujus calculi, frustra tamen
assurgent, le cunctaque transigentur, per solas
acbi
aequationes puras rationales
notandum tamen si tota aliqua quantitas
sit negativa s omnes ejus literas fore
vel 02C vel  +. vel = 1. vel 0. et
si tota sit affirmativa omnes erunt vel +1 vel o
et quando incertum sitne affirmativa an
negativa erit ea vel + 1 vel - 1. vel 0
nam Y- 1.
et  - 1 quae serviuut pro
impossibilibus adhibere nihil necesse est
praeterea si litera aliqua ut b significet + 1 vel - 1
vel 0. ejus potentia par y ut b2, b4. 66, etc
significabit, vel +1 vel - 1 vel 0.