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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 14
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29s ept. 1680.
De Logarithmicae aequationibus. et sement
Scheda I. Calculo curborum transcendente expressarum differentiali
pay.1
seu comparatione calculorum differentialis, expo nem tlis
replicats et insiniti
Ntdu
4 aequ Z. Ergo dz aequ. fa 7 a
exprimatur
jam inventa,
a per seriem infinitam, methodo
et per consequens a
per
faci habetritur opinor
has
similem seriem infinitam,
differentia finita inter his duas serio, infi
jimo non finita, ut in fine schedulas sequentis depretens.
nitas, quia altioras ipsius du potestates
negliguntur
quaesitam.
quae differentia dabit tangentem
itaque duobus mocis eadem
opera inveniri poterit a
uno modo dum
 exprimitur per seriem infinitam, in qua
invenitur cujus differentia
us
dist
a
t a se invicem subdracuntur, habetur
differentialis infinitae differen
tiali supra dictae aequalis.
Hinc nova
erit b+x ag. sitqu Sa aex constans  e fiet:
ta tunc ratio b+ H seu CX ad seu WY  ad CA seu b. est
multiplicata rationis  seu  C ad CAS in ratione C_ sive KX
seu b
logarithmdate ipsigse. seu in ratione
sit b unisas erit 1+H aequ. ()
t
on nngentendo
Ponatur C esse talis, ut sit ejus logarithuy Cβaequ. CA  seu a aequb aequi
l.+ _ aequ.  l at2b ad minus hscribendum +
posito sclicet _1+N et X esse numeros
a diversa parte ipsius unitatis 1+_ brevitatis causa vaemus V. fiet:
foret. 1+R aequ. 4C
Aa
consice.
1C et b7 qu  lb (Tetragonistici, itemque cur prop. 45. us scholium jungi debe
D equ.. Eandem aequationem ut exprimamus per series infinitas
randum est quod etiam demonstravimus. Si sit f. equ.
2l10
b, 41
fore L ad (1) ut n - n + p - p +P, etc. ad (n) - (N) + (1)- (2)
1b 3b +b3
si utraque ratio sit mivoris ad macq vel ma
56
 Y ~K
sive erit.
pro Logarithmica inspiciatur figuratra ctatus mei Tetrago.
nistici. So CAequ b. AN aequ. M
b+
quantilites
finitas seriebus infinitis aequales
methodus
ad 9E)
prentialis
modus dum series infinita aa t serres infinita
facile
a
pay. 2.
inven
invenitur pe aliat Seriem infinitat, alio
est
civeniendi plurimas
s
cb 3b 4b 5b