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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 78v, page id 00068198:0156
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d
ey -
dy = Y(aa - XX) cx
Aa- d) dE = (b sea ne) 7 dx
Cum 7 Y sunt progressionis Geometricae etiam dy
sunt progressionis Geo metricae ejusdem; itaque logarithmi
s
d
sunt iidem terminorum qui differentiarum. Citerdum an
ol erit yddu = dydy, seu erit
ta
dy: y = ddy: dy. Itaque et fdy: y = Sddy: dy
videndum an non aliquid hinc duci possit ad quadratur
a
a ex hypothesi. jam sit in exemplo
a dy = V(aa - XX) ex Fiet alogdy b  log (aa - XX) = loq yo
Ergo loy, y =  ((4+ X)   log (a + X) + = log (a - X) +log dx
Fortase seu se
saltem quadraturae speciales pro
Hic nihil nobis obstat, nisi log. dx
2eo casu, ubi sumendo ipsas y progressionis Geometricae
Hinc derivabuntur
ee sit dx ipsi du incomparabile, adeoque et ejus Logarthmus
2
si e sunt progressionis Geometricae aay: y = ded
b
ady = ydc = Caa = XX) dX
1
log ded =0, ut lug a. cui respondet
est constans
possumque etiam concipere idem y quaeri ex alio velut L
ita ut relatio deturinter Z et x, adeoque etiam inter
X
2
5dZ et dx habebitur log. v. nova laequatione,
A. log. d7. Videamus an
mon sit casus ubi coincidunt dz et dx nempe . ubi
a quam cum aliis ingredietur at
3
applicatarum ad  et ipsarum X appli
fanguis et ita  composi
porr dq et dx dantur ex se
ua curmae ipsaruus.
e
invicem, ob relationem infer Z et x, itaque  habebimus
Catarum ady 
tollendo dZ habebimus dx bis et duas aequationes jingendo
squationem unam
inter se tolletur et dx habetiturque log. y simpliciter
S
Cogarit ndstam
vel Z aut en his formatorum
eotica
ibistamen spectalis. quace
a
non et quomodo
pest verduda aequatio um novus habettur vabor:pit
y: 42
seuubi
hoc artificium
idendum an
etiam ad differentiales affectas applicari posse
sed lice
E.
e
ly: dx =  XXtyy,:aa Rlogy - logd = log(xktyy) Qua si tolli posset
ubi haberi poset aliquid absolutum
n
stus haberetur et habeletur bs