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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 395r, page id 00068196:0785
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duo sunt palculi Analytici, unus
communi seu Algebraicus, substitutios
num, quo aequalibus substituuntur aequalia
alter novus a me introductas; differentia
tionum. Aequationes datae cotinent
esd  vietitaliter eas
viitualiter eas quae inde de duci
possunt, nec per deductas aliquid potest
deter minani, quod non et per datas.
sed duplex est modus virtualiter continendi
unus virtute substitutionis, qui ost commum
alter virtute differentiationis. Et hic
rursas, notandum: _ s  in aequa
bione ejusque differentiatione quacunque
um virtualiter, et quidem sola virtule substi
tutionis seu simplicis carculi, continemi
omnem aliam differentiationem ejusdem
aequationis. vig. sit aequatio
1)am = In fit (2do) adm = ldn + ndl, unde
3tio) n = adm- landl. Et ita differentiando
exaq. sustalimus m. jam ex aq. 1. etiam differentianb tollamun,
Ex aeq. 1i fit (4to) n= amil, unde difficentiando
5t). dn = alam = am al, :l. Unde si fit
sel atdm  Han;  seu sto) am alam Uau; cl
Hos valores am et n ex agqu. 6 et 4 subst
in aeq. 1. fit abdm-Udn;: d= atam ladm ldm;: dl
quae est identica
345)
+ semper
un possibile aequitionum tangentialem
reduche ad quadraturas pprimi erralus hinc paleret
si faciamus. X. a = _ Za; via et
yia = Z. a; via rationaliter tollamus X
et y ex aequade data lpugentiali, inde videamus
an licgat orietur, aequatio, ubi hoc generalite
instituendo, vel institutum fiugendo aestimari E
poterii, an semper possibile sin toleiliteram
9. si place: possimus facere ut in valo–
ribus rationalibus ipsarum X: a, et y: a
neminator sit semper idem Ita faculjor
pallulus.
Niel viteci porerit onres facilior
 semper liceat blea a
Utiliter interdum Inversio institui potest
 ratione inter dy et dx fecrendo, litera-
odinariam contra pro dx, vel au X vel y
prodibit differentialis
si X et s ys simul tolli possint differe
+ audo rec redacta est quadraturas, atsumendi
ly: dx et literam ordinariam assumendo po
dydy: dxdx = xty: a sit
si
v. c. N
dy:dx = Z: a fictque ZZ = ax + ay, hinc
un
ydye = adxtadu seu 27 dz: dx = a + Z
= dx quae est reducta
et fiet a 22
ad quadraturas
Ergo ex data X datur Z. odeoque et y quod datur
utique ex X et Z