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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 94r, page id 00068198:0187
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sit FB4Z et BC, Ry  A, f et Z= x + f et g xse
ot X+f= y fi fiat  ubi notandum non et mirum
abi differentiandum secundum F, ut repercatur  Eiqua intersectione
Lacta sed quod mitum non quide falsum oritur sed tamen nihil
producitur, si valorem inasionalem ipsius etf quaeramus.
a
x fit lgrus = Vx  f et differentiando
L3
1 = _
 posito 6 gcanda fiet 0 = vx df: f + lod f X dx sad ita evanescilx
sit
Sin sic maliuu: y = X fit log y = g. X. sed ita fiet
V df  fd v = 0 seu dxfo quod non licet
in exemplum X + 2Xf + ff + Xa + fa = yy fint 2Xd5 +2faf seu f--x
+adf = f = a + 2f,: -2
F( 10, 11, a, et dari per y solom
sit generaliter ( 10 + 117 + 12Z + 1323 et. fiet utique
uis
0= 11 + 2. 12Z+ 3. 13Z7 + 4. . Inde jam pro Z substituendo f+X
_ Hinc jam quaeratur valar ipsius Z ex aeq. 4. E quietit Z = (3 dcnde et quia Z - f + X fint
f2O-X quem valorem subptituendo in aeg. 3. habebitur aeq. quaesita inter X et y
Hinc plge potast generaliter, sed ut hinc  ex aeg. 3, ducamus aliquid pro
aquationis 3 quae eut aeq6))
tangentibus inversis, quaeritur poprietas langentum aequhi ubi non negtiqent
jam _ 10, 11, 12 considerabuntur ut differentiabiles Et quia in casu concursus
 dze du ∞ dx. dg. et habebdur et in aequ.  erit af  dg: dy, Z, Y. et
(8)
quia hic in casu concuisas ddZ: du = dx: du fiet dque= dx. Ergo habetur
ex 07. 6. fit aeq. (9) in qua dx, dy, Z, y. Ude jam Tollendo F, ope
aegq. 9 et 3. fiet aeq. in qua  dx, dus F X, y.  cujus constructio haberi
potest. Et notandum plures duai posse ex raeg. 3, ad faciendam 6 qo varia
ratione diferentiandi. Sed si aeq. 3. contineat y modo transcendente,
Ita  amen ut transcladens sit unica quae differentiando tolli possit
labebitur et unicus modus in de deducendi aeq. 6. ut careal transcendente
Elsite erit etiam calculo investigare quomodo lico  non
ut rectarum concursus facil curvanu, itat et rectae sprovolutio super formalet facit, curvam puncto
in ea sunto. Idem jum fiat alia curva, cujus dibersi situs eandem formant, seu quae super alia
incedit. Quod si non sitidem punctum, ponenus punctum descibens durante provolutione
cta normali ad de
curvae progredi, simul in ejus tungente, ita sic motus compositus in perpendi recta a puncto curre
ad punctum Glactus cunm basi ducta et in rectuntonu ad n lin recta tangente circulum
probolationis, et in recta tangente curvam datur a oblocitas in Assumta Dantur merementa
radiorum adeque et arentatibuum Ergo
2os n avi odab. pad 370 ad +
duvisens vy u vy ans ugne se sodham
Suopolgo sop v dsuesa vi Heo ravisens v
de   to in tavemot p, orgdose  dagmait
an
vi S mon nost soabet st B oylesem  de
Jugaysi 3d eo   vy ans sus, yv)Pd I5. 7.
uvav,  sd Huato Y  ius. 7. B
unvyono. 7ohroh,
aris
ubi