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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 95v, page id 00068198:0190
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nunt
et jam ante
jam valaibus ipsarum jam valore ipsius MH, similiterque invento valore
BL, qu qui erat ydy: tau du f dx. Htabem et d utique habebra
et BM et BL: M H =, W + Z Xdyidx:  Z +y- n = c datur aut
p seu BL: M per solam y. jam y W:  x- Z = du: dZ H
sublata simul et x, prodibit aequatio in qua y, W dus, duo, dx. Hinc si assum
dx idu_, quae resolubilis per quadraturas, et ita tollamus ex ex aeq. havene
aequatio diferentialis consunctibilis. sed non satum res accommodari potest ad
atum nam nisi scil cum dam estexdatae, in qua dy, dio, 1s, 1d, tollendo duo
ex priore, ubi yeo, dus, dio, dx, sicunt tolli potest Wn Hoc atem video fieri
polse, quoties datum du: y2to per   av y
du C -dy dgidx: d2 + dW = _8 evanescentibus
am in
nines riet
 Habemus. ergo aeq. in qua du: de
et dy: dx, et ya duntur existunt. Net itamen hinc commode pro
omnibus fidinariis praeter contentas in v.
12 D a aa e cm
CK
Tangentum inversis duci potest
si sint tres quantitates CB CB, CFG,  quae cum sins
sui
differentiis ingredeantur aequationem eta maneat
aequatior vera, si pro differentiis respective substituat
tur respective, E9, BL, HM; erit CP (transiens
per puncta (C, e m,t normalis ad
curvam 1. CC.
3
eren.
jam
i 
et ex sit X
CBisit  y, (ab CFGpt
fixo et ponatur dar
(puncto G mariente
aequatio resolvenda, diffementialis in qua exten
X
dy do y y de, 88, videamus an
noa
jd
tatis assumi possit valor vi ipsius _ per   y et X, ut
substituendo pideat aequatio inter v, y; X, do, dys, dx
Nec opus est novo calcuo Tantum vab , inventus ut ante
1 rud vos
substituatur in eaelt et 
B. L
2
p
omanent valores inventi  ipsarm M MHdet MB
ces.
tantum opus ve adhuc valore EP.
jam KE = Xdx: 1ax + d
erpo E9 jam EG = XE. Xy. X. Ergo E = ydx: dx + du En
aut
naq hi valores ipsam E8, BL, Hm substituantur in aeq. differentiali
fabucanda ad curvam cE assumtibilem u et fiet
 dys 4B yx B fdx F so A Adus d Ai dex (duot dy dys , 1a a tu
dx
ubi tamen, video nos non proficere, etsi  plures lineas seu quasia
focos adhib eamus
Notandum et, sempero posse summari. Adue duo- dudys. ax 
is d dque adi
Euthynsm simulque posse inveniri relationem interiZ et  c
si aequalio esset inter X, y, _ de dy do posito seX, y v, e
tna mnarum
AB, BC, CFG; dareturque relatio inter X et y utique posset haberi d
V per simplicem Euthynsiu quod si extaret. sit aequatio aliqua
differentialis inter X, y, dx du, i faciamus X = B v, toq, et y-v
sdvalore substituta videamus an liceat obtinere, aeq. in qua v, d0 do, dz, sed non
u ipsam W , erum haec ad aliam Methaevum pertinent. Hac
vice contenti esse debemus, quod habemus generalem reductionem
imo re considerata
nascitur
prodis infinitis nova spes reducendi ad qvadraturas
inversam, cujus cunque gradus, id est differentiatium
quadraturau ad Enthynset
otem. Necpo ponatur vdou dy: deo = y: a, unde et ady. deo = dy: a, ete: itaque in aeq. d
con tantum tungentiam inversam sed et os
lneat
t omnes ipsiuu aftectiones ol praeter unam
prs
et
maes
nis sest in quam
agere i
ua
auales
nevissimam. Mancitibus ipsius X a
e   usi   i l  t
 g
1
t
ation
tou caq.
axis
 dau
in
t 
n
tonen
a
lug
e
e
poprs