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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 90r, page id 00068199:0179
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aa dy + mY aX +andx = 0. sit a constans, X et y indeter
minatae primariae m et n dentur ex X et a. Ajo hauc
aequationem solvi posse, seu inveniri y  libere, A
methodo tali: multiplicetur aequatio per h quae ponatur itidem
 determinari ex a et X, et fiet (2d) aatidus +hm ydx tahndx -0
et fiat (chmax = aadh secto) sinax = aa log. . E
Et ex 2 fintet nahus + a shndx =0. Hinc quia ex 4 est
61
ex 5 et 6
mo
sindx: aa = h. pesito  logb = 1. fiet
aa b
V
+ )R.
 Et ita habetur Y libere
1max.aa
dx. 
patet etiam hinc formulam non summabitem
libere, ut  est ea quae facit aeq. 1. peddi
summabilem si muetiplicetur per
et
sindx: aa
inde prodire ag formulam contentam in aeque
ele
quia habetmeq ay+ mydx + nogax Attt
it eergo dis
y = 10 Fr. e fiet +du vat
+ uttrvx
d P =(1mo )2 dy ydhu tay. sic ergo
y
yy
tkA+ tgax
Hinc sit formula 2o)  du + M, 91 + ny yt = 0
1A
rara
dy my  , - dy + mydx + n dx = 0
fiet
LKTaX
t Tdx
eM tx dy
(4t) terr:
3tro)
multiplicando per h, fiet ((- hdy +kmu dx): 9y) + hudx = osc
Yd
osito
2t
et va siariti ut.
y
yu
et debet esse hmdx = dh seu (inax = log. h
et
(S+0)
dut (8
et ex aeg. 4 fie 7mo) E: y + stindx =0 seu y = h: Stindxbis
1
posuto log h esse Sindx sec aq. 5, et ita solvitur aeq. 2
nempe -dy + my dx + nyu dx =0
si sit aequatio du + myde t n qu dx 4 y
Et save
hoc compretendebatur jam in praecedente, nam
648
ma au + nax =0 posito = =Z, idem
y
yy
est quod Zmdx + dy + nax =c
sequia ut patat ex frac p. 3. nondum habemus
ady +. y ax L. qy dx + . etX =0
Ecibemus autem summabiles aequalionet formulas haadus +hmyax talnax;
et Kaady. + KPYAx + Kqju_ posito h= (smexi aa et R =. .
hi summa exambabus erit summabilis, quae orreranda erit formulae dato e
ibilemnem itidem per datim aequationi datae ( per datum aliquam a
mulli plicatae
es in unumat
sun
Et haec methodus ulique procedit. possunt plures
i potest et formula haltiplic per aliam, ut fiat sumentones
addi saque ib. corte algudo quae adain primm
etm nrau
tervau
etur c
=Nit
faxt.