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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 91v, page id 00068199:0182
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videndum jam an hac ma altius proced possit
ad  usue gradum et.
videtur et alia esse via sit dy + mydx =0 utique est tracta
bilis, fiat y = +v + Y et fire tdv + vdb + dr, =0, quae con-
ferri potest datae
+mtaxB +mrax
f de + 9ut h= 0 multiplicatae per Y
et fiet frdv + grve hr, ∞o et fit dr: r =  rax- nax
et t = fr. sed ita in medio deest arbitraria. itaque oporleret
fdo + quax +hdx-o multiplicare per KY, et fieret
fkrdo + gVXrdx + hKY dx = 0 et dr: Y = htidx. md
et + = FKY et dt + mtdx = (gKr =) g: ts. sed vereor
O
ut res ita procedat. praestat igitur dia prior
du sit ac dydus +tfdys + agydxx + hydydx + Kyydxdx + aalaxdx o
sit . 100dy + us) ex tuag cy ryex t afx, mult per rsdyribax
ad e
nult per 
fiet 10 15 aa dydus + aasaydydx + 1 15 mult per 13ady + 4 Rydx tS adx
12. 15a dpdx
+ 1014aa...
+ 11. 1ta yydxlx 112. 14 aa7 dxt
+ 10. 15a..... 4u1
+ II. 15aa..
Haec aequatio comparetur cum aeq. data O. et fiet
(1m) 12. 15 = al Edosi. 13 = aeti 1 af . (3to) 11. 14 = ak. Habemus ergo 3114
15, substituenda i aegu. sequ. (4to) 12. 1 + 10. 15 = aF et (560) 1. 13 +10. 17 = ah
et (6to) 1 12. 14 + H. 15- a9. ubi in aeqque 4, 5, 6 substituendo valores ex
agg. 112, 3. fiet ex ahit acio ivalu at, et habetur 1:10
ekaeg. 6 firt 1 ak Ex aeq. 4 fiet (7mo) 122C. 19 + 10a l: 12 = a5, et datur 12 :10
Ex aeq. 6(1Ct (∞00) 12(a K: 2) + Wsal: 1= aB et datur 122M Et denique
Ex aeque fiet (9no)  IRB: 10) + WaK: U = at et datur a: 10
Ergo aliqua harum lationum datur bis, seu habetur aequatio inter datas
unde aequatio data prius est praeformanda, ut salisfaciat huic
conditioni, quod videtur fieri posse, cum sit non nisi unica, et duae
abitrariae possint assumi faciendo, 1F tV+Y
cubile vidtur sequi nempe in data
 suit solum
C ayay segnaxda L0. videtur sic res reduci posse ad quadratu-
Hinc aliquit snca
m rationalem maltiplicando 10dys + u x 20 per 13 dy +1d nam frt)
co. B dydy + 10. 1dx dy + 11. 17 yaq xd = 0 sit 10. 14 + 1. 13 20
 11. 1
10. 13 = ea 11. 14 = aF
Hinc tollendo prius BeM4 fiet 132 _0: 10 et 14 = aK: H. quos valore
substituendur fiet: 10 (aK: 11)  1aC : 10 = 0 unde prodit eandem
e i = 1. 102 = R: C. calculus probus, sed reditur accurate ad
Fdy + yd f. = d9 hady e tmyax Fhncx =0 posito dh.h = indx est tormula summabilis unde
priorem difficultatem
se  fy+9.
fet fd9 + y d5 = eg + A fody + hfmgyax
e
+g
hengar t9hulx
+ Ihmydx
sed si m = 0 posset s manere
indeterminata et nabet.
potest generaliter ex endus toydxt
udy f.dy +. dx F.. ydx
25ydy + yy df. + dy 2 yaK e +fdy + gdX c0 fit 25y y 1yyd) +Xag .gLX =0
fyu + Ky +
Atfycys tsgyya kb) t Kygdx
e et faciendo b= -2 rodnestat  ydy