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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 99r, page id 00068196:0195
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sit data aequaitio afferentialis 100 + 10 c + 1ococo +101 deo =0 fiat 6 = 2y +20
et fint +100 +m
110. 26 + 110. 21y
120. 2020 12. 10. 20. 217 4 120. 2. 21yy
101d20 +lothhi y _
+ 1DI. 21 dy.
Hic efficiendum tum ut coefficientes
terminorum gu et du habenter se ratio
nem constantem, tum ut destnatur
ut terminus y destiuatur
per prius, eut 120. 21. 210 101. 21 = C seu 21 = 101C : 120 et ut evanescat y
= = 1204101 + 101d120, C :, 120. 10 = = d21 : 27
it fiet 20 = - 110. 120.10 = 101 d1 2oC = 120 dotC, :, 2. 1203, quad si (20 sit
constans, quod in arbitur est fiet 20 = 110. 120 H +101. C, : 2. 120. 120. seu si 120 = 1 fiet
- 20 = 110 + d101 C : 2
aa fdx teyydx + ady (4=0 F dari per X et
sit ergo data aequatio f+gy f+ gyy +esCy F du  -0 posit (C esse constantem
quia semper data qualis imtio ad hanc  reduci potest. Et assumatur sit
Aemmatur dxpono fdari per sit dx constans, et sumatur dxa dx a
sumatur y= ad v:dx erit f +Cdodo vel y = W, neglectis constantibus, fiet
fiet f + co dvdv: dxdx + a ddv: b = seu adxddo 1 cAvdo + fdxax =a
sipt aa f dxdx + aac dudo + a adv =oseu  fdxdx + cdvov + aa ddv =0
Zd ba HB dx + hax = 0, posita h constante, et differentiando
e
fiet  dt x + dy de + y ddv + cZ dodo 0 i destrnatur terminus de,
et fiet F aadZ: Cx et dt - adz: Cx
aa
+tcdvax
Assumatur
Multiplicetur a45 per aa: Z et fi Aeq. 5 pest destrnctum terminum do, multiplicetur per ac: Z
siet aa dedx + aa ddo + c qrdo  fsxd gaa ddv + cdpdv, 0
et lit dt= f4 dx: aa = (per 7) =aa ddZ: Cdx
fiet cf7 axa + a ddZ =0 Maltiplicetur haec aequatio per r, et fiat
2
ct YZ du + ardaque  ( d(p 1Z) ) a dpaqe 1 a p dtZue  efrxtrex ta rdaZue
(
fit r= p et a pdqe CspZdx seu AZ Z fiat p X et prodibit tandem
7
1du = c fq Xd seu adz : Z = C fx aX vet a+ (  = C (fxdx
et X dy + edx = 0. Tandemus _ Z = C fdx. X quod non licet
q
Bursus pdque + edx = 0 per 13 sed nondum hinc possum venre
(151) La
ad desideratum. fiat  Z= bd Redeamus a
= du = duob
r
(ed y = BV fiet, cf dadx
Fiai 7 =  b et du = dn ba et dique = b ddn b tandu b a
s
fiat
et prodit cf exdx + a dem + a duon sed ita recidimus in aequalionem
jontam
non absimilem iatae
(n +m. a fut d7 = (g dn + nag + adm,: a)
et ddzue = (dat an qu (gdn + ndgue F adm) + gddn + n ddque Fiandgs + adam
Taciumus
et protit rC f dxdx + ggdndn + EgnGdgus + nnd gaue + 2 adm  g
tagdan
radmndy
+ 2dndy
g constans ut tollatur n. sed vides absolubu et duda, et ddu tolli nom pose
taadmam
+a dam
+ an ddy