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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 364v, page id 00068196:0724
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 363r); this page is its left half.
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VX
dy: AX = ax + yy,: aa
du y = Saxex + Saxgy
a
dy -a ax dx + S la auxe + sexraxyys + fax y  seu y =   + fax yy
Se
+aa a
aa
aa
fit y = XX + X (dx X + Sax X fax q + sex 1et sar gy
y
ra a 4ue
L +K,  + erc.
Ea P20a
d aady = axdx + Cyy dy
sit y = _ 10 + u X + 1 X + 13X + 9 X erc
est = 1 +2. 10. IIX +2. 10. 12X + 2. 10. 13X3 + 2. 10.4 X eu)
1. 11. 11 2. 1. 12 2. 11. 13
=aadys. a1, 1. 11 +212. +3. 13 +4. 14
+ axx
t a.
r. 12. 12
+5. 15
st 10 20 et 1 = 1 fiet 12 = A. 2a et 13 = - 1. 3a et 14 = 1: 4a et
ia
si ponas 10 =0 sit etiam 11 = 0 et sed habetui 12, fit 13 = 0 et 14 =0 sed habetur 15.
C redy 10 + vdy edy = 10 + uy + 12y
O= 20 + 21y + 22 y  + 23y et. d29 + y t t y d 20 + 21 y + d22. 7 + d23 y
+ 1. 21 dy + 2. 22 y dy + 3, 239 dy =0 seu Ody = d20 + d21. y + d22. 1 + d23. y
seu fit ed21 + e d21 y + e d 22y + e d23 y
1. 10. 21 + 210. 22 + 3. 10.23 +4. 10. 24
+, 1 21 + 2. 11. 22. + 3, 11. 23
+ 1. 12. 21
+ 2. 12. 22
1. 21 + 2. 22y +3. 231
etc ) (4
ell p=0
MM
ek
Ponamus abesse 12 erunt tantum linees du in linea aequ. 9 quod est minimum
si coincint it coincidant mulliplicemus per crucem, ultimo temino se mbsoluto
ex
fiet Eeldri + 1. 10. 21 =  d21 + 2. 10282 + F fF 2 1. 1. 20. 21
Si, faciamus 22 =0 23 =9, et fiet 1. 12. 20. 21 = 12C d21 + 1. 10. 12. 21, is 12 =0
habetur d2+ ex ex 5 et 6 trabebitur aequ. sine 121, cujus ope dabum dabitu
relatio inter 20, et 2) hanc differentiemus fiet nova aequad
in qua 20, 21, dio, d21 po, ita tollendo tam 20 21, quam d21, habetur
aequatio in qua sola incognitarum extal 2 et 20 et d2o. sed ita inci
dirum in problema aeque difficile ac datum, nisi sciremus 20 et 21 et caetera omdi
esse quantitates rationales per X. Hi calculi sunt imme usae difficultatis otlon-
gitudine sed puto thecremam odi posse
sane datae 10, 1t possunt ordine tolli, constat
sed func descendet 20 ad multus aeferiores differentias adeoque apparebit
tandem an tale quid sit possibile in rationalibus.
si absit (2. sola superest aeg. 5. et habendo 2I pro costante
piet 1. 10.21 = 2.02 C 1. 11. 20.21. seu 20 = 10. 21 : 11.
e dy  10+ 11y O2 20 +21y 42o + du y + 21 dy = seu e2idy = = ed20 - edu1 y
= 10. 21+ 11.219. ser +10. 21 + 11. 21 45)Confer cum aeq. 2. fiil 10. 2.LI e2tdro-
1 +C d20 + C d21
10, 21. 21 + C. 21d20  11. 20. 21 + 020 de1 si 21 esset gans fieret 10. 21 + C d 20 = 11. 20
sed retenta L 21. diveilatur aeg. b in duas e(2) d20= 11. 20 (21 et 9 102
et 10, 21. 21 = 2. 20d21, Ex ag. 7 fit (d20: 20 = (11: C. Et seu log 20 = S11: 
et ex aeq. g fit (10. C: 20 = - 1: 21 Habetur intur generaliter quando dys et y
non assurgunt ultra gradum simplicem, nec ducuntur in se invirem, quicquid
demum sit de habetur solutio per quadraturas. Et verum esse sum exsiertus