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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 110r, page id 00068200:0221
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integris
Et quidem quoties id in rationatibus obtineri potest
habetur semper curva algebraice ut constat
Assumamus aequationem hujus modi quaesitam tanquam datam
eq
do hv B dxmx + dy nyaqa
15
prode substituatur
valor ex aqu. 12. nempe du aequ. adx + vdy
(24) 2v -y
) dxmx+ dynus
equ.
hV
ergo a hv dx + vhvdus aequ 2V mX dx + 20 ny dy-y mxdr-yrydy
et pro dy ponendo  dx per aequ. 18. et in aequ. 24 substituendo. 
destruetur ax et fiet:
(25
aahv + vD hV squ 2 a v mX + 2 vvny- ay mx vynus
Unde ponendo AV esse fractam ex vcompositam licet
dationalem ut haequ hocego  f v..
et eodem modo
9..
decaeteris, habebimus tandem aequationem sine fractis comparandam
Cum aequ. 11. quod si non succedit, attollenda est aequatio I1. ad
eundem cum ea gradum, vel potius ne attollere opussit, quia
incertum est alterntian tolli debeat; ope aequationis It tollatur
aliqua litera ut X ex aequ. 25.  necesse est omnia
destini seu prodire aequationem identicam, quae est pulcherrimi
methodus evitandi comparationes ergo loco aequi 25 scribetur
C26)
aahv + nnho aequ 2aV, m. vv-vy +2onny. aym. vv. Dy. vym
quae aequatio debet esse identica. Ergo primum erit:
adho + veho aequ 2av m. 00. NNam ipsius m. v0-vy
pars est mvn, et in reliquis solum v sine y non continetur:
de reliquo explicandum jam, ut ad identicitatem perveniamus
scilicet hx eril aequ
et
243Y + 4 v0 + 5 v3 duc)
12 + 13V + 14 v + 158 etc
Movego 22 vvc 1772 + 23VV +24V + 25v er
32 L33W +34v 35n ete
quia autem hu significul tractam ut 2+3n +anv +5u3 erc aquhv
2 + (3V + 1yB + 15V3 etC
revocetur ad ust egras, fiet: h_ ago fB. eritque suaego213v. 
qu
quaeguer1m
et ita porro. et mX aequ a o et aV aequ 2+ 23X +2AXX + 25X
fmgatur 
3X
LBv cgr 32 +38X14 +X 15 ∞3
Hia si sit xaequa . fei βX aqu _B + BQ+ ER +....
+A
gandum generalem Methodum exprimendi polentias binomiorum
vel omnino polynomiorum
irrationales 2
e
u
Quid si hv,  et tolia contineant
Generalior opinor Methodus haec est et quascirri
potest on omnino succedat transformatio sit aequatio
differentialis data inter X et y. assumatur alialitera
 cuius relatio ad X et y et detur relatio inter X. y. Z.
miqu quaeratur differentialis, cujus ope tollatur dx du, restabit
suati ex t i es i spe nrbitimuiam tollim,
dy
quae nocent