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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 199r, page id 00068200:0399
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De Transformatombus Zrans formatio; differentialis ad tollendam onstautem vel
differentialium probe
notanu
Quaudocunque
a tollendam implicationem
vatur a
dy: dx
e
X: 1 solvi potest
problema
per quadraturas. Itaque si detur dy: dx = X, y, a, res eo revocanda res esset
in potestate,  modo transfermanto obtineri posset 12 4. dv: dx = X, v.
dy: Ax
et sit c. a = dg. dx. et B= 1 10 + Nua +21Y+ 12a+ 22Y + ay et
rursi)
ubi 10, 1, 30, 3 ese. 
a
V-50 + sla + 5, grvolvunt X, sed non a  se+ 3( a + H Y + 3242 +q2y4 B+ ay et
2
+52a
70+71a + 12 ae +734eR a. ubi
50, 5, et, 70 y ets. involvant
tam X quam Z. et ita valor
ipsius y haberi potest rationaliter, nam si per olam Z esse expprimendus
 forte assurgeret ad altiores potentias.
lit _q
d1
dete dyt
a
et diffecentralis ipsius 0g. 3.
30+714 +724 +73a
50+51a+5a ( a471 + a d7r etc
3
=70+7a etc. ad51+ a d52 etC
Jam ope aquationum
2 et 3, tollantur V et dy ex aeq. 1 fiet aequatio (4).
in qua cum 10, 11netc, _1, 22 2) et, sint data. sed 50, 5is
et 70, 71 72 ete assumtae: debent ha ita esplicati ut
im 09. 4 evanescat a.
Sed hoc non videtur minus difficile, quam ipsam ippolicationem
directe tobere, sit ergo
du;  = 10+ 11y + 12y etC. ubi 10, 11, 202( et 39, 3 
continent X +o,al e
dx
20 421 y +21 3 et
rursus sit y = 30 + 31F+32V_ et dy = d30 + ∞ d31 + vd31 EK + 3lB + 32. Lvdv + 3 3
440 + v d4) ete. ut alatetem 30
40 +41V +42 V ek
3
qoialem
ex
mnam
norum aequaltonum ae2 et
uet ag.4, in qua efficiendum est ut simul evanes catva vel saltem effuema
estut evane cat remanente solum. de vel saltem efficiendum est
idem est ecti aequ. 1 say: dx non haberetur zahonalite
in
am nhsomimus aequationes esq (2 et 3 manent ejusdem fonnes
e
am u
quod si et ruusformationes de cunus aequationem differentiale
xirationali reddere rationateu,  similus videtur melhodus
es scil.
oeum habere. Videamus. sit ergo data aequatio sit compendii causa.
co = dyidx, et cel 10 + ny +21 co + y1o + 21Y+ 22(0 et c = 0
et 5g, 2. et 3 ut ante, et in 4q. 1 sollantur co et 7 per 5g. 4 et 3.
et praeterea
habebitur aeq. in qua V et dX) e X latens in numeris fictitiis
Ut transfor mandas cvas ra quadraturas irrationales in
rationales quantum possibile est sit aequatio 10 + H y + 12y + 13 ek
quaeritur Cydx rationaliter.. fiat ut y2 30+ 3Ver ubi pr1 ex aeg. 1. tollatur y
hunc delideraretur ut potentiae iasius V evarescerent in ag. Z nova. sed viver jam hosc
40+4iveu
non esse possibile. Nam si e haberetur non ambigne ex _ X, utique y quohabelur
e
nonsmbigue et x et B, daretur etiam non ambigne exX contra ag.