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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 109v, page id 00068200:0220
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Vdus aequ y dy + X dx
(11)
vy aequ’axtvy
(12)
ex et aequatione 11 sequitur dfferentialis: 2V avaequ a dx + vdlus + ydo
81
per aequationes 3 et 10 est dx aequ a. Unde ducta DH
dys
perpendiculari ad pco. occurrenti axi in H, erit AH
sem per quantitas constans; aequ a. est enim AH seu a
ad A seu V, ut dx ad dus seu at Goad 1oL. Ex
aqu2 est:
Ax aequ B- y
dys
 aego a. Sed nihil hinc novi
X
v Trediret enim oqu. 11
Tantum videamus an hinc comminisci liceat aequa
tionem reducibilem ad quadraturas.
(19)
aequ. 18. erit, vdx aego a dy. vel adqu - v dx rqu. 0
(20)
et loco aequationis 12 scribatur: adx + vdy + ydv - 2v dv aequ. 0
et loco aequ. 2 scribatu:
(21)
ydy +Xdx - vdus aequ. 0
Ita adhuc plures differentiales reperiri possunt adde
quas inter se conjungendo tandem ratio habebitur con
ficiendi, aequationem differentialem ad quadraturas
revocabilem Nam et possumm plures invenire diffe
rentiales, et praeterea possumus ta quando inaequaliu
gradus sunt ex altare inferiores. possumus etiam datam
aequ.e 1. mulliplicare per formulam differentialem.
Et hoc ulilequs est quam sollere aliquam literarum a
vel y vel v. sic enim non amplius in potestate 6.
variare Nimorum ex aequationibus: vo aequ ax +vy
et ady- vax aqu. 0. Haec methodus affinis est
dio santeae et arti tollendi quationes incognitas.
satis autem apparet quae conbinationes, ut cum habemus
vdx. vdus. Xdy. Xdv. y dc. ydo. sunt sunt
sex termini, qui vel tollendi, vel efficiendi qua
sictiles datis, ut vax aequaliter affecta cum xay.
componenda ergo aequationes septem ad hoc efficiendum
sed cum non sit in potestate efficere, hoc modo
cas sex aequationes, sine assurrectione ad un vel vy.
hinc potius aequatiohes 19. 20. 21. multiplicemus per 
intem
drbitricrias ex A  simplices ex X. y. v.
Compositas, et aequ. I1. per simplice integram ex
dx. do. dus compositam quo facto apparebit an
detur satis generalis formula qua destrm possunt omnec
cibi termini different in alterius differentrales ducuntur.