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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 163v, page id 00068199:0326
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du aqu dCa lego = aegu Z. dque seu d  aequ + = q X tde aequ + Xdy q ydx
y X+dy
seu dZ aeq +2 dy 4 dx. Ergo dE aequ+ 4 dx. sam yZ aequ. x.
Ergo fier: de aqu + dy 4 de
d.
 aqu y aequ =. Ergofiet:
Ergo dus aequ. + dZ x
Jam aliunde dus
Ergo.
c
aequ et Z..
dy. . 7 (1)
Z
E aego dx
y2
du  + X dus + da
2 aequ. F dys Z + dx 
e
b ex
aequ +dZx +
X
dx Z
dx y aego dxX. Ergo sax y ayu s
datur autem Z ex X  ex quadraturis per aequ. 1. Qo velore
habito lubstituto in aequ. 3. in locum ipsius Z habetur saxus seu aren
figurae ex suppositis hoc modo quad raturis seu per logarichinos, aut
vel quasi
figura quasi logarithmicarum areas Et haec vicissi hoc modo
reducentur ad quadraturas lves.
d Xdy aequ X adus + dy dx
d
X da 
d  aequ. + ddyu f ddx dus p. gn aequ.  X... y. n
Ex
du
dx 3
dx) X. y.
X.. y..
l vatorem ipsius ddy, ergo tollere
cpri
diventur
relationem iuter
homogeneorum Habebimusque
aq
d.
in vatore ejus leges
dy. dx. ddx. X. y. seu valorem
ipsius du per dx. dax. ax. X. y. servantem leges homo genectum
Est auter qu dax homogeneum ipsi
dx vel ex
Jam habemus et valorem ipsius du servantem leges homogeneorum supra
X+ ax atque ita habebimus aquationem servantem
leges homogencorum inter dux. ax. dg. X. y. Z.. Tollemus y ope y.
et ad hibendo adhuc aequationem quam ingreditur ddque quales habentur
plures, puto tandem haberi posse aequationem tatem. ut abia
parte habeatur aque
inter duas quantitates,
habeatur: ddz. dz. 7.
ita ut ab una parte
ab altera autem parte. dax. dx. X.
Et ita pulo nes reducta erit ad qua tratiras
a
A B, X. BC, y
AY AF 
AF, Z. AL, v
EF: EC:: FG: CM
F Gaequ. d7.
CM aequ. dX + d
dx: ly :: v: 7 dx-
 et dla er ao
aego Z Z
C
duos valoret ipsius aequ Z
dho monlicet et pro va  substimendo
valores datum pen petu
datur axaltex datis ux se ex dara X per X et y
..
 7aequ. X +BF  et F
BF: y:: dy: Ax seu BF aequ. y du
seu BFaeqo 3Z Ergo Z aequ X + y
eodem modo v aequ. y + xV. sed tollendo