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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 2
# Folio 8r, page id 00068047:0015
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3. jul. 169)
16 Jangentium
 inversa per quadraburas ravales
resolvendo datam C prius sine exaltatione si placet transformataa)
in partes, absolutas seu quadratura datas
de transformaoe geaerai pro reductione langi  ad conturas sene
)
by+ ce d + lxinx + gdy + qdx =0
ey +f)
EX+ pp
 et sublatis nominatoribus fit:
+ bn XY + bpy + cpd se ex , bugX+ lp Y. + L5 X
+ eL.. alee.
+ bn_ XL. + bp Y + CnX
el.. +emus +st
+t.
me. c
ey.f enxipp= en xy + BnX. (Cp) B
+ b n yx dy + bppydy + ce n Xdy A pp dy + _ le Xydx + lgx dxrme y dx tonsx dx
+ eng + eppus +fng
+ enue +Gng. + epp9.
2
quae comparanda est datae. Sae Quod si in data sint  cubi a absoluti
lentemus lollere ut si sit in data  Rx 3g p + 3 X dy + ZHX y
 3012dX + 302 Z dx + 211 ZyAZ + 212ZV av + 121ZY4+ 1E Vav videamus
031V dZe + 032 V dv + 121Zv dZ+ 122 ZV dn
faciamus Z = m. X + ny et v = pX + qy, licebitne sic tollere X, y
sane habemus quatuor arbitrarias sed ea aequivalent solum dea tribus
Video, etiam in aeq. 1. glys et ydx esse imtiles et jam
later has arbitrarias in prioribus. Itaque nil lucramur, nisi
sic procedamus: bg cc
byy + ccg+ e
fy + 99
du + 1x+mm
cyf
nx+pp
dus + xx+ nimX+en
PX + 9
61
reducatur haec aequatio ad carentem fractione; deinde explicetur X ety
per Z et v, suo exaetatione prodiens aequatio comparanda erit data habelumus
autem nabitues datae tertii gradus. Et quidem, habemus arbitranis
sed aequalio 3tii gradus habet terminos 12, itaque res sape quidem
non tamen in omnibus  succedit
Si O sit in num. gr. g, , in nominatore gre. et qsit gradus hi
maximus, quod si Be +h = e+ 9
deonen e + vel 2 + gh uter horum
Siit et terh
d arbitrariae autem
ob C  D sunt bi CR _g+ n - 1 seu 2C+ 3h -1 sed ob G arbitrariae
sunt tot quod terminorum cor summa correlatorum saria sunt in
gradu h, id est quot sunt unitates in A+1,: 2 habemas
ergo arbitrarias 2C + 3h - 1 A h+ 1. sed in gradu sunt
termi e +h sunt termini (bis ob duplices differentiales computandi) eth+I et h+2
para
ergo aliusque resprocedit, sed non in altioribus.