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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 211v, page id 00068200:0424
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relatio inte
vil
X et
item relatio inter y et v7. et
sublatis X et y. substitutisque y et Z srelatio ita explicetur, ut possint
tolli omnes termini in quibus differentiates in indeterminatas percurbate
B
it saltem formula perturbata summabilis
ducuntur, vel ut relinquatur
An autem res semper succedere possit, inquirendum
si detur relatio inter t et X vel inter P et X. res semper
B
etiam proredit, pone enim esse F vel p aequ. (DX, X D; fiet XD: H: dx: d
Ergo ox aequ dus Ergo datur quaesitum ex quadratura hyperbotae
X,
militer sit
e
paego 
Ergo fiet 27y aequ
eti
)
e
peia
fiet cumssit P: y :: dy: dx. fier yaus aequ, dx
e
elerum tollere literas, idem et
ac si quis diceret loca ordinatae
aD sC
et abscissae sumendas duas alias indeterminatas
et ordinatum, convergentem e abscissam vel simile aliquid.
F∞), ct solutio
dentur, perturbutae. sunc non opus esset explicare
 ex sola cormula.
Videndum
 ax +yy dy, freri posset acia in qua tolle-
an sufficiant vucores ipsam X et y rationares
perturbat
problemalis pro positi simul ac semel haberetur generalis.
implicissime: y aequ
a +b V + CZ
f + gV + hZ
l+ mV + n Z
+ 2 + et
et X aque
2. et do dz
s
u
ponaum ergo
Termini autem dy
magnam parta
tollendi, item Oncti ex Z in tq vel ex V in B.
eruut
-
cuniue sint provetum
triginta termini. dubilari potest an suffectura sint littra arrit rariae
prodibunt ax. a
huc ad hibitae puto tamen suffecturas quia licet fe einere magna
alioqui tortendorum partem, siadhibilis illis formulis perturbatos summabili
o compendio y aequ E
et ax aequ. 2
-
mo na si res procederec. 
ob fractionem commune
2
et X aequ E; ergo dy aequ Cd5 = D aC)
a
L 40000a
ertaeque D)
Ergo fiet: vydu
eryy de equ. dC
1
decem
8
3 + 91 4-278414
8a
4F2 c4 quod nimis prolixmus. Sed mirifice contratietur calculus
Ergo fient quantitates lod litera, ut dimensionum
ut. C
aD
difficultatis si fintit dx +dust extrohibilis seu
et
ve
y Sdy +dx
quadratie tunc enim solum cidhibebitur
debet esse y dy +ax aequ YDZ due + XO 4 form. summat.
2
a +2 ZB 
N
2
ad hibens intera aequationem
ax aequyus xthyt
Ergo yy dus +7 ax aequ ZOaZ + X
dzx + +7
+ 22, Z0 dzue +2, 4, VO x
Videndum quomodo possit hac aequatio qumlit tmonum dividi in
finqo
dias summabiles, seu in quibus exanesca differentialis. Quod siet si demta
quada a parse dextra formul dc aliqua ducta in _2 reliquum manet sum
mabile. Hac opnor metrodus ad hac facillima. ita enim evanescet u x
semper
in omnes
drctam,
nisi simul
, 2