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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 62v, page id 00068196:0124
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interim sufficit. Melliodum esse apertam calculand
generalis sime per relationes
si aequatiosit differentialis verb. gr. xdx + ydy yax- 0
cujus differenti differentialis  (posita dox = D) et
dx + ydius +dy - dy dx = 6.. Saciamus dy: dx = e:a et
bddy: dx = co: a et ex priore fet _ ax +ye - ay 20 ex posteriore
fit: a b + ayco + b ee = abe = 0. Quod si ope differentio iferentralis
et
 vellemus cum differentiali componiere aequationem Et actabilem,
 (3
tunc ejus forma necessario deberet esse, X + e c + y C = 0
ris enim solis modis omnis Membra sunt summabilia et summando
nova obtinebitur aequatio secundum e, nam se co ex primiturpere.
Ut igitur sine consis calculi tentamentis ex relationum
natura appareo per  quandam Hyper analysin appareat
qua co= de..
an res fieri possit tantum ex aeque2 sollamus C, et co per
∞4q 1 et 3. et prodire debet identica. ex aequ. 1 est
), a - ax: y et ee= _ aa = 2aaX: y taaxx: yy quae substituendo
Y
in aequ. 2. fiet: a b tayco + baa - 2baa x: y + baaxx: yy - ab + a bx: y =0
seu ab + ayco - baa X: y + baaXX: yy =0
.
et ex aequ. 3.
fit X + a.  - X. y C + y a. 1- xy =0 quarum duarum oste
tollendo co = bax:gu  = ba XX.y = ab: y = X: a. 1 - X: y. + y. a. J. X: y: a. 1- X: y
d
quae aequatio debet esse identica, quod divellendo obtineri potest
si res hoc curdo non esset
possibilis liceret assumere ad huc tertiam ebdd
si quidem possibile est
B ndddus: cys3 et progredi ad differentio differentio-
diferentialem; et similiter farere aequationem
1, e, W0, et W, factam unde
fingere tractabilem ex X
de inde porro unde rursus identica tandem elici potest
.
et
land tentanda ejus possibilitas. El Et ita poro pergendum
Donec vel demonstiari possit causa impossibilitatis in quocunque
progressum vel habeatur desideratum seq semper enum
l
vel une summabili aequatione bractabili seu ad quadorsuras
educibilia oblenta licet in inferitribus differentialib
habetur nova aequatio peo superioribu, quia semi ax quiape
constans ducitur in carentia diffeento differentiali, simplex beb
jus posentia.