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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 312r, page id 00068196:0619
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Hic inter alia usus relat onum generaliu
Si sit aequalo dy: dx =  valori per x: a, y:a Huijus differentialis
duplex  ddy: ddx = x  adx valori per du: adex, d  altu, X: a, y. a
possiumus quidem scube 
in tollendis literis quam aequ. 1. et 2. nam etsi centum adhuc habeamque differertiales tamen
onam
coybinatio tium, biniu renrius binio conbinatio duanim ex aequ. 1, 2 et relique suptarumeperitur
collat unam Hliteram, non potest, tertia deinde tollere ad huc aliam, adeoque
on
aequatio differentialis, in qua una quantilas (ex his. X, xay a, dx, dy, ddc abest) atest
Actumnum a relationem inter y, du, day, a, quae sit nempe
generaliter addu: d e salori per y:a. Hac ratione per aequationes
11 2, y vane tans formen t varis forma aequationem componi possunt,
quod s semel contingat, ut unam  ex liberis collendo Conto his quantisclnm
collendo contingat simul evanescere aliam, res reducta erit adquadrituras
derum loco aequationis 3,  adhibeamus aliam generalionem assum eiliam
sit ex alva per vert = valori per n: a, y: a et sumatur relatio
addt: dx= _ valori per +:a. Quod si, am valor ipsius  assumi
potest talis, ut unam ex his quantitatibus, x, y a; ux du ddx, ady;
tollendo simul evanescat alia tunc res erit reducta ad quadaturas
Et haec sunt omnia qua fieri possunt literis X, et y ue retentis
vieri Assumi dende st variatio literas X, et  explicando per alias 
abi si Z et V ubi ut ipsis sallem substitutis, _ procedat illa
s evanescentia spererogationis. Et quidem si et celatio assumatur
inter A y BZ, V, a, seu X: a ya Z valori per y: a, Z: a, v: a.
et rursus ya = valori, per X: a, Z: a, v: a. dabitur adhuc semet
ex 7. inocose X: a e valori per y: a, Z. a, v. a. Et aequando valores
6 et 8. fit y: a Z valori per Z. a, v. a
Et pari jure etiam
x: a valori per z. a, via. Sed non licet hinc inferre quod
habeatur et x:a per solum Z. a, quia nempe deest aequ. absoluta
inter X v loco ipsius daeqa ti differentiatis. Assumtis
ergo valoribus  eB  etig. q est 10 et substientis in egg. 1 et
iseg. usque ad 5, videndum est, un uliquandi substitatione tacta liceat
ubidendum est an aliquando collendo aliquam literam
Collatur alia. s per se sponte seu an obtineatur ecanescentur
supererogatioris. Qua oblentor publlema est solutum
sit aequatio