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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 362r, page id 00068196:0719
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Set Aequatio data resoluenda differentialis proposita
aadu = axdx taydx +xydx + Xydy = 0 Fiat X, = 300+3102 + 301B, et y = 400 + 4102 + 401 B
Et explicetur ope Canonis peculiari scheda ex hibiti. , fiet formula in qua
ex, +V, 2aZ Va, e VaZ, Zd,  vZdZ, vzdo, vodzue, 22v. quae erit summabilis,
si sit eaq= Zdu et sit coeffiens vdz, aequalis eoefficienti Zdo
Et si sit eoefficiens ZV d duplus coefficientis 27dv
- - ZV dv .----- Quudz
In Canonesfiet 100 = 0 200 = aa 110 = = a 201 =0 101 = a 210 =0 111 = 1. 21 =1
explicando
pec 2  120, 202, 210, 102, 210, sunt 0.
et ergo fiant coeffivens vaZ et ZdV aequalis fiet (a. 391. 4 D) A. 310 40) = (a 310 301 A3 B1. 410
ut fiat coelliciens 3 Vdque duplus coefficientis ZZd, fict 310, 310. 401 +301. 310. 410
fiet (-a 301. 310)7 a 310. 401 (+301. 310. 409 + 300. 390. 401 (4300. 401.410) + 301 400. 410 7 =0
ag. (= a 310. 30) + a. 301. ct10 + 300. 301. 410(F 310. 301. 400) + 390 400 401 (+ 300. 410. 40)
et fiet 400 = t a 310. 401 + 300. 310. 401: 310. 401 - 301. 410 et dividendo
per 310. 401 - 301. 410 firt 400 = a - 300 vel 310. 401 = 301. 410 so- 410. 401 = 310. 301
=a 301. 410 = 300. 301. 410
seu 410: 310 = 401: 30 1
310. 310. 401 (+ 301. 310. 410) + 301. 410. 410 (7310, 401410= 2(2) 310. 301. 410 + (2) 310. 410.401
Ut fiat coefficiens ZuZ duplus coefficientis Z7d0, fiet
fietque 30+ = 3tor sra 301: 4 et = 401: 30 = 310 3V 3F 310. 4108419. 4187:9 310.310-310. 410
Ergo fiet vel 401 : 301 = 410: 310 vel 310 = 410
(310. 301. 401 + 301. 301. 410 ff 301. 410. 407 + 310. 401. 401 = (2, 301. 310. 401 (2) 301. 401. 410
Ut fiat coefficiens ZV do duplu coefficientis Z2dv, fiet
40t. 301 det 401: 301  410: 210 = 401. 49 - 301.401, : 301. 401 - 301. 301
sed video non licere facere 410: 310 = 401: 301, nec licere facere simul 310 = 410, et 401 = 30l
Ergo vel 410: 310 = 401: 301 vel 401 = 301
itaque possibile, non est, ut aequatio haec fiat summabilis
quid si  sit _ e m X t ny h+ mX p y + pXY+ AXXFrgy
h+ mX ang + p Xyt qXX Frgy, max + nay + px y + pydx +2qaxt erydy b dx rchystendy totuar
ss
_+ mx + ny + pxy +49 + rgy
erax rgydy
Haec conperenda esset dutae transformati
Alia chethodus du = axdu ay da pytx
0
dx e =
+aadys +xy dy
x
caa dytydyX
Caa dys L ydy) ay + y ax y- a X
(aady +ydyX
agtyna
ay + yx - ax
agtat valeris ex nominature s
sed hoc meltionus pauto perplexia, quia x