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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 282v, page id 00068196:0560
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differentiales
pus est ergo ut aequatines simplices exslideruus solvi posse
doceamus. at si sint unius incognirae, erunt y +. dy + y. =
y + ady +. . dly 1 g. = 0 et ita porro. Has
f = 100 fieret 11-
pro ila C   109 , 1 ty + 12 ddus = 100 essume tq y + Zdy
+ Av dys + vddus
av
1
12
10t = 1 y + rtli us
fint 10D = 128Z et (Z+ dv = 4. 10  seu) Z+ du = n 0. Has duas aequationes ut solvamus
1Z - - dlv + H do - vd 
= 10 v si esset 1u - 
Wd = v: 12 = Zt du, : 1 = dZ: 10
fiat Z - _v. a et dque =  d8v + fdv:a, et habemus duas aequationes
012
1e B  adg V + 12G do , et b_B + adv - 12 V = Fiat Z =  pv + aG, : a sit 10 = D1. fiet 4   - B
fiat du = p D dp + pdB + a , : a Ergo 10aV = 12 dp V + 1 psv + 12 adg et uv + agt Mado = 1 a V
sa V et 12 p do + 12 a d de = 10 av - 12d p - 12 a dg,: 12p = 11 av - 12 pB - 12 a: 12a sed
sit y - _WV, fet ex 10) + Udus 4 12dadus
seu i(t ita non licet tolea v, quia ascendatur ad pP +p
Aliter si sit Z = pa + dg: a v = quo  + d t9
Fot nolpio + 11N aH +n Vadio
11du W + 12dip d1o
12 da  s
1096 + 10 + 8 = 12p deo + 12 co dp + Y d e + n6 dr
22Z 12pcd + 12rC + 12 gdco + n2codq + 12d18+ 12Fdg = 19uo + ut 9
(e 4 lr - 10 +t) B
fis t = = βY. ut evanescat a
multiplicata aeqque. 1 et 2 addantur in utum fiet
in nr -utg (127 + 1dt- ut s a
et ut oua nes cat e fit 1Er + uBY4. 12a βdr - 12 ardB +  12aβdr + 10BB
12t a + 12 (3Y, d8 = 0
ergo nonlicet destrure simul  et des sed videamus an liceat destrine 8, et ded
non sunt simul
rec et B asiendit ad B(
de, evanescit ri
seu g= - pB: a. sed
quia ile fieret D= (3Z, et ita non nisi die proorieat
129dc + 12Pβdco =0
sed ita destructo
 destrncta peraq NV. _ proco, fit p  129 12β ap  1039 +. 12 ap + 1radg.- H a a
tollere simul  e  et
ob deo, fiet
permussi hi duo valores psius 9 et ipsius E
Ergo oportot
ponamus p= 0, habetur g ex aeq. Z et pourmus + =6, habetur l ex aeq.
librae capitates, sed una.
Reassumaiuus ergo. sunt duae aequatines 100 = 12 42 et 2Z + 12 dv = 11 B
(it V = qco et 22 rg fiet 12rdg + ndr = 109e0 = 0 et 1erG+ 12 gdco + 12codque - uqcd = 
et addendo in unum fiet has duas aequationes puore multiplicata per β, posteriore per a fit
(20  ut ergo tollantur  et co, fiet
11a + 10()
d= - a et da=
fiet do de 2 q: BY, inventis q et Y, B manente arbibraria
+ 12 ar + 12dq( +12a9 dco
= 119 aco
e
si
+ 12β3r de
+ 12Bdr  = 10β910
in constans foret, seu ipsa Y. Quod hic non licet
et seu deo = 12r 9 - 10 B9c0; 1249, sed
sed ex oqe6 fit deo = +ne taga - 12rG, : 129, quis duos valores aequando fit
quamnon licet facere constantem, alioqui et
et ergo (212 a91
+12 β dr G.
+12 a Y 8
12d9c0 sed hoc inutile, quia nihil aliud prodit, quam
= 10 (3 9 W = 0
= 1a 9 co
+ nadu 1o
quod assumsimus ut _, et co eranescant, alioqui
potuissemus haec rursus differentiare. vel elia,
ld tollere ex aeg. 5.
+co + 1t8 - 12qp dcd
Hac ergo nimia sunt
+11900 + 11 +8 = 12 9deo
-12b..
12Y
A superiora reundi redenndo d_ = -12d  - idrd a - = - 12dg. - 12 at.
liet itaque ut tollamus ded, fint pt = Yq seu + = rq: p et Z = pC F r∞, :a, et v = qco + 148
seu Z= Pco + re
et v = P9co + Y48 sed ita fiereb v = Z9: p, quod est contra intentum
Si utrobique tolleremus et 8 firiel. 10tt - ntdr = urt- nrr- urdt quae aequatio
Ubi quia assumi potestC in ratione determiinata ad Y, habeti iun rar
atque adeo quositum sit Y r fiet (ren 1) Y (10+ 12 + 11) er 12 rde seu axir = cotur cer. 12
 unpur ta= p pr ut g 1alus
i
du = dv b
dduo fit v = B N