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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 129r, page id 00068197:0257
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Calculus diffecentratum per aequationes gerarales
ottxes
0+01 X +012 X +03 X +01 4 X F etc
+021 y + v22y +823 y +024 y ete
L2
+ su X + 1IEX L13XT3IIAX, etC xy.
+ ay +8122y +f123y + 1r4 yt etc. xy
Ruxirx+BBx et Xy
=f2217+ f22gy +2237 +f224 etc. Xry
+ Y3 CCX +(3 12X + 6313X2+ B314X etc 
+B 219 2B 21  163 239  53 (7 etc Xy
eu
seu 0 +3IX + 31y + 32X+ 32y+ 33X + 33y.
fiit Ngg. 30 dx + 30 dy +36 dy + 3edy + 32 ex +32 dys + 33dx + 1) dus
Na 0+ 1o1t fo2 + f11Xy +6 12 Xy + fuxie su
Compendio Aequatio ad curvam generalem
Quadratricem sic exprimetur
30X1V+
Naque d xor ax + dfor dus
d pii, ex Xy +  dx + fripdus
00 + o1 + 02 + 11 + 12 + 21 + 22 et C. aeq. N.
f12 dy A1 G
sit dx Xis (2) Nax +firsudus
522 dy.. Br2 (2) dx +raydus
231 dx X Y31B)X x +f316) Xyd
332 dy .. 1326) ~y x +326) X dx
+02353
ubi 00 signi sicat constantem e+ significat etX  oX 1013X etc. at 02 significat Orty+oyid
Ot significat o1IX + O12X +013X +0Vt Xe et i  fochy tol
pesignisient 0cy 10225 erc.
9 significat 111X + 112X + 113X ete in xy e2 siguit. 221 y +1227 +1257 etein xy
et ita pono. In qualibet enim coefficiente trium noturum prima nota significat timensiones
ipsius Xy. secunda significat utrum in multiplicatore potentiae abxy, contineatur.
Xau y, si nota est D. coefficiens tunc continet _ X. sin 2 tunc continet
y. tertia nota cotinet dimensionem ipsius X vel y. Et ita 214 significat xex
e
tarm
erior est diam
Herentialis erit: (dX d 11 +21 + 31 + 3p etc + dus d 12 + 22 + 32 +42
+ () Ey 1 (1) 1) + () f1 X y 1(1)
n
s 9
+ () 11 X y +Xy.  t dx CyyY i+  + B (2) Xy 21 +2 + 3) XG 3I52 etc
Nihaequ
a
vel possumus autem pro dx ponere a, et pro du,  ponere Z
et compendii causa scribere dx A+  B ae La D Ma + N, + PZ. vq. H. N.
fiet: Z aequ. C a L + M a
substituatur in aequatione data
N + P.
Ait +  yaerX LorX + BX +oUX Aliter y COK LOLK FOIX +05X
umerEx AX
+
Y. uxtEX +X EX
1
Alitero  vihil aequ 3, 00X + OIX + O2X +03X eu seu aequ Y o. y + y ry ere
y, 10X + 11X+ 12 X 4 3X etc
V, 20X +2IX + 22X +23X et
et
I
Lc
Nihil aequ. _ y do dx + (). B. d y do a + 9)0 
y de dx + d9, 1 dy seu y di a )1
5 d2 dx t ) 2 7 dy y de a
W IE
y d3 dx + 6) 3 3ydy y d3a ())3 774
e
fiet Z aequ L a. ht jum aequatio
sit jum equalio: ZV DZ + Z + () L u. 4. 0. posito (e) ogo Cat X 4(6) X 16) a erC
et (et v b) ox 6) 1 ∞ +() 2X etC
et quidem si sit (t 2 abt Z aequo 0. fiet (0) + ( L
O. T. HI. III. sunt mudis it aequalio 18 (0) Z + (1) Z aequ. Nih. tiet: M (0) Z + 2 a (1)
seu  O. + 2, + II. 29+ 21I. 3. y + IV. 1. 7 (9) _ dory dix y dle, es
debent coincidere O0 () 1 a Fot) et O. item N 1. 1. (0) + a do (1) et 0
item I1I. 3. (0) + a d2 (1) et 2
item LI. 2. (6) + _ a di (1) et 1
un unm eoseot perereuus ao tarenr srrate
Saegu
Ergo
AZ