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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 145v, page id 00068196:0288
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Sit jum aequatio aa Y dip +2C5 dCo + aa cod
(alculemus alium Canonem
30 430. 31 2 F31 xy
40 3031
hdt = 3831 dx +30. 31Xdy +
x
yax
dy  ydx
40. 3031 +40. 3
m
46 h + hdh
(33 g ex 5o. 3 xdyaresib e 190 3 ly re 113 y q. 1i 2y 17
= P cOr uX L I Xy+ I2 Y+  (EOFUXFAIX dx + srot uyt duya
30 + 31X
30 + 30. 3IX +3F Xy, quius diffra est 30. 31 dx +3I Xdy c  dh
e
 2xg37
12
quami aequationem diferentianto prodeunt omnes forma
130.31 +31 Xyay )
yax
Calulare etiam possumus eatom determinationes aequationis famonicae talis
sit ( dZ: dv = 10Z + 1 V, : 20Z + 21V. sit 3
so
e
30+31y ) 30+3031X + 3Pxy
praeter X’ ax et x dy
pxax 430. 31 x dy + 3031 xpo.
30431X  L 3IXy + 322,6) O
V
50+ 51Z + Suxy + 5+ ~
et (= 40+ 41X +411Xy+ 42F Nam aequatio 1 est resolubilis per quadraturts. Porro valores ZecV
50+ 513 + SIIX9+ 32FQ debent habere communem denominatorem D et fiet:
Fd0. 6d8, :3 21D - y d  = 100 +119,:, 200 +21 D sed hanc aeq.6 explicando ex
aeque 4 et 5 assugetur ad X dx. quod si velimus solum assurgi ad Xdx potest fieri
9 constans ut sit de =0 et 50 = 1; et 51, 511, 52  sint 0, et
Quod si velunue
conserinre e poterimus saltem pacepe sit = e, et 5220 vel poterimes
vel retento 9 oportabit saltert Sacere 41, 42, et 311, 32, esse 0 sed prostat
ut dixi farere constantem. Hoc posito ex org. 6 fat
20 d0 + 21 D d0 = 10 d D + 1D d D
et
C = 30+ 2. 30. 31 7 + 2. 3031IXy +2. 30. 32X F 311 Xy + 2. 31132 Xy, 4 3232 4
jam d d0 = 31dx + 311 Xdq + 232 4 
d
OdC = 30.31 ex + 30.311 rap + 2. 30. 32 Xdx 4 3IL.31Fy dy + 31IGL X dy. + 3. 31132 X ydx + 252 X a
+2. 32
+2. 91. 31 +31. 3Y
dy 31.31 hax 21. 31 7 ay
2.32.32)7 xaxydx
dd0 = 440. 21 14031 +2403a + 41. 3u
+qu
+ 41. 31
yady. Gdy
41