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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 110r, page id 00068199:0219
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nquisitio in aequationes Tangentiales reducibiles
ad ordinarias, per Homoeeptotas
 sit equalio generali; Honoeop loto.
(40 = 1007 iox +UA By + 12X, + 121 Fg, + 1X + M XyF 13, XyF 11 4 1329. + 14X9 F 15X er
e
est
iffast it ruraus L 2Ax A 212 Xy dx X XAy +g.  rkytyt3  Zyar BXdy 14. dp 3  ijax ex re Xy tqu 2. e qu s GA 
 rs su
yax
Pay ryax xidus p’ax ydue
sit jam aequatio data d ye  cornen n
 1 ydx ydu
du
Ex F 3H Zpu gin 32G 55F ux 3
 ∞ Hinc ex aeq. 2. tolletun du tam si pro dus ponatur O pro di puonctus D a fidt
o-nso tm
O- 1180 +1. 2t X +11. 4 x9 +.L. p, B. F 1 Sa 15 733.
+I1. 20  vm. 2 H(2 fu 2 A. B
xo
34 u 322
 in
1i 22
2
e
2733
or 2 ra ta par gniso 2v 2u 
qula
3
24
srru 2p.   huus 2
o   111. 22
2121 28 t 3t. 31
13  
  1ut. 22. M. 2 
3
4
yd
32t
+SEC Xydy + 23X dx. + 35 X dus etc. Dertendo hanc aqua- fec. Yay  4t 3 tau vy + 2u +  G
Analoga
pus ax vamerit in fictiti  prasime, sut 2A Nepupe iissepa est 
tionem
33
 yi
23
227 24 X 25y
et ductur, mqua sud d romoentota restituit homoeoptosius.
sequitut s
pay
B1 Xy 34
23xyh 2tZ
in valore tali esse homoeoptotas et si valor ex aquation
34
uiu . e.
homoeopeotae; lex tamen certa est permutationis, quae substituto
potandum non posser. i
121. 22 121 2d e1. 23 ca. 1
Sit jam aequatio ata differentialis generalis semplex homoeoptota O= H ay hau  vag
de
s
at Ergo aliq aequalio
secundum do et dx e etiam generalis simplex homoeoptota, ea per omnia similis erit
ipsi 3 nisi quod pro 20 vel 21, et c. substituemus 60 vel 61, etc et per 31, 32, CM substituemus 71, 72 etc.
xt FSsrara gelys a rys tan treitus abuegerern in dy it stitus e r aboar nta 16, 2 X ay
hay
xuac iaque ydx
abqua aequatione 5 potent intellgi decude aequatio 2. Hinefic aty  (86 bi Keayrb  sun iabe eup v +6ax et
51 X0
aque srbemus o2 b 
uide aquando  valores 6 et 4, instolutul muliplitatione per crucem fist
 ruru
1.se + 1X + 10.61 X9 + 2012 X + 209 atxy 4 10.73X, + 20062t ∞9 + 2673IXy + 2034X
BIXy 74e
0b2
B3
ama es
Defficientibus seu n
o o+ vibu  2o LXy + 2061, i t 2oCu. 34. + 10.63 5 t, o. bu Xitro. 631 Xy, 1 ~ 64 5, +206) 1 410 6H Xy +2065 L, et
73
tat
o itiraoli comsina
20n
2371
2160 . 21 61 21. 7 4. ba
31. 60 L31. 7 3
Ager. Boet 4eii1u r
10ge
+2b
400 80)  quo 810- 7 + 310310
314. 80
3IB1
191. 908
Ix hoc asequatione 6 mitabile
2162
31. 7
+40826)
L2uiio
+ 2000
40obio
32. 40
74
731 X
732 fy 2H Y9
institata jam multiplicatione per crucem
ib prodibit aequontio:
+42 72)
21911
+ 3072
qV. 7101
+4030) (+48 G2
+26120
13
20. 10 +X
+2162
+3b121
1411. 81
+ 2sV
1320
12
+12. 61
+321. 71
330. 6 + grr. 800
+Xy +411. no
XV 2C.8I
est X et y pari quidem
in hac aequatione 6 ducta ex duabus in =. 610 quabus X et y simul pEF - a. 6d
ntur patet. 321. 800 X et y quidem pari jure 320. 81
tantitu
tractari itaque opqus 20. o
uti sed posito
esse transpositione
seu duobus laferibus ut eodem modo exprimantur. verum quod memorabi 32 eoo lissimum est aequatio
equationem fieri nihilo aequalem non eodem modo ex
ista hoc modo nata dividi potest per x-y. Et sic mutatur it homoeoplotam, in qua oimnib
positis intulo aequalibus x et y eodem modo tractam. Notantum etiam in aequatione b evanescere combinatus
ones in quibus X et y pari jure atuntur, seu quae sunt potentiae ab xy. divisione facta res sic stabit
C ry- etc 13 4400.44
a
4003
27 Xy Xy
VdxtBy
d
ist
B
440.731
12
3
ain
23161
F231. 100
400. 83
62
400.740
4210.730
+220720
+230710
+240. 900 (.Y
400640
10. 630
Xy -32o.b2
330.610
390. 8a
jure utuntur, et
+ recter
x221.90( - 210610
que62
ne
63
(6)
t
esr
a 22b
+ ex = 0