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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 197r, page id 00068196:0389
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in 205 f 1643
24 2da= raydy + 2 xx dx + yyd
problem
in literis
Sit y = ( x 10 + uX + 12XX + 1X + 14 X + 15X + 16 X 117X ri9 X cu
2 γy =
Efytus
Kyduy -
+
XX =
- aa
seu 1.
11010 +ll10 X +, 10 M2 X , H 1on X + 10IE A. 1015 X _ o. 1BX  10. 17 2 L. 0, 8X et
7, 71. 11 +  11a12 R. V1. 13 2R. 11.14 X. 11.15 + X. 11 1b R. 11 17
.12. 2 B.12. 13 9. 12. 14 f. 12.15 A.tE 1b
13.B G1514 4 13.15
)4. 14
+2 11. II 3. 11. 12. 4. II. 13. 5. 11. 14. 6. 1. 15 2. 11. 16 B. 11. 17. 9 11.18
FLNX
4,12. 2, 5. 12. 13. G. 12. 14 3, 12. 15 812. 16. 9. 12. 17
R13. 1 13.14 8.1315. 9. 13.16
 assumamus 10 ut datam, quamtaalibe quale in libet
si sit 14 = 1 ecit H= L
Melius sic
Gsi, gy = 20 + 21X +22X + 23 X + 24 X 125 X + 26X + 27X+ 26y
et
+ ydy = 1 21 +2. 22X + 3. 23X + 4. 24X + 5 25 X + B. 2bX +7 2y X 1828X + 9. 29X ex
4 ZXX
= X
sit 2 = - 20 - 1 . F n=
Ergo 2 a 10 B, 1. et 10 24 = -23: 4 25 = + 23:A5
et 26 = 23:94, 5, b 27 = + 23:, 4. 5.6.7, etc. 
Ergo fint Lgy = 20 + 21X +22X + 23X - 2 X + (23X- 24
4
sit 0 = (D ( = X. L X + L X - L X + 1- X - .
Ergo
1.2
23 23, 23
superest ut iaveptigemus 20, 21, 22, 23
possumus antem jactie 20∞0
fet: 21 = -20+ 1,: 1
22 - +201, :2
23 =13) = 20 (+ L. Ergo si 20 -0 fit
2.3
23s 
1.2.3 1.23.4 18 3.815 1.213. 4.5.6, 1.23.45.b.7
Lyy - 20 - 21X - 22X ( X) = 12. 3V - 23X + 3X (=X3)
2.13
er
G 10. 11 42. 10. 12F +3. 10. 13Y, A1C.14 PY. 1D. 15+ + B. 10.6 +y, 101, X + 818. 5X 9101g et
 1.
8. 19.14: 9,14. 15
4.5 4.5.b
5
ui etiam 23= 0 (do- 1X+  X etc. Ergo do= 1n B. dp 72 1. 23
et si faciamus 23 =0 res redit ad ordinarias
et fit 2gy = X - = X seu yy = 2ax - xx quae est aequatio ad Circulum
Nam ut expediamur: G ydy = adx - x dx visen dy: dx = a -X,: y
ag =  - 9y = (E aa) - 2ax
seu fit 2ax = XX = gy, ut ante ergo haec aequatio resolvit, problema
Hugenianum nempe  dy: dx = 2aa -XX = yu Idem tamen
i
pote  2 g 30 Cyy 4 +2- 1X - 20-1 X = 20, v. posito 12V ess num.
qe 
egus =ogux Aux(x 21. 6V - 23(6X + 13. 3XF BX seu Lry - 10 LL 1X C. ur 2X -20B trox. 2X
seuseus q sit
dy 2.20+2X. X 220
tr umme
+67
ecipitire
Htinc si saciamus y 20 = L firt y9 = 1, + 2X. XX-  Eenmlit sd B, 2. 20a = n fiet gy-
220
a+
et - x esse loga.
mum
Senpotibr  sorid 10+ 
Sin fatiamus 202 1 46 = 0 seu 20 = -5. fiet 2yy + 5 = 5
Hliud problema ejusdem:
e Gu
posite Lex esse Nonmasius loqe est x
uia s
na dy  dy: dx = ax - Xy -ay,, aa + Xy
l, aa dy + xydy =_ xy dx + ay dx = ax dx aa dq + du + dx + dx = a dx
sita y a50 + nX + C X + 13X+ 14 X + 15X + 16 X  + 17 X + 18 X
E xHds Am +21 1323 1424 +5e 16. 2 1x 17 12 1919.
xydys = , 1. 21 +2. 2 1B. 23 + 434 t5. 25 tb. 26 +7 27. +8.28.
y
sit yy = 20 +21 X + 2L X + 23 X 424X es
2ydy = 121 + 21X +3 23X +42 4X 152sX e
222 = f.11 +al2 13f. 13 = -7.1. 12- 2. 19. 1
-13. 23 = 12+ 13 +4. 19 = 8. 10. 13-11. 12
10 +1 +12 + 13 +14 + _ + 1b +17 -:4. 24 = 13+14 +5. 15 = -1014. 3 11. 13- +12. 1.
aadue = 14 5. 11 2. 12 313 4.14 5.15 646 717 8. 18. 9.19
Xydx =
= axdx
a
6
5, 25= 14+15 +6. 16 = -15) 18. 15 - (5) uil 47 1)1219
s et puo  ponendr rutorem fiet dea rursus ex aeq est rydus
seu ydy = 5dx 1aD  sydy = sax - s v dx, seu
Cr 2ytoa na ampex.  ds = sdx = hyyen  Gd
idx -Exdx de vii hud e rytus. id rxdi xdx
5u = 2yy-
d
yy = -10 + 10V. et x = (dv: 1 -  Eydy = 10dv. seu ydy = 5dV
yy21.+ 2x - Xx - v iam dxX = 5dB: 1. B. Ergo als  dv= dx- vd 
2
17 Seplemti. 169
1d 20geF H = H+ 1
Fia   = 11
 1 = 2 = 103: 210
48
2
si I1 = 0 fit 10 = 1
Ergo peuinde est ac
si fecissemus x+ dZ
 Zax + aZ + Lxraf aadx
Z+ x
si 1tn num,
et l log. fil.
fieret Z=yy
= posito 1-H
esse num. et
X esse logs
 log. T+X
num. et
1X LX +L X etc
=-N. posito
l+ P + (3 +
Ergo si con numfils 12 123 723.) eCC
4. 5. 6.7
6+ 1 -X
si 
CA=
BM=-- (
1. 2. 7. 23
Ergo 1-n num
et al log. fiet H= l- 12