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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 13
# Folio 5v, page id 00068084:0010
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Huc
30. 30 d31 F A 30. 31 d31 + 30. 31 d30 + 31. 31 d30 + 30. 30. 31 + 3B31, 31 + 3(3.
31. 3e d31 +
(21. 31 e d31 + bede +61. 3131de
30 + 5ip + 60 d =0 sit v = 20y+71
160471406 a ) F60. 70 dy
unde nil
novi
22t
31 C3(. 3Dde
BDeBD Cd31
B1. 3)e d31
50 + 51V + 60dv =0
fit )50_
+B)3I + 31CB13D + 3F
V = 6947 + 20Y + 7yy
51. 69. + 51.70Y +51. 71Hy 
60 dbg + 60troy  yy + 60. 70 dy = 2.60.71ydy
10 + 11 V + 12 yy + 20 dy + e y dy
C in duta
omittamus 69 et Retenta 7) sit Fotam datam multiplicemus, per abitrarim liter
ut per (07+ 60.71: 21, succedet eo ipso termiaus ullimus ydu
et fiet 70 = 260. 71. 20:21. ponamus 7l esse constaintem et
fiet 51. 71 - 212. 60. 71 :21 seu 51 =260) 31: 21 = 2 11. (60)71. 2 7 60 dy
et reditur ad aequaver tractabilem. Error calcudi
Repetamus 2.60.71 = 21. 2. 60. 71: 21 est identca
(6d
o
Ex dy sil 60.70 = 20, 2. 60. 71 :21. Ergo 70 = 2. 20. 71: 21, seu copendo. 70- 70. 2
bi 89 est dete i
et 8g = 2. 20: 3 data  ex yy fiet 51. 71 + 60d71 = 212. 6089 seu 51.  =21 2. 604) -60 dy
et ursus 51 71.89 +60 71 d89 + 60. 89 d71 = H. 60. 89. H1 ay vd8 + By
rursus 51. 70 = 2. 11. 60.71:21 - 60d70
L2.6o. 89 60.89d7t d, 0 = 71 L89+ 89d71 et fot er
Et fier 51.71. 89 = 2. 11. 60.71 : 21 - 60. 71 d 59 (- 60. 89 d71)
sed ita evernescunt eltur bo et 71
et fit 2. 12- 2. 20: 21. 2] = 2. 11. 4 - y
An sic 2 = Yt = 21. 2. 60 r2 20260 E7) = si 2. 11. 2 = 2. 12. 21 89 - d89-
poramus abessi 12 et 11 fiet  dy0: 70 = d71: 7 se l0g. 70 =  log7 1 + h
u 70 = n 19  71 posito h esse unitatem cud seu rectam cujus log. est 0
si multiplices prius pe bo fiet 21 = 21: 2 et 70 = 20
et fet 1c tu
12 = 2 d21, : L. 21 = 11 - d28, : 20
sit 50+  40 +q2vo + vdo e sit v = tegy +
1288 + 4289y + +2. 60yy + 189dys +6pdu
sit 1 =   460 yy + 89) + 88  fiet 4d e
fiet  89 = ∞. 41.
41 d08 + 141 489. + 741 d60
10 60. 41.y + 60. 41.12 +5∞. 41. 20 80. 1 Jay
sit A2 in data rave ad 4) habetur 60 per y7,
Ergo. 89 per y. et 40 per y
m + nVV + pVdo = 0 sid sit v = B Squy + ry+ 5
Ergo vao = 29y dy : 2 + rdy D. 2. + d9 qy. + dry.2 + d5
ergo in +nvo + prdo  =0 =   P H 444 n 3 trrys 1rg77
An sic
fm + fm bv + fmcdo afm evo + sutr vdo
t
C
sit p = mC et ginc = siph seu g = fh: c seu habeturus
et fhn: C= fme fit n= mec
sit v0 = y vdo = dr: 2
Rd5 ultry redquu H rdy + pguydy Seoinc
ar tpar = c seu ref + Zg def
+ gnov + g vdo
Spotestomulti qu
20.
b pus + exqyt ep yy+ fpgdus + pq ydus = 0
b +Cy + eyys +8 dys + 9ydy
, r = 25: 9 n. = eg
Vel m + nv +pdv = 0 per hb   290 + do
omo
e
(Ymsec + (msh: C = F m fit h = e 5C
20 Ego 20220 = 13. 20 +2220
si 10=1) fit)
en 11.20
6
obdy
fit (r= 259
sit n = hp et ex ryfiri hgt Ldq = et
etdatur 9 pem regulam inventar
puitus ex y, fit hif2s q+ 2fdqu 9  eq
Et posito E et s esse datus vel proutes sumi
habetur 9 ubi pro ha substituendo
valorem inventum eq-: dq fiet.
25eq (- fdq. + 5d9 + gdf, id
est fit df: 5 = 2C
Si 71 sit constans habebitu 60 per y dy 70 per dy,, 51 per yy +d30 + 431 y+ d e yy + 31 dy + 2. 32 ydy in y + b n.
Sed pursus 51 per 11 et 64 et ruoriur determinatio
In universum vel 50, vel 69 omitti potest
2.12. 60.71.89: 21. 60 d71. 99)
sit q- 1
p= g
3
sentemus in  in nea data oblueri possit ut s) 3 
Sit 10 + 1cd + 12 (4(d + 13dco + 14 cdded. et sit 1d = 209+22
fiet 10 + 112084 3
pa F2Mo y +. 12. 204) + 13tay
13d32 F 13 deo y
22 d22 +22d y
20d2 y trodrogu
+20. 20 ydy
debet esse 14. 2.20420+ 2 20 d12+ 20 dd2o + 420
=2. 20.. 12 26 f ol = f. 2. 20. 20420
lous lo ce vui du
potest S’omitti
neodi
deo - dic trotus 
sil 30- 31e fil
fiet +50 + a1
+S1.71 51. 70y
V = Er ergo
do = dr: 2 er
vdo - dr: 2