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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 167v, page id 00068199:0334
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3022 + 31aZ + grad
1drx- V8, 10.20. + 22021 aq + 1. 20. 22 aa 2B + 2. 21. 22 àq + 22 22a
lm Z - (1, 20. 30. +1. 20.31
1. 21. 30
In = ln, 30. 30- +2. 30. 31
(_ = lB, - 40. 40 - 29041
. 21. 21
1. 20. 32
+2. 30. 32
-2. 40. 92
-2. 91.9V
- 42.40
X40. 40=20. 20 20. zoml + 2. 3onl = (20. 201l + 2. 20. 5oll = 50. 5oll. fit 20 = 30. 3on - 50. 1l,:, 2.5
ex terminissummnis
et 40l = 20l + a sel seu 40 = 30 n (50b + (2) 50l  = 30. 50m,:, 2. 5ol - 3om
lebemus ergo 20 = 30n - 50l, : , 2.50l = 3om et 40 = 30n = 30. G0m + 56 l,: , 2. 5ol = 30m. Et parijure ex
erinouli 22 = 32n =sil, :, 2. sil - 32m, et 42 = 3i n - 32.52 m +5  l , :, 2. 5 2l - 32m
exhis 40-20 -50
Ex termino secundo C2E1G (30 n - 50) + s1. 2 m. (2. 56 = 2om  t   (30n - 30. 1om +507) = , 41
tenultimo similiter
2. 2ut (32n - 52l) + 1. 2 m (2. 52l - 32m) .  ., (32n - 3 252m + seG) = 2. 41l
un iturum
et aequandus valore, ipsmp. H
compendio sicem et  36Bn=  zol et 3Cm 5n = 00 s et musiplundo per rucem
p1o2. 2l. 50l52l - 3im 5OLsID: Em. 2 5ol si lF 2. 3th. 2.50lSil + asolluset
Benniile
Crhonrum. F. 2. E1l; 50 Ly2 Sen + 31 n 50 L3L Dm (= 21. 20 2. 50 (32 set - 2. 31 3on 25ol 3212m)- 5dH 51 5.5M  20 mn ditem
Elonm) =2. EIl5OL 32n (= 31 m 3ol 32n) = 21 3om. 250l 32n) F 2.31. 30n 25ol 3in + SdUsc3En (- 30mn. 313n
L5EL 5ol - 2m ) E = 2. 3m. Z alsel F2313AMEsil sot VS  ySOL (E mn. 31. S0L,
tr. 2ILse posem a t 3Im 52 L3osom (+ 2(.3 2m. L52(3050m = 2. 31. Ln Vsel3Von) 53 eH 21 90. som + 32 mu. 3DSom
purm L. UISXLZNG3m Si 130n) = 2 32 m 2 52130n) F2. 313V R sd 3on 45, El 31. 582
Htujus aeq. ope habetur 21;  31
dmfror sou et astui vot)
b
bfoX
31 _I(32 52. 50
Hma o es
+2bm (130 s2
retunt. 3onc. 
3 Emn313on
+m sit ( 21, E 5osum A. 4 (30 5iF L. 50)(m
nes pamputolicere ut fuail 31. 5B 30 52 20
Et hac sequatione dibisa
per si32. 60- 30. 52
31, - 4. 50. sn. =2(30. 52 + 3250)hm +2. 30. 32lun
1. 50.5m
R - 1. Z Z2MMA
Nisi malimus esse 32.50∞30. 52 =0 seu 52350 = 32:30 quod sane etiam ex
duobus valoribus praevideri poterat, quia hoc assumto duo valores ipsius 41, statim aequantur
Tantemqua Et certe in a pluriam literarum saepe insigne resolvendi impedimentum es
ae hypothesin excogitare, qua aequatio facile praestetur. Eaerum u aliquam saltem
Y aequationis radicibus suppeditabit
non fiat A similiter 21: 31, a 41:  ut 20: 30, et 41. B1, ut 40: 30.
Ex Termins medis fit. 2. 202.324-21230 (+ 20. 30. 32 lm + 21. 30. 31m ( 1. 3+L  20. 30. 32 lm
Am in temino ens psterimus cedo fe relinquere 40 inexplicatam, quia continet 21
22hL 2. 20. 21 l +20. 31M +2130m + 2. 30. 3. M = 2. 40 41 l. fea fue
40 autem et 20 continent tantum 30 et 50,
quibus non videmur hactenus indigere fit ergo 4+ =, et q = ∞d 228. 21. Y ∞. 32931, 
2. W. 228. 32B. 31. 21 f. 10
2.20. 20. 32l + a. 21. 30 l +20. 39. 32m + 21. 30. 31 mt CB _ 20. 30. 32m
+ 2.30. 32N + 30. 31. 3In 240 Ace -2. 92. 40= Ait etqig
= 1 2287 ,, 720. 320. 21. 31 +9 320,.317:40
Unde ex duos valores aequando sit
peracta Fiet autemEt - B 30.31 (40 m, 2. 220. 320 +((30. 3l qu (40 m - 2. 2o. 320l) - 4. 30 (40- 220) (2. 90. 32 (2 20 l + 20. 30 r t238 2)) Seu 2
sed 4ul + 220l = + 2( (357- 305om + 50l). + = 38mm, : 2.50l- 30m. igo 40l - 22oll = - 2. 30 mml (30 n- 30. 50M + 56 ) -  L 30hr,: 7 qu (2 3o l. 30m)
seu 40b. 220l = 3on - 30. 50m +50l 30 +50l +  3050lm = =3dmm, : Z sol 3om = - 30mm: ,2 (t. (ol. 30m)
2. 20( 2. 40l + 203om +2. 30n = f2, 30. 500 30. 50m = 30. 50lm  (435. 50ln = 303mn, :, 2. sol - 3om = 267 24030.3an + 40. 31. 30 = 2. 40. 38. 9 2n +2. 40. 30 nM
30, 20. n +2. 3on = 2. 220=635 ma)  C0 em 4 4. 30 solm - (2) 3d mn, 30, 2, 25ol. 20m
404 2 4d- 220l= 30- 3056n + 58U (20F L30m) (250l- 39m), : 350l- Zom
iin adde 320 l. 31. 30 fiet a  2. 30. 32 (50t mm 5. 39. 503 nn - 2. 30. 50) n + 16. 30. 50 llnn -8. 3035olmn 30 mn) + I. 40. 30. 32n (4. 50 l ( 4. 3050lm) 4 30 mm)
quod dividendum est per qu (2.50b. 3om et mult pli candum per 4. 30 (40 - 220
qu - 20 = 40+20, 40- 20. et 40 - 20 = 2. 501 = 30. 503:7 2. 50l - 30m = 50 et 40 +20 = ,39n - 30. spM,: 2. 5ol -3om
Ergo 40= 20 2. 30350n -3958m,  : 25c, l-30m
30. (0 - 2202) 2 2V + 3 olersqu  + 30. 31 (45 2. 2d0. 320(21 l. +2 1 3T. colo 20 30m
+3440 en = 32013;
ubi modo caveatur ne 21 sial ad 31 seu ad 2Y 30. 32 se ut 20 ad 30, neque himiliter 41 ad 31, res est
Fictantem 230 (40- 225) 2l =
et 91 possumus  sumere ex explicare  ex Termino 2do.  non
explicata in eb quanitate 40, ces neq vel 20, et
AB compendio 22+ 2 2ol+ 3em sit 50. Z20
et 2om + 2. 30n =, 320l, et fiet
posita ergo hac aequatione, 52:50 = X: 30
 Tantum cavendum me 2Ca  et 31f
292. 40 a , 5. r1. 41H
41 = 0b. 220,. 21 + ∞5. 320.31  : 40
Porro ex terminis mediis fit
adeoque 22: 32 = 20: 30 et 42:32 = 40. 30, quod quidem hactenus videtur licere, modo
fit 22: 20 = 32: 30 = 4h: 40
2.3 3 gent
7Z141a2f3iaa
40075