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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 168r, page id 00068199:0335
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Quo tulior sit calculus cem in cumeris exhibeacuus. Numeri per et notam otterminato
habeantur quasi ea abesset.  et lsint numeri pares sed l siqunt sonarius simul tet naus
ita n= 2p et l = 69 Ergo 20 = 30. 30 2p - 50.50.64,3, 2.50l  m seu  69
m= 3Y Iq
2,- 3-39p atg 347 :, 269- in seu m +- sp 234, se
2-1st +B G,. 60 et 18 = 1 136, 1 c 5.6 31Z
M + 209 = 3p =259 seu M = 459 - 3p id est si q et p sint 1
fiet m = 42. comprobemus 2- 33 2. 18- 150,: 60 - 3. 42 quod succedit
habemus ergo n = 2p, l = 69, _ m = 459 - 3p et 10 = 20450, erit
40 _ = 7. q od 1t debet luccedere nam 40 =  9. Ep - 2. 3. 45 9 4 3. 5.3p f5. 64, : 1069 2 9
2b = 9. 2p = 25. 69 +2. 25.69- 3.5, 459 +3,5, ZP,:, 2. 358- 3459 + 9β
_ 2+5 = ex 9.  - 5.5. 64 4 2. 5.5 1. 5.  459 + 3.5. Y. 3: 2. 5. 69-3 459+3.3p
n2+5 = (9. 2 4 3. 5. 3) P + _. 75 (4-9)13:,  r 15 (4-9) g + 9p - Daeg 759 + qu 6
sed video nos ninls cire determinaffe 50vel 30 pret
porro 31 = 2 130.32. st 32 = 12 et res procedet nam fiet 31 = 2 Y3. 3.4
3 327 = B29 18 puo impto  120
21m +2. 31R = 41. 42 +2. 12.2 =9304
21m +231 = 2 42 + C 1= 2 21 l4 1. 31 m = 2. 21. 6 + 12. 42 = 252 e 504 = 73p
s 5. 516 18-6+0 + 150 = -46
5.6053460 601305  3.3. 2 -3.G.4
et fiet 756(4(32 + 430 () 6b,: (-462 = 41. 6, 1on 15b. 132 +930. 66 = 2. 6, 462. 4
cilas smbemus (2 AG t rg M)  1 ( 2 + Z. 3m) - q00 gyl ,  At. 462, -. 31 66132 = 99 l, quia 4un
sed video i concenti simus abjectione Underaria, e aoveraria spunt, poe aqidem rolinquit quod s4
66, 22 sive abjicias goue 1
inec veros nnmeio ipsos velumus, posse nos contentos esse omlitere l vogu
4 fiet q 6 2 5. 91l = 135436 (2. 21 l+ 1.31m) + q 66. (2 m + 2. 311) n = 4OE pro-
is posito tusquod succedet in Abjectionibus fingendo l= 6, n = 2, m = 42et 31= 12 5544
32 = 12. unde 2.21lF 1.31 m = 75b et 1. 2A 2. 31 ∞ = 930.
22= 2. 1233 =  itaque in probatione numer ab
 441+ 2. 1. 42 53 42+ 63 421. 13.4874
B 120a1 61 1
16 = 0 = be  a vdi Ha
uo unq
Ergofiet 2. Ergo quaerendus numerus qui per Novenarii abjectione in relinquat  per H denati, 4
F. 2 30. 32n, + 31. 31n 2. 40. 40β2.30)1-41. 4il = ita. ubi extra comprobationem per numeros
c pro 41 subsumendus valor nuper inventus. Est autem 91. 41 = 132 (4. 2 (+ 4, 21. 3.m. + 3V mm)
+662 (21. 2Imp + g. 21. 3IM  4. 31 nn) + 2. 132.66 (2. 21+ 2m, um+ 2 2nBB: (1 462.l
is vator substituendus in aequatione propime praecedenti. unde odra
secundum 2 fol t4 36462.  + 4. 30, A62M. 21 +4 463, 20.3
3817 2 I - 4. 307. 132 Um . + . 46, 2. 20l. Z2W
-7. 1grbb. Im - 2. 36.13 bb.  H
 2. 38. 132. 65, 31. Mm
F4. 469. 20 32. 3o lrit
+91964 f. 2. 20. 32n
+4. 465. . 30. 32 In
4 . 465- 2. = 3opnA2 3dsolp t3 8. 5o lu t 38. 1 o ni. 2 30n0 ba s8I -  965. h. 40 
4, =it  (imib sm) + iESIL (32M + 2 b6n)
=0- + 62.00
-. 13E. 4  303
6622
2. 176+66. 42 = 99 fiat at 2. 1al +66m = gga. 17222t 2.l6. 2
P. 13265. 2. 4)
pro po
fiat 132m +266n = 660a. Ergohabenus a1= 99. 2a +5609 462 Ergo 32 = 31: 230, Ergo per 1008647
et 4(ll= 99. 21aa+ 2, 99. 660. 21. 21a1 7060. 42aa, 462. 
2. 20 β1. 2. 30) ll421Il + 20. 61. 2070 m
hanc aequationem habebitur
tur saec aequatio per 402. 2.30 ut 29
+21. 3lm + 30. 20(31 2.30)) m +2. 30. 20 β1. 230) b +35ln-2402
8(99. 2taa + 2y9. 660. 21. 31 aa  4560. 317 aa 3: 462) =0
l + X. 38.463. 31. 21lm
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
y (40H - 3 2ol) 31. 30
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)
sit 202 10 60n 40 - 20 = 14000.4
f238. 465. 214 = 0. 130. . 21  (32 + 30) 30 = eo. 18. fiet
 X. 49. 666. 31. 2t a Y. 36.99. 2iaa
eoia
4627-99F 00. 990aa
30864 99 150 = 200. 9900aa
Eit 0ogquaa 21 + 2. 00. 9900 aa. 21. 31 + 00. 121  462, l. N  = X 30. 462. 00. _ 
00.14 462 lB)
eqpuolt si nrit. a t  ( D L. 20. 36. 462 In 31
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
am  30.20
Termini medid
3.9. gi =6
=. 668. 6... mm - 4. 30, 31.  mp
: (- 3 At nt + 2. 30. 50 I (= 50
jam ob Terminum medium est
(X. 20.46
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)
1609- 1359+90
Hin an b
Is numers est 125. itaque fiet aequatio, 2. 20 (3∞. 30)l+ 1. 21l + 20. 32m + X1. 3(M+ 2062. 30
Z = 3. f. Xp - 25. 849, :, 2. 5. 2.4- fon seu
siet enim 31 = 24 12 sed si 32 faciamus 27 fiet
30 -58 = 9. 2p = 25.69 = 15p - 1509 = 132
=20.32:30  id est in numeris
Hinc ex C quatione
12. 2 + 12. 12.2 = 2. 7.286 =41. 41. 6 =0 seu
ehice error
 40- 20 = 50(40+20)
CL prrgessent + fieut m  122 unde habebumque
122 20∞ 1 156- 18 = (3
Ergopro Ab scribumque
Erutum in eoquod b debursi
orimrsi
abjectionibus contentisimue
 W 12).3
 in numer
be q goq  ut X 14 + 288∞ - 275
  teu
192, et 30,5079, 5 30 =3 et 50=5,
31 = 2 Y40.50
v
130.660. aa. 3
1a
abjectionali habeatur
 o