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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 20v, page id 00068197:0040
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ZF2 =, 5.
218
Videamus an BOD. Vaa, seu Od. Y aa vel OD +a sit diisibilis peroc
sit C = 12F 11t + 1227 + 10a D = 21t, + 224 + 20 a sirt OD, ad - 11. 21 h  + 12. 322 2 + n. 22t2 + 11. 2out +12 20al + 10. 20aa
O+ D seu 1H + 124 + 10a ducatur in 21F + 324 130 et fiet
Extrmini hq ah2, L  fi  Y fit - _ 10. 20 a + 00 00d
12+22
coinc
10+ 20
+ 10. 2 ab +10. 22 a 4 +00. 00 aB
dentianda
uhser B  et . +. a gih 4 X l doaha a 3oa 4 + Lonua
2 31 Eo3l. 10320.
Ex termino s  sit 1. 22 + 12. 24 = 11 4 11. 12 22 + 12 427 1 21 mul iplictur hoc aepuatio per W C ut2C. 1+ 22 seu per MA2 F 1. eF12 21 (4 2t
Siet 11. H. 22. 22 + 1212. 21 21 + 2. 11.12. 21 22 = (11. 11. 12. 22 + 21. 21. 12. 22) + 2. 11, 2(. 12. 22 (F 12. 12. 11. 21 + 22. 22. H1 2D+2. 12. 22. u. 2)
(11. 22. 11. 12 + 12.21. 11. 12
et fit 11. 11.21. 22 + 12. 12. 21. 21 - 2. 11. 12. 2122 =0 seu _. 22 -12. 2120 seu 11. 12 = 21. 22 et fit 31 -32
Extermino Z puodit idem hoc solodisutmine, quod pro 1, 21 tonitur 1, 22, ut fiet   g 2 t 1. 6. rar 2. 13 2. . 2 Z (1B A tront oproa, 00no d 10. 22 - 21. 20 = (12 + 22) 00 AB. a)  Ergo per 2 et 3 aequantur
11. 22. 21. 22 + 12. 21. 21. 22
Ex termino t fit 11. 20 +10. 2 = 10+ 20. 1 21 + N 1 9 2 10 10 a + 00 0B. fiet 1. 1 25. 25 119 28. 1. 5- 2 10 51. 1 1  sto 1. 4 oatt M. 4r0 p) 00r a0 B
Ex aeq. 3 (tellendo 22 per a q. 1.) fit 1. H. 3 (2) 20 20 + 10 10 12(2)7 12] - 2. 10. H (12)20. 12. 21 = (10. (127 11 H + 10. 11 (2) 21H 13O M 1 + V. 20 2 ip1) e0 0d 
11. H. Hrg fiet H H. + qu (∞ 2 q (10. 21 1. 20) - (10  +10. ~ t 1, 20 + 2021) 00 00 - 11 (10 1t + 10. 2t +n. 20 + 20 21) 00. 00 b
Ergo fit y = 12 Ergo 22= 21 superest ergo 5q. 7. per quam datur relatio inter 10, 11, 20, 2)
quod si ergo βCD +) aa dividi potest per O + D, poterit tota aequalio si dividi per O + D, et restat
aequata in qua pro c et D substituendo vatores per tu et 27, habetur lantum aequalio
simplex inter tr, et 4 seu n qua ut +.. 4 +. = 0 quod est desideratum,
Nempe aq. N Divisa per O+ D dat (1 4aa) (+ 3) + (i 4an ) (3 + D +b +C) + 3 (31k + 344 + 30a) =0
ubi pro (, D, 31, 32,30, β assumendo valores inventos fit haberetur.. +. 4 +. = 0. 
Nota quia q adhuc arbitraria est putassem hic tbum eju potuisse adhibit adhiberi utiliter, faciendo
on aeg. 7 faciendo  00. 00d: a =
qu (10. 21 - 2C. 20): (10. 11 + 10. 21 + 11. 20 + 2021)
porro in B: a labet. 9, et invento. D: a seu B: Y potest inveniri 49
porro in d
sed video eo iorso quod I _ 12 = t 22421 redigi t et 2 ad unam litera
seu non dari nisi in E t+2. ergo in ultima aequatione non forent duae literae
itaque proinde res erit qc si suntiserans ( = 116+ 10a et D = 216+20 a
et fuisset D = 1 2168 (6D +) aa =  14 2564 + 14. 20 a6 + 1020 aaq
(et O+D = (11 +2) 8 + (10t20) a, qu
quod ducendum in 318 + 30a dabil
ex 68
fit 31 = 11. 21
30 = h0. 20 a + 00. 00d
10420, 1+ 2 = 1011X10. 21 4 1120+ 20. 21
0 +20
+ 10. 21 a5 + 00. 00 40
(ur2I) 36B+ urri oab + (ot 20) g0aa
20+ 2. 11. 21 40 20 + 41t . 00 ert
 aed
200. 00d
Crprc31ab
200100H
(010.11. 20620. 20. 1 21+ 2. 1010. 11. 21)
qu 1 (102 1. 20) B:, 1. H + 2t. 2.
10. 21 -1. 20 = 00. 008 = 00. v0  unde habetur 99
Hinc ex aq.  s ( dividendo per O+ D, fiet (1- 4 aa) (O+3 + brC) + 3β8 + 30βa = 0
1L + 21
et pro D +) ponendo valorem fit (1- eaa) ((1 + 21) 6 + otro)a +b+C) + 31 ( + 30Ba- ubi ut evanescat 6,
fiet (neque enim determinata reddi debet) fiet (1 - 2aa) (11+21) + 32(3 =0 + 11. 21 (3 = 0
et (1= +aa) (0a +roa + 00b + 0oc)  + 30B =
1+21
in quibus duabus aequationibus substituendo no inventes valoris 30, 31, 4. adeoque   B, Y
hab  pote prodibunt duae aequationes nova, prastandae ope arbitrariarum 10, 20, 11, 21 nisi quid
Ex duabus aequs novissimis sit B. ( ag) = β: (4an - 1) = qu (11 + 21) C_ B (104 20) a + 00btC), 1020
subsit, quod impediat solutionem. Ex da
11. 21
10.20a + 00. 00
seu 00. 00b = ((10+ 29 a + 00 (b+C), 10. 20. 11. 2,) = 10. 20.  qu (1t 2) a 44) 1o. 2 qu (10. 21- 1. 20)
qu C1 + 21))
Habemus aequationes duas ad huc, huic conjungendas
B seu L seu
bc - aa (bbi cet ibe) () 10. 21 - 11. 20)
= qu (00, 11421
Hujus aequationis ope habetur  (qu. (1+ 21))
hatetur H. 2 21: 11
 qu (11+21) seu
1. 21
2 - 92 (5) qu (11+ 21)
4 -1
I1. 21
fiet
d: a = V: B
(3. Z = (10+20) a + 00 1b+c), 10. 20,:, 10. 20a F 00. 00D Ex c9. 2 fit 21. 21 + 2 f4. 2) + 11 = 0
seu 21. 21 + (2 + 8), 2 + (4 + 4 P + BB ) 11. 11 =  28 (D + 48 + EB (1)) 1. 11.
seu 21 + (2+ B) 11 =  1s (4Bd + BB) se 21 A) +(+CA + BC) = 2 A _ B
ruitus ex 1 fit 10.3 = 20, . 1+ 2 = 00 1B: a) et 10. 2 - 20 = 00 18 + 21 0o  et fit 21 2 00 ( a) + 20
10 - o (B: a)
quCa r2) : 1. 21 =) B:  seu 1 + 2 21. 21 + 2. 21. 1 + 11 1  (B. L) 11 21.
4 = a 4aq - 1 - A da bc - aa (bbtcet 2bc) = 1) a. et fiet
10. 31 - 1. 20, :, 11+ 212 00 fB: a)
fet
inde ex ab fit 1N0. 2121Y, 1. 112 20C2. 10 202) A(0. 1. 1. 20 10 o 1 X 1 20. 2  v. 10 21 21
unde tandem
seu Exerpino