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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 125r, page id 00068199:0249
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3 +00 H
1100 8 - 127. 9000. 1dIL. 117
3100.12957 =27. 00. 0,9. 112. 112. 112..- +27.10.312112 112. 12a GQ + 27. 18. 3. 112. 1 A2a 
3r00. 100 pGG-
1. 00. 12 p O) = (r s 12 . 5d
+00. 100 ap E
-0d a 
-00 a4
Erpolabubr
3
t
54 H. 30)
u 431 00. 00, 00. 112. 12 p...
1∞, a0 _. 00. 112. 112p... + 1. 1031. 0B. (12.12pE + 1. 113199, 12. 12a a p
130
11.
 uti nonin semradato 9. 00 00. 00. 12 a p
sus  Lu2 00AOL 2. 12. 12p PG 4 Z, 17. 00 (1 11. 112 1 ap e
1t 3. 2eroro 3
000d 1 1 - 41.  40. 31 112. 12. M a .1.  g.90
quit
simplicu
Tesset aliqua +
in
valit Rihilo
1. 000000 e ombun
an
1o 10204 00. 80. 11249. . .- 1. 1 v0- v000. 112 aaq
quods emo bs pl 2 1. 31. 11242 W aqu. , 19 c. vc, 12 124 c
Bet Vrent con
mtii sequales nihilo porent. quo
oporterot esso
simul Pevalor ipsir
er Aequationem qua destruitur QE. habetur (18. 31712, sine 11 et 31. is substititatur pro eo in aeq.
epotest suppleri
qua destruitur 2. Et iac aequatione posteri qua destinitur e, pro valore ipsa 11. 31, substibuatur
hujus vator ex aequatione qua destuitur absolutus, et, ex aeq. qua destinitur  sit aliqua
in qua reperitur 1+31, simpliciter Ergo quin habe sine a et 31. Quia ergo invenimus
tam _ ∞ 10. 31 + H. 30, quam 11 +31, itaque habetur  1 et 31, simplicile et rationaliter
etsimplit per 10. et 12. Sed nunc non est opus ips ipsis 11, et 31, sufficit quaeri
haberi 10. 31 + 11. 30 et 11+3I, quoram ex  per aequ. ex e habetur et H1. 31, sine 31.
quo valore  et ipsius 11 +31, substituto in aeq. ex absoluto, aberunt 1 et 12, et
supererit aequatio, quam soluum ingredientur 10, 30, et 112. sed porete. 30 = 2700 10
ata omnia reducta erunt ad 10 et 112. possunt autem aequationes efferri compendiosius
 10. 31 + 11. 30 vicetur B131 _ 11. + 31 = 113 et 10+30 = 107
Et ex aqu. qua destinitur FE fints 127. 00 I2a + 5400 p - 18 00. 103. 12, -, 103 131. 112a 
ip aeg. qua destruitur a G fieter. 11. 31 HE 4 00. 131 2p + 9. 00 p ar g. ∞. 118. 113 H2 13. 1311i2 a  18. 9. 1ot p id
v0 
Ex aeq. qua dessimitur absolutus, fir 1211. 31112  aap + 00 lmn - 08. 113, 12 aaq - 113. 112a
ex aeq. 3. et valor ipsius 131 ex aeq. 1. fiet aeq. (4)
Ad has ergo tres aequationes cuncta reducuntur
in qua habebitur valor ipsius 113 His valoribus substitutis in aequ 2. habebitur aeq. 65) in qua
3
Ex aequ. l. habetur Vator ipsius 131.
in aeq. L. substituatur varor ipsius 11. 31. 112
erit valor ipsias I1. 31. sine 11 et 31. jam valores ipsorum H3 131, 113, 11. 31. substitutis in aeq. 3.
ine
(repertis in aeqque 2, 4, et 5) substitutis in aeq. 3, liberabitur ea ab omni H et 31, et habebitur
ditur aatem jam
depressionis ver
aequatia quam ingredicatur i tantum 10130 seu 103, et 112
facilius qaeratur, 103, an 12, et an non posse forte depressionis malioris resolutiors.
commodiis causa cum fructu aequatio resolvi divelli possit in duas. Utcunque sit, modo
arbitrariae 103, et 12 in ea non plane evanescant. sufficit ad nostrum scaepum, neque
enim refert quam difficilibus aequationibus inveniantur. 10, 30, 1, B1,  etc. 2, etc modo
inveniantur. imd etsi ad imaginarias deveniendum esset modo
nihi proveniat
od l +S 13 Vaag f 13. 12a F00. B3I 12 app 1 9.0o app - 18. 00. 1E. N3 app H3 13L ME nap ob. 103. apque to 1. 3 1
absurdum.
lti valores inserantur in aeq. , quae commodiis sic scribet ( ei. 3 (2 7.  a - 103a () + 131 (00. 19p - 113. 12 a) + 9. 00p. 1900. i. 1p. B. 1619
Exae, 3. II. 31. 112 00 ma + 98. 12. p2aag f 1
aet habeb itur aeq. 4. seu valor ipsuis 131 sine H et 31. compendio H. ex 3, erit 11. 31. 112  00 hun L 113. Iaa (0F, et
ert ou octaas, = 06 f = 00q + ATk et ex aeg. 1. 131 a2 13l 69. 00. 013p : 203 ent (023 = 54, 00 - 18. 103. H2
et 203 = 10Z. I - 27.00. ila ex aeg. 2 fel 11. 31. 112  203A F 3~a g + 131. f 112(B0 0B ap - 113 693 ap) - 180d 11., 1BpO3ap
+00h = 0, ubi 9 = 27a -loa A 0o= 90op 1034. itaqe ex aeg. 2 fiet 06 un 2osat 113. 12. 203 fg. + o B 3e pi 13 u, 
19 112. 113, 203 ap F eo 203h =0 seu 113 n ou 203mng eot. B23RapP, : 12. 203 112. 923a p L compendo B: X 113
et ip aeq, fit 11. 31. 112, 2030G + 003. 023 pp - 08. ∞. 112. D: 2 - 18. 112. 203 00 ap D:  +00 203 a h20 Ex aeg. 3 est
11.31. 15 a P = -00 matod p   fB: A, unde duos valores ipsius 1. 31 qui aquab aequati habunt aequatione (6) literam ab H1 et 91, in qua
Jam notae pro compendio assapta sunt explicandae. Explicentur autem primumm et latm quae involonnt 112, ut o2 3 et F et B  in X Asspegit
112 ad spartum usque grad
saudeo tamo ut FD. D
lee
orene
n
2 cb qui s fieut 20y  14,00. 3pu, 103 -5 4 1 1300- 8 00 +0C    te ps
astendere ad gridum stum sed ardeo opimam elont fatd ita tils q et inen tat 12  in .  
trr anque ae se prteratu
Fiat a1 + 3tL
nocete nequit
et Agt E i2M = libo lmn. acp. IX
du
Hacd
27 - 10+ 20, L eX 4P E
27lmn 00.-905 arp t00 . 0+ 50) aagtoro) ed lmn
+0demn = i op 1. fint 11. 12 4 3. Moate lnc inoener iacoghitaru
qui
10
LH eH
o