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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 29v, page id 00068197:0058
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rit
+BDn ut 3r 30.3obbrB + 2. ZobbrrC BZ Hbbcc ZZ
4110 -. -  - - . - + cebbr rr aa + Z. cc bbr ra a Z + Ccbb (  H. ZZ
_bb
 OdD5
sit r= c+f
Videamus, tamen an non liceat facere e) constantem magno utique alculi compendio
Ergi Si esset C= obix, ex aequatione fundumeritati fielet
do
=aat1, 40
sit C = m et  D = fiet mDD - bb D + cem = 0
sit jam D) = 30 aV + 40 aZ:, 60Z+ 56a, Et fiet
FM)D.. . . . . 30. 30 aavV + 2. 387aa v Z + 40. 40 m aa Z3
= mm 5)
abb13...- 3160 .. ..  30. 60 (b6 a v7- +0. 60 5bb a7Z. = 30. 56, b 7. aaP - 40. foz n n 1442
MM
Enm,
26b)
+cem
+ 5b. 5b cem aa + 60. 60 ccm Z2 +2. basbemaz + 1. bo sbcem az 
Et fiat 40 = c + 60 = a. Ergo, oCCaa  = a a Cbb)  aacC C) =0
 fit ox 2uacem - uac hmm
Ergo exito. 4omaa
o. siqbt za profilo-
+6060 cem
tccaa f aacce
2aacCf
L= ac
F ad, c bb,
caycets
Quia bbenim = 2Cm, hirc tota aequatio diridi potest per m
desructa tma
atb, a b = Ba - b1, c
Tollitur e sublato termino aZZ, reperio toli etiam terminum aazue, num
nam fit.  Rc. 56. 2cm aa Z + 2a. 5b. cem aZ=c
itaque tandem ex aequatione nosta fiet imo tllitur etiam VZ
Itaque calculus tam facilis non procedit ad scopum
30. 3 a ox
Videamus an evitare incommodumliceat, non assumendo 40 et 60,
ut fecimus, sed quaerendo, (compendio sit bb +m = ag, et aequatio ad destruendu
nimum
terminum Z3 est 40. 40 aa m - 40. 60aag + 60. 60 cem = 0. Et si
Hinc 40. 40  40. 609 + 60. 6099 - 60 60gga6060a am n ce
mm
qa nm
seu 40: 60 =   (_ aagq- mmcc): am
40. 40 aa - 40a60a9 + 60. 6aagg- 60 60 aague  60 60cc mm
amm
amm
fiet 40: 60 = ag + sCaagg - 4 cemm), : 2 am
si faceremus ag = 2cm, se Haaggs dumm) =0 recideremus in priora
et fieret 40: 60 = ag: 2am = 2Cm: 2am = c: a. Sed si facerenus
ag = - uem fieret 40: 60 = - 2c m: 2an et posset esse 40 = = c et 60 = a
et fieret bb + mm = - 2em et mm t rem  ec bb et nim + 2cm + cc = cc = bb
et m = H(Cc - bb) = C seu M = f-c. Videamus jam an etiam hoc modo
destruantur iqe et a7, Ut vereor ne sit idem. ll e pro aZ f  2Cm Ca +2aCCm =
 et pro vZ vZ, fit -2. 3oema +30a rem. Ergo relicta adhuc m, faciamus
Faciamus
40:65 a ag + (aagg- +cemm) e: et 60= 2am,
vel 40 f0 - bb +mm + YCb + m + abbum - q ce mm)
bb +mm = 2mn, fial 40 = n r. 40 :60 = n + Vbin- cc): a
nn-ec
Et fit aZ, = + Nan -c4)) 2mn F a ccm. = ram_.  e _nlun - c)
Haec stare possunt
=a 2mn = 2am, dena - cC)
ut Quia r est arbitraria, modo apta, faciamus nn = bb + cc, fiet m = n + C et 60= a  - nt B
aZ, +2 (n + + (un - c))ma
mm - 2mn + nn = nn - bb fit m = n + senn - bb)
Vemamus ad nostram aequationem et his valoribus pro 60 et g0 substitutis videamus an destruatur 22.
o= nn M H2nomixbbmaa au-a (-armub) Laaccm fit bb FcC = nin, ut oportet
no mntbb ponendo 2m, fiat 40. quaa  =240. boAN + 60. bocc fit 40 40 : 60 = n + Y(pn - cc),: a
seu m = p + C
seu 240: 60 =. n + b,: a, sen 40 = n + b et 60 =a, ut prius et  quia mm +bb = 2MN, A sit m = n + Y Cnumbo
Repotaums quraes
un FEkb +bb 2 nF X
nten
 tecai
0. = 2