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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 159v, page id 00068198:0318
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sit quadiatus seu
Incipiomus denuo et (facimmus B = 7 firt L NA = am seu aa ss. + 2afr ac Z 4 ahag + 4 aht Yac
a5tac + 4a95 tac
Rarous sit D quadratus sen h= B sit  gp = aq seu tanf A rafriabo = tahaq. = + alita ab
( et subtrahendo uem aequationem abalia, fill.
24stab - 4ag5t ab
arrib.). = a ast (b-c) = 2afr (Vab trac) A(aht + ag5) (Vab + Sa c)
et divident toium per fab + sac, fiet (rC- 45t) (tab. sac)= rafY= Aaht - Aag5
uaerenda jam est adhuc una aequtio. Et quaeritur primum an liceat procedere
ad huc semel eodem modo, et facere   quadrahs seu 3 = D fieret . ZHA - aK =0
seu taas eragrtac surahaque =aat lac
+taC = 4ag5ac
et ex aeq. 1a fint 4afr sac = 8aht + gag5, et fieret
unde fint
2t
Fr= 2h+ + 295
SWvatrasst + aa +
fenique ex aeq. 2 et 4 firt La  arrib . C) - 45t (b. c) = 2afY (Y ab = YaC) = Naht +  ag5) () ab + Vac)
frZ 2hF 14, 295 per 14.5
arr(b - c) - 4 a5+ (b- c) per aeg. 6. fint
itaque non licet sa 2= DC, vel, 5, 4 3 adeoque non licet procedere
imo mec hoclicet, et alia cheiu cexreheni non possep
ad raequationem 4. sed faciamus ex diversis
fiit l - VCH - 4am) = r + Is (nn = AaK) siu (HLY rEB - 2L E = (H + AM - gam - Aa K + 2 D (H. can y p. 4a b
seu quamm. Fa aakK (H3) aatm _ = 4 alm M = 4 al VIK (F l HH) St ILHN. R - allak
seu  a qu (MGK) 
LrK. alK = Gum
si etet H=HF, sed, ut = L, fieret a (m+K) 
ob A= - L fut
m- K = a, qertat
+16aa MK) =ANtam
Htmpa ag. N = ita dividamas in
at +rsac = at ty tab ph  s ut er ) at. 2s
ost fi
nfiat I= BN = 4a L et HN =l- gam
an 5tac ab+ stab similiter explic t + F) ull
+aa, 49+ + + ab. ag- tsac=aa suagati) ant ab - a 5t ibc
ntsi
an +5 rab
ah - SNac
95 ac (+ ast 1bc)
Cagan Kags vab
 seu m-K = , (ht - 95) (sab. + Jac), : atits fab, an s ant vac
m+K, aa, 
M+KCO
Pagati + anit tab
=ags ac - astibe
agati =att sac
is aha silab abi-siac
+agsrab = astibc,
seu mok =a, ragh - 2ast lbc +  (ht + 95) (tab - tac)
3:, aahhe albilar.
etab + tac = (3
Vab - Hac = Y
an +3 lab,s ab - 5 tac
In = aa, afaf -afa ibC: at +5 ab, an - 5uac. Ergo ex aeq. 4 novisima, siet
a  qu (ht -95) β3B, an YFab, ah. siac =  afArab, af rtac, a, ragh- rac t bc +(ht. + 9e) H.
+ Yat vab
set ingens compendrumt
Taq qu (astr tab) aa (ag - F 1ab)
ecidramus etiam an ex. 1 et 2 additis in unum fiat aequatio brevior al terntia, ut ex subtractione 8q. 3
= na du (af -r Vac) aa (ag+ L Vab)
fiet 2aaff + ax r (bAC) - gafir (fab- sac) = _ aatiqua +Stabb +C)  +aht ()ab - dac), seu fiet
2aa (+ hgH) + queet (a(bFC) (45t - H) +B a (lab - Yac) (fr - 3ht -95) = 0
A. aequam tamen calculum prolixum aequationis a et inde dedudae 5, evolvamus,  tentemus compendium, ponendus, m- K~0
enam FK, et quia posum potudm El =  all -am) = L + V (L NH = UK), fiet utique
( l +  HH)- ZIH = (L HH + - am 2  l -am,  = am), seu L Unr  cn D + anamm = = las - q aml
Taassim = LamXM
seu U + AN = sal X ut supra .7. sed ila fiot l = H et adeo C = E cntra quod nolim
quid ergo si faciumus m. + K = firet aaum = exaeg. 4, aamm = FllM = ATM, seu M = U-AM1. 4a
et K = HI - l: 4a : ob mK=0 finc ag F t ab R, an - staq = Flac - ag, an +5sab
aaato  ah ag+gh tiab = agstac = est rbc = AA tac = ab ag + latsHbC = a95 tab, seu fiet
raahus + o e - 2 a5t sbc + abt ( ab - fac) + ag5 sect in hacaequ. absunt f et Y
superest iaquatio l - BA = Qam et explicanto
tist at Cant aberta entatis audn  abslac A aerq sab, at e+ tab, phaeda
Merva, Caass t abrr + rafritab) (actin + assc = 2ah5 saC) =(aaff dac rY Lasr Lac) Caana + ab 5s L 2 ans bab)  id
1ra, ad + lab, ab +., aalil + asse m 2als vac
phas dibri8 pen o qu Hop lidi. sit
Ar YY L ASt et ex ex 5et 6, tollendo t, sieb fX = 2k(rY: 45) F295 seubs rsrs- tirr, 2gB
sud hactenus calgulam non intrant b et e
et quia puanescit
quod non licet
Itaque n lo
u habereda
nem