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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 22r, page id 00068197:0043
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(X, X - b, X- C) formulam continet subvinculo, quam explicatione aliqua deprimi velim ad formulam rationalem
secundi gradas per quadratum rationale integrum multiplicatam et divisam feci  X. a = qu( hvaaf;, v+Y) sed
hoc non successit. Ergo faciam X: a = qu (hob + alvt aaque,:, suv + arv taar
Fiot X = B = aqu (hvorer) -  qu ( 50v + ete) et X - C = aqu (hvy + etC) = C qu (svo+ etC)
a qu (SWvk.)
a qu (svot etC.)
fine
Unde a X- b, qu (SuVtet.) = ach vv tetC) + Nab (suvretC), in aChov tetC) - tasov + etC)
Et iXub, qu (suotet
aahn b55
Aperi
jute
a, X- C, qu ssuv tete)
aa, atih - c3t
vD + naftar ab V + a3q.t aat iab
ah +5uab
ah + stab
seu compende D = vo Alo ram, 
D = votpetaque
9 = BBAHPtAK
in vy aasartabx agnaatitab - 67
ah- stab ahastab
5= vot potaque
v1 + qut tariaev + a + aat sac in Wv + aaf-a )ac ∞ aeg- aatiae Z
an+sipo  ah +sval
sen comprndio S = Wp + ABtap
d = vv alv+am
C = ve+ NvtaB
ab - 5aC at -sdac
Nomprndio Cx = vv + v + at
2
= e+ L( - Y( l = am), in, vt = l+ + (Z l - am) = 5uq hic pat
= v+ ZLN(ZH-au), in, v+ = 1+ Y(Z AA - an) = BI Hac
= v + = p- d (app - aG), in, v + = p + (C pp - a9) = GB auut
= vA LH - s (LAM-aX) y in v+ L e + A (LAH. aK) = 30 dac
Opus est OSD8 constans ex octo radicibus sV, 2, 3, 7, h, I, d, D, habere s cegales
ita pt tormnta secundi grabus m tres tribus aliis aequales, remanentibus dunbus tantum
radicibus nullam  aequalem habentibus. Ita OF  non continebit sub vinculo
nisi formulam secundi gradus secundum V. Hoc ut quam commodissime efficiamus, tentemus, an
liceat facere 6 et D quadratos, seu B =  et h = 1 et se = S
Ut S sit quadratus seu ut sit Z = F fiet  AA ∞a =0 seu AA = 4 am, ex explicando
fiet seu aaff Nrac F afrrac ipahag tastC tg ah t sac +4495 tac
Rursus ut D sit quadratus seu ut sit h= D fiet pp = aq seu PP = Aaq et explicando
fiet. aaff F er ab - 2afr dac ( )et ahagrt astb - tant lab- 4 ag5 tab
quod si ab aequatione 2 subtea hamus aequationem 1, fiet
+aass + rrab - 2afr 1ao = 4 ahag - 4 astb + Aaht vab + 4 agd Vab =0
=aaf - rrac - 2a fr Vac + gahague +4atC + gaht tac + 4ag5 sac
quae aequatione divisa per sab + hac, firt (XY - gCt) (Tab - tac) - 2a fY + 4aht + 4ag5 β3( = 0
Rursi si addamus inviaem aequs  t et 2 2 et 1. fiet
Iqo col ninus
2aaff gaagh, + (rr - 49t) (ab + ac) +Casr  galib + (afr. + Aaht. + 4ag5) (Y ab -) Vac) = ) - 0
fas aeque. 3 et 4 ad usum commodiores puto quam 1 et 2,
superet
la
rexpentus
1
aqu.
u redisset, si sunsibuns 
 fiet =l-H=l -am) = ZH + IGWI = aK) reprri non licere fatere l =H, nec m = K
quanquam Rorum unum ex altero sequitur, positis scilicet prioribus B = et h= 1. Tentabo
rta
6)
tamen compendium tale, ut fiat =l = S(Z HH - aK) et LI = - M(Zl- am). Unde
Zl = =AH = aK, seu L(H NH) NH - l) = aK et ex posteriore L (HB - U) = - atm
Ergo fiat ak = = am seu m rHC = D K = - M sive K + m = 0. porro
ob   m +K = 0 fiet ag+ t sab, an - sNac t (ag - F sac, ah + 5ta b) ande
siat ags tac, (at bC) = (ag ato + 295 Jab = ast Hb seu
ese aC
 abtrac
e +ant tab
seu agat = ags sac + ahtrab = ast ibc + agah + ag5 tab - altilac- astibe -0
aht (xab + sac) ag5 (tub t dac)  t B
seu raagh + (ag5. + aht) (+ab - tac) - 2 a5t Ibc =  (5) = 0, a qua
aequatione ab sunt Y et f, et res reducitur ad duos valores sitr et t:9, quorum rationum una
per alteram habetur. Superest ad huc explicanda aequatio YH H am l- HN = 4am
seu (a taarrab + 2a frsab, aahih + Spac - 2ah5 sac) (a Hf tuarra c - 2a r Lac, aol h. 4 5sab + 2ahs dlab)
=Ab 4, ag Laat sab, an + susab, aath + scac - 2ahs tac, qua aequatio evoluta ex 30 parsibus
constabit sed pedeo nos posse compendiose procedere, in qu tibus aequationibus quatuor, si seponamus omnes
la borduse un agu.  et 6, ntitus nb a hiber e g9. 1 et. Z, quam Z et 4
int, non possunt
habere divijores
comium
duo  () G
ut, auto reperi