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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 30
# Folio 113r, page id 00068124:0225
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 78 lines, status machine
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et
-
1
dd nn + ddesum  . eem + recp ima
aa qu 244 tima
aaY +2ab smn
videandum an gab possit esse quadratus et ytc simetiter
quonn  addmn + raddp sina
bee..
y+b = a3 49
2aad9
similiter y+C pro b ponendo c
Ebeex eemu +2 eemu
2abdr
aa rr raor snn
vel
ut g+b, yrc sit quadratus, oportet, ut vel singuli sint quadrati seu facti
ex quadratis in communem divisorem. ut sit  42 eep radr = Ead B9)
et per hoc dividi possit tam adomn + agu quam eemn+ag ut
ita enim eadem modo procedet divisio pro y+ c.. Sed praestat
singula quadrato aequari cujus lutus fsmu + W, fretus
 quadratur Ejus smn +2ffpsmn. aequando inneulori valoris ytb.
narow, 2at...
fietus addssabee H  ad d. bee- ass sunt aequationes 5. Et similiter pro
De sunt 5. Ergus 10 literae autem sunt bina in m, n,  q Y, 10 ed sonto tamen
unde videtur sufficientes cum sint 12. sed puto ad huc paciciores sufficere
Nam tolleido b, fietb simn  aaroro addum aequ:, beemat aurr
= 25fp + rafo- raddp- raadque: vec p+ radr
 sed ne opus est quidem long carculo semper duplicalo. inveniantu
2d et Y, literae lalentes in bi a alitera( et harum valore substituto, supererit
collatur b, ex agque. reliquis et quae superepunt agq. erunt coes. sed
Cum non nisi una supersit non est operae pretium  Quiequid sit calculus
non pt esse admodu difficilis literae in W, simpliciter inveniuntur per duas
aequationes, ita restant solum tres aequ. ubi incognitae assurgunt ad quadratum
et cum adsint super numeraria, vdebur calculus esse in pte. sit 10 = (10) X+ ()
fiet (W) - add (p) +aa d (4) + sebee () + abd (Y) = Eaf(p):, aa f m = (m) X + (n
et (20) = adq p) + aa d (9)) + b ee (BB + abd () = a ff(pH,:a
+add im2) +bec () (1) + a (49) + aa b (rr) =  aa (W (io 10), ob  X
aff..  et + add ((m) (n) + b a (99)) + aab (rr) = aa (V 1)) ob X
+bed
et ita in
caeteris
ubi (10)
et sed)
et (m) et
(n) et
beses
et + a ddz (m) enH + 2a (9) (9V + 2 aab (Y) (rV = 2a a (W) (W)) ob X sunt osta
te
+b ee (((m) (n)
=aff so
Habemus ergo quinque aequationes quibus est opus
Tollamus (20) et (Cad D e aeq. 3 et 4, S, Restent tres
tib aquationes quarum ope si invenientur halebuntur valores ipsarum ()
et ipsarum Cmn et ipsarum (M) (2), cumque eadem adhuc semet lnveniantur per c
pas aequando hos valores, sublatae erunt (m) et n), et restabunt tres aequationes
etti 00 = 37. 98 pro coefficientibus, 9). (1), 1) (Y) et dieis
non tamen statim id apparet
in D +8 et in D.
in
dOtb 2=
60= 49 -b3)
Empfuto  + D N
f-
seu Dd- 8Y sit extrahibtis
irrationalibus, esto edtim
D= fab + V sab +aa
= Irao= aq
(fit 3D- 77 = HabRaa 
ubi min p, q, r vanabiles
semplices
a
Eaa. seu B- aV2.
lam tamen nec D nec e sit
ratimalis nec D+ 8 vel
D.8. itaque prastari
possunt aliqua
ab + an