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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 170v, page id 00068194:0340
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=340
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a + b XX an hiqque datur summa ? ar+ a fx +b~ XX + f. x aequanda
Y +sx.
quadrato, fiet: XX coco + 2XC0 aSr + aer 1 ergo
aef + b=X + fXX aeqo X coco +2eo a s+ sed nihib hinc
Et X equ l ainque
a +b X + CXX + dX aeqe. quadrato ab a nz + n Z + p Z + 47, crc
fiet: a + bl +m Z +bn ZZ +bp Z + ly  + br Z3 + b5 Z etc
sit
c. +2Clm c luzz + rclps + 2cl9 23 tdr 2 tvels Z
temm Et remnZ 2 Cp Z denq t Cmr Z + demsZ
sit formula a + bx + CXX + dX aequanda quadrato fiat X aequ l+ m Y +nVI
eut XX aequ. U+ 2lmv + ilnvV
+ mnon +2mno + nu v
et X aequ. 1 + 3Ulv + Elln vv
et fier
a aequ a
+ 3lum on + 6lmu v + 3lnev
bx aego bl + b m. B + bn vV
exx aequ ol+ rdm V +2C vV
+ m v + 3mn v + 3mn v + n3 p
+emmon + hemae + cnnv
Ax aego dl + 3dulv+ vallavr 
=3d lmm. Br + 6d lun v + 3d lni B
paantroo+se
ptapque pron-
pptrpquEpront ipso
44 vn + 29rv2 + 245V
+dn v3 L dnia v + 3dma ri + dn v
agu quadrno pp Epgo prim psv 2gut ErsV SV
arr+sVs
Habemus aequationes comparatitias septem sedetiam sumt septem litere
qquo 2qre te
pro comparaivne. Sed  possumus obtinere literam ad sus unam si efficiamus
ut in ipsa a+ bx + CXX + dx sit uia arbitraria, quod faule est: Imo imulit
quia jam sumis in priore explicatione latet
fet ee +ref +ss aequ. hh.
debet factum eom horum duorum esse quadratus, ut
 e+ f aequ h
1+m +2 Stem. nAp . 2
t_ l + Sa pp- 11.
in 1 - Spp - 11 dabit pp. unde fet: H+ pp - H + 2l Spp - U + 2 pp +  pp. 11
fiet denique 4pp. Ergo Sl+ spp = II + St - spp. 11 aequ 2 p.
SX + bX4 CXX + dX + C + X + b XHCXX + d X + e
= X1+ 2X q+ 2X
x +S+t X+rA XD+ SXx = pt + q+ +r X- X ago 2 Sp q er 
Sa +bic + cxx +
e
aequ. V. fiet; a +bX + CXX + 2l+ l, aequ vn
a +bXL CXX
Sa+ bx+C seu (B a +bX LCXX + El a + bXL EKX + ll aequ V
An sic.  _ - spp - 11 + m squ v. a + b X + CXX
2p + m  aequ v.
S1 - spp. 11
N1- opp. 11
Saatere,  aequ Su+aata +
aatex
vago 2 S aarbxr san x
aa +CXX
fer