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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 62r, page id 00068197:0123
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lx ratur taane a
 t
X+ b = al sorm, vin, vrp)  (vAY, vit, utiot
q vfrivet, vtu
, ic, tld
sint m et  aequales, item Y et I aequales, praeterea fiat X +b aequalis quadrato, et xtc aequalis quadrato
seu al, v +2aV+ rum vmmH) V + munt
pt 2m en H) 2mnt
q va  ri vr fyrbuv + mtt
sietque
at
ErrF
sit (N + sutag) +  (vo F r Art)
aequ.
 a qu v+ m). (Btnor
sit etiam ven, vet  = d 
qux+ fv+ ag)-v ratyp aagu
= quadato Ah, qu ( uvris tl x )
substituto C, loco b, pro C ponatur , et pro D poratur Q
at
hsversvras) - (ovrrvert) = O, D
C quadicatus seu
sit vva 2mvrrum ~ ve + hf Xe B) ibq asteritibus
h+ Nba
hribus
fit hf. + + 1) ibq : 2erb9) = m
et aghart 1b4 - mm =  qu (hsrltet) ibq
seu c4
h+ibq
h+ Ybg
ahrtu, h + Ibu = qu (hf +(Y+B) Nbq
Hinc habemus m, et g
possunus facere A, B a ratione estante a. cu (Ntnt,) atriado; et B in rtione constrate ad rta, vtt, aneer ad B
itaque tentandum an possint AC:  esse niratione constnte et, D:  esse in ratione constante
quod si non licet, tentandam an 5 et e possint habere radicem communem
sed hoc provideo lien non posse nam si 6 et G dindantur per ibq, retinebun radicem cemr, Ergo
et summa earum habebit radicem communem, Ergo wetfotague, et vvrroert, habebunt
radicem coem.
Ita etiam O et 5 habebunt radicem communem; et ita radices reliquae
ipsaum D, et D, deberent aequari radicibus reliquis ipsam 8 et D, et quidem decussalum
radix ipsius (3) radici ipsius C radis ipsius 3 radiciipsias B, quod foret coprendrosissimum
loco ipsius vn +sy +ag, scubatur ut e, vek sit e+K = vtr lebet esse
debet esse sed ita fieret aterntia ex ipsis VtY, vel v et, aequalis ipsi v+ n contia hypothesin
taq redemnm ad C: Q in rationi istante et D: f in ratione constante,  seu C et G
vel prunt quadrati, et in patone constante, et 9 et  erunt in rahione costante ad ven vt
seu cv + Lf + (Y1t) 16qe + hag + rt 1bq ~ veo, hs (11A _q hag. rt ICq = quodato ib um
h + fb4
htibqs
et aubo aequandi quadrato pb. vt M
et similiter
ha Hig
ht h - scq
ex + hf rtc ibus hag- rt ib9 ~ Wup h Hrat) 1q Magt rt teq -v+ n, vat
sba
sit llt +h (rB  X  H
h=Ybg
h +Cq
h+ scq
(6+L)Gibc
hast h(raibus L hficq () qube -lisis) -hsi re cq tsitus Sisde
d
 et sit  st)  Y et divisis omnibus per hea sit tr+ L - () ob = - ( + t ah) sc
riu. sit F + t - f =d n Et  (hag  h L 1b9- rtq be) = hhaque -hrt scque (C xt q+ b0
=haq rea
tit (tet hag) (rt - a9) Ab = (a- rt) sc Et sit
 haqibe
rt = aq
sed ita e coincidunt vv + fv +ag et Wr+rn+rt ergo etiam
V+F et ven coinciverent, quod non licet.
Ilas exitus non apparet
C vem, Vin, vio
q. vir, vit, WtW
XtC = al (vim. ven, Bp)  + cq (xtr, vIL AL)
X. X +b, XtC
Vv + 2uYtrr
vo +2vt LH
inac
ax = B, ax+b = OB arte = D8, fiet OX 9D = 69- ab = D8 - ac, fiat
 = OD + ab,: () = OD tac, : D. fit ODD + ab D = O0D F aC 
ita res redit ad solutionem hum aequationis dioesanteam 1) = ZVD = ab v + acZ
sit Z2V = ZVV + coYZ = abv -a a3 + cov7 et
et - ZVV = - acZ+ covZ seu - xV = actcoV seu
fit 7Z +eoZ 1, c 7 = 8-  c + Y(ab + L Eg
fial. ZZV + CoYZ = ab v, seu 27+ coZ = ab
quo+ ov = ac
et V = - 2 10 + 1C ac + 4 0c0)
Ergo efficiendum esset ut simul coe + 4ac, et coco + 4 ab essent quadratu
posset ut ex aequ. s fieri
ZV = bp = cZ et
et sit bez - be -7y = a Z = ceez
-v = a DC fiet Y = 7- aa - cze:4
abi tollendo Z, omna ficient detenutm b-3
Vitendum an haic aequatio non possit 27V _ - ZrV = ab v - ac non possit reddi rationalis
explicando Z et Y, sed de eo peculiari plagula, ubi pro Q est C, pro V est