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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 18
# Folio 6v, page id 00068231:0012
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ut radices Cardanicae reduci possent ad unicam radicis (ubilae.
extractionem, ita et videtur idem feri posse in al horibus
verbi gratia, ponatur eadix sundesolida  esse
Xaeqo SC+ Im + Sa + Sp et haberi es per ilquom
ponamus dan aequationem (E + .. 13+. l +.. l4+ P inveisa
methodo exaltationis reducatur reducatur ad hanc
1425
e
q
l
3
et habebitur H. seu
12:5
ta l
1is
1055
+.
aeg. 0 qu
1.t per quadinto quadraticam, qua
semel habita habebitur m
cubicam et ata porro.
4
 seu im ex data
1.
per
videndum an regulae extunhendi in dices ex tinomis
quae extant apud schoteminm meis artibus ad trinomia
et C. promoveripossint adhibita incacabula continatoria
follente irrationales nam et ibi jam initium de differen
tia quadratorum, aquae sit ex ta + Sb in ish- 2(C
ut producto tollatur irationalitas ) ad hibetu
Elegans obscinitio proiivenendis compandtose simul et exacte
femalis aequationib, prationalitate iarentibur. sit Xaeqo lamenap.
et ponantur viq. estae tm. n. p esse sindesolidae radices Tollatur pringumt altollatur
ad 15 ponendo aeg. X mahiap. e quia in C0 et valore eant X+ N p. seubatu
ego his compendiose  b strmando semper P sinde solido liberatum, extra compen
ium. Inde productum adinando secundum M, et aequationem ubi est m
ek. puitus onia surdesolidata cnceptis illis ec
plo pis geaitonamus in copendio. Et aequatio
attollendo ed  m
e
novam duinando secundum eus prodibit iterum R. n M, R. n
in quibus est p
unde itrum mulliplicendo attolletur ad neo re ea. quam plodu
parsu comperdio scribamus pervalis metus extracomnen dium ipli
1
se
. Et ordinemq tam secundum
4. p p. P. n, quod nobissima
e
u
 p.  P
plicatione attot ulq ad p
omnes irrationales, et quia semifer ex
t
prodibit
 multi
 ita sublatae erunt
 se
extra