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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 241v, page id 00068201:0482
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ed
satus erit ret dem nlegro ordiri, epe e quasi de meo quarere
ope collationum: Esto 2240 + 16001 cujus quaeritur radiu Cubica
quaeratur primnum, an a radix ejus esse possit binomtum, cu rationale, cum ipsa urationali 
esto illud binomium. d + er - 12. cujus cubus: d3 +3de - 12 436d e + e 1- 1728
namfestimest confeundum hoc factitium eum dato; haberi solutionem.
va5
Generaliter: ad + e tab, multiplicatum cubice dat: ad3 +Bad C ab + 3adeab + etab
sive ad + 3ade Vab + 3adeab + Cz ab t ab. sive + a d + 3ae sab
p
+ 3ad eb + ac b
Nam radix ex ab est + ab. ) Hoc productum conferamus cum data quantitate binomia
Hoc confera ex rationali etradice quadrata composita at +m an necesse est
esse  b  incognitam pn. datae, itemque +3a de
+a cH H ma ac denique ad’thadem
aequari ael. Ex ag  erit multiplicata per d, erit d dmaden itemque
C.
3ge
exaeq O d. a1 l- 39deM, Ergo  a el - 3 dn e  dma
3du
d mao + aetid et ex aeque  fit. de  a ade
3are
Ergo maed fde d +9 aden  a el. Aa rectius facilisque sic ex aeu atione
 habebimus vatorem ipsius d, qui est d mat taen inserendo in aequatione C fiest:
enque d ale snmae  aetuy
dma idae tnmat aen at a e
o
19n
ma + a en
ma frma’en +aen
quem valorem conferendo cum superiore ipsius d xatore, patet fieri
cubum ma  aen,  multiplicatum per a aequalem quadrato ab
a ate-In mau
extrahi possit sive multo magis si ex quadrato extrahi potest cubica dinensones
deprimentur). Vderu compendiit opus essante collationem, ne ad calculus Bam
probixos assurgamus, et primum quadrabimus ubrumque e nominibus cubi factitu
fiet. dd gad Sed rans video errorem calculi a me commissum ponfendo
alicubi a pro d. Resuntis ergrs collationibus aequatia f D fiet: 3adetqena
et aequati Ofier: a d + 3den p al, Mutticlicando D per d, fiet:
a d  mad + aend ve ad mad+ e nd, quem nalorem inserendo inaeq. 0
3at
c= 3a
fer: mad + end +3d eat haden al
amad + end +gaden ppatl
1 t
et du
3al
 nmae f en 9a en
at dem dps, na 3 + deBquarum duarum aequ atdonum collatione
3ate
invendi t et ipssa de. sed num ond commpendum accedereote:
depermaquadnlim ade + 6 d cb + 9a26
ad
= gaed eb +6ad E2b de582
in et
cubica 3
cujus radix(+) a (V 4B
eba
E quod aequabitura-madn
see multigeratis omnibus perde
riliater () ms d) (+)a 3t (+) raden et tus (+ ad (4) daen e (3)..
ejas is
d-
 ergo prd 4)a de substituendo e batorem (+) a i(o)) haden  fiet:
dad
d
a (7) aden d (3) i Ergo pest) daen, substituendo ejus
valorem (4) a l (+) ad  ex aequatione O. fier:
() a d (+) ael p7 3d 5(3). . p. sive  C4) at
in  X 1  B ab ain  d _r a po  Aliuneoi
A
tiletu cerim e pori e
1
ma en ac
t
ha
oetgien
binonisi factiti,
et expricando F per
oe