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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 29v, page id 00068220:0058
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qualibet continet duas radices, seu radicum
combinationem, sunt autem e combinationes numer b
ab ac ad
ac
b
Cc
Xtx + abj 1
X +C X tqod
F ubi a + B
su Nempe a+ b vocetur y. quaerendo
terminum secundum. divisoris, ergut a + b = at C ) at d F btc f. B
aequ. 3 a ++cd aeq. 0. qui est sumnomuum s possibilium
et summa rectanguloni a + a b +3abc
+ eb
Hinc si
aequatio pro Y caret termino secundo, aequatio pro Y
carebit etiam termino secundo Ascendet autem
ad sextum gradum.
sequationum tamen quadiaticarum inter se
ducendarum ad procdelendiam aequavinem
Tatam combinationes sunt tantum tres
Quarum unas
X + a X 4 ab
 in X + C X + cd
itaque squ si ab + cd quaeramus, ascendetur ad aequationem
tertii gradus.
nam tres tantum sunt casus:
ab + cd, ac + bd, ad +bc
atque ita evitatur sextus gradus,
ad qvem ascendit Cartesius
et alii
X
+ Ix + m
X + nx +
 LXE + mX + lpX + mp
n X pX + mux
In X
Comparantoedator X + GX + Y X + S aeq. 0.
sit m + p aequ n. fiet: pagotam 4 + lX + hX + lh X +mh
ergo
Im um
+n X +n + mn
Ergo ln aeq. 0. siu naegu - l. et I aequ h - 9.
et Ih m - 2lm rqu. Y. seu H aeqo Nr. aequ. h- 9
seu rr aequ ht (4hm + 4 mm
h- 9
(4mh as
th - +lm + amm
Ergo rr + 4hs - 495 - h + ghh aequ. 0.
pa
uimu
seu h3- ghh -4) h + 495. aequ. 0. Unde habetur h
cubice
est autem mm hM +  tit aequ = tih - s seu M aequ.  h + S+th -5
et P aequ =h -  hh -s et l aeq. dhtiq  seu Y
et naeqo Y
+Sitih - 5
h- 2m
-