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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 34
# Folio 4r, page id 00068247:0007
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resumi poster modo pro 11 preramus 1β, me fiet d. g. EA Z
si sit polestas: V
suot
CZC2, b
D2 Z. P2 Z.v er
12, 3.
possumus Z, resolverae in quolcunque B intlo se aequales,  vel in
imperos, vel in alias quantitates ralunats vel supias, vel finelas, ut si Z sit 2, C seu y est. id
quatratue
porendo y  X+ V binomiu hoc aalice in se multiplicatu eut, etiamsi non scrbatur. Vx7 
n quadratum
sed v. g. pro1. compn sumatur  Bunde binomira erit compositum ex quatuor terminis, nempe
fiui: y 1X +X 6  qxt une faile antelligi potest, endemmdo etiam
binomia explicari posse er binomia, potestatem cujus exponens est irationalis, vig. 12. dividendo ea
in partes quodcunque aequales. Horum omnium venitas tum numeris ti calculo explicari debet. Prioris
et calculo et in numeris, posterioris non nisi in numeris. Notandm vero hanc formulam in qua
exponens fractus, semiper reduci posse ad formulam exponentium integiorum, ope aequationis: sed si epporentes
sut irrationales non videre me modum reducendi ad ordinarios ulcunque formetur aequatio.
Illud tantum siperest exentiendum, an aliqua raoe sive arte possint ipse B. esse maquales,
ut scilicet necesse non sit exponentes cresiere vel decrescere aequaliter. Caeterum vatar ipsius y, ita more
communi expressus, daret: 2 X + 2 x X) + 2) X + 2 V2 1X)
VH LX + 2FXY + 37 X + 2SV3X + L Y. Quod facile in numeris experici
licebit, modo X et V intelligantur esse numeri quadrati, nempe sit X ⊓ 9. et Y  4, fiet:
19
69
V e X + _Y. A 9 + 4. p 13 jam 13 13⊓
+X ∞ a XSXY + 1YX + 2YNX, + 
unde
169 Ee +29 136p 108 + 108 + ~ 46, 48 + 8 Sed hic calculus non consenit
V
Idenque rei investigandae causa scribamus: bX + cX IXY + dVX + 27 SX + f)
dicll
aX + a7 X +4 et gumoris inunum irrationalibus caeterisque ordinatis:
=CX IXY. et quadrando,
+b XD(+ dY Xps f,
B h -a 1 l-2a.. l - a..
B X  + 2 BDV X V + 2BF XV +D
..
+ D2
+2DF
 -2Ce ....
= e
X)
+
jam ponatio
2y
ABF. b⊓ f. adeoque B, F. it item C e. quod ex
iteu, ipsa calculi natura pendet, cum enimi X et 7. sint in definita
altera pro altera sumi potest, neque ulla diversitatis ratio intelligi potest, cum non nisi
situ sive ordine varient, idem enim est X+V. et V+ X. qvare et quadrata
ta eorum eadem. aequatio ergo per V hoi F divisa, ponendo et
pro  F ponendo B, et pro e ponendo c. fiet ita stabit
B X + 2BD XY + aB XY
e
+ 2BD X73 + B ) 4
Jam haec aequatio cum alia simili ejusdem valoris conferatur scilicet:
X + 2AX) +
Xy
productum ducatur in B, fiet
12
BX = +16(X)
+ BX
ducatur in X + hX) + y. fier:
+Bh ... - + 2 B2.. .. + 6hX) 4
= B2
Hunc formulam priori et similem tantum sed et coincidentem esse intelliui potest, si fingamus
non + B  + 26....
formulam b X + C X 1XY ex esse aequationem duatum tadicum aequalium potius, quam formulam
quadrati binomii unde suffecerit eam potius aequalem poni nihilo quam aulteri ax 
adeoque pmissa c a. ponemus B et b, vel D vel d et F vel f. aequale. Aequationes ergo
+
tntur dine, unas per  D B alla 2Da + Bh = ea. adeque
H
6a
collatit
e uac
penonum asterm ban coterie pet. ustes eAeeapto.
= 2at
i