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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 366, page id 175905688X:0388
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=388
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
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866
TAPPENDLX DE CUBLCARUM
HIOc eA, ordinara aequatione, habebitur x x ∞y N L 3 a a. IInde
g
extracta radice, tEv D ) 8 V 3 a a- 27y. Ilinc, sin aequatione
oliminvencaxs xt F aar F a ab in locum a substicuacur valor
it
de
inventus LY 8 V 3aa =y7, et in locum x ejus cubus, qui est
E aag=y38 3 a d V. 3 a a  2yY, obcinebimus aequationem
V3∞ F. F3 aaya ab. Cujus ideo veraradix crit linea A.
Lodem modo ad inreniendam LC, si pro ca PonamuS Z, atque
ab ipla tollamus IC ∞ = X, remanebit F L ∞Z i x. CInde cum
quadratuum ejus sI
Lx Z t  x x: eric icidem Z _ Z H L x b
∞ 3a a = = X v. FlOc eA, ordinata aequatione, habebitur
XX D Z N 3 aa. FEFu, extracta radic e N ∞ L 8 V 3 a a
2Z
Isinc Pirurlus in aequatione olim inventa a3 ∞ X. L3 a a x F  ab
in locum x Tubrogetur ralor inventus  Z 8 V 3aa = = 22 et ip
locum x3 ejus CubuS = 4 4Z
a L L obcinebi.
muS aquatIOnEI Z.D FPadZ aab. CujuS IdCO VeraFaCI
estlinca FC.
Ex quibus colligitur, (i aequacio propolica fuerit xi∞ F L3aax
aab, eandem duas admitrere veras radices, quarum minor A P ob.
cinetur, s ex ALvet IC dimicia base primitrianguli AB C, au
feratur recta FI, cujus quadratum lic xe quale eriplo quadrato ejus-
dem alcitudinis BI; de major, si ad AI vel IC ipla FPaddatur.
Ommino ut tuic propolicum.
Ubiporro adverrendum, quod, in eadem aequatione x3 ∞ + F
aax-a ab, ob mutuam radicum a quarionis hujus certiae ac le-
cundae Formula reciprocationem, tertia radix (Ic Falla, quae per
AC. balinprimi crianguli AB C, delignatur, quae que iplis peris
AF, FC limul Cumpris eA aequalis. Pc contra li ae quatio fuerit
∞3 3 F- 13 a a x- F a a b, quod praeter VeraM, quae per A C extii-
betur, alia duxe extene talla, quarum minor est A F, de majorFC,
quae limilicer sunul Cumpex iphi verae A C Cunt aequales.
Denique quoniam omnesliles _quationes ad xquationeM
polteriorisProblemaris rerocari queunt, pocerimus quoque pron
ine peutras POlIEX XQuacionIS ∞3 ∞ 2700X  32400 ralores radicis x sc ex
BaS. 362. PIimere; Dicences e0s per diamerrum circuli A I; designari, in
re 363. Quo li inscribancur tres, rectae, linex inxqualeS AB, B C et CD
1