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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 128r, page id 00068201:0255
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Sit aequilio cubica data:
+ PY + aqY + ar 7
b.. 2ac. + aed2
+ pV +aqV tary
Multiplicanda per aliam cubicam ardinacio
et exaltabitur ad quadrato lubicam:
+ b y + bp .n +baqu. + bar
4acu. +acpi. + acaqu.. + acaer Y
tad.. +adp. +adaq. +a dar
(+
ubi primum calculi facilioris causa intererit fieri pF FI c.
et aequatio  ita stabit: y X aqy  aer Y7 acqqγ + acaer y + a dar F
ac... ad..
+à daq.
Jam excitetur aequatio cubica alia ex tribus aequationibus quadraticis sive planis.
tam sive ex quadrato quadratica ex duabus planis excitata, et plana.
jum quadrato quadratica ex duatus plunis exscitata, Y + E taf Y ag) rah
ex duabus planis excitata intelligetur, si modo ponamus esse
nei.
1g  cg l
atque ita quantitates
 = fl + egl - g’a
+ 4 a l + C - 4 af
ex calculo Huddenii,
pag. 495  eti
e. f. 9. l. manebunt arbitrariae Compendis
s0
2
autem causa quantitate n utamum, donec ejus valorem explia substituere
per
necesse sit, et multiplicabimus quantitatem 7. per hanc planam
t
CV + am  + en 1 0 Nempe
4 + e V + af V rag Y + ah n
y M y. Fam 110
y+ e y + af VY +aegV + ahY
AM . . Haf. 1 ag + a hY
nan +am un tamem namat. tamug. +amah
40
10
Ubi ut appareat primum quid ex calculo faciliore oriatur, ponumus  similiter.
(11)
etop et supraib. vel  et fiet loco aequationis 10. hatebimus hanc:
Y X1af V taeg y +ah y tamaque) + amh o.
tam
tamf
quamaequationem comparemus cum aequatione b. ope arbitrariarum
C. d. m. f. g. l. quae sunt numero 6. aequationes autem colla-
titiae tantum 5.  ipsas autem f. g. l. in novissimum locum differemus.
ac primum ex collatis terminis tertiis, erit 4c
(i f + im - g.
64)
ex terminis quartis erit: d g - r. ex terminisquintis; f9 + mg - 9 at + nf. et
erit m  an = f9 + q () ah + q erit ergo CF at + f ex junctis 12. et 15
9-f.
s
sugceis denique terminis Restant collatitiae aequationes duae, per quas dr  nih ex
ultimis sive d gr- r 
19)
sive aur + fY,  (+99 - rq  0) ahd ( 49), sive 5. 4, Y (21) H (7) 1- f, , -9a
9 f
et ex 18, fiet: 9 - r, Y, q- f(23,
(24
an 44, q. f s h et ex 21
s
ag- ar
ag -a
15, 4a exs.
128
 a bo X 1a. 4 519 soc C) Fs Hateu, ergo hos vluges peros istus h. ex mibus saciendae aequa.
q
ah, +94. f a, ger