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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 7
# Folio 9v, page id 00068004:0018
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 10r); this page is its left half.
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qua sciticet sais nius radiris rentus)
regulis Cardani non isi quarundam aequationum Cubicarum Cresolutione
haberi exe diserte asserun. (axesi, quii etiam, summus utique vir quod
nihil magnopere resolutiont agrationum a per ir irationates radices aequationum
altiona ineniri non fera Adeo ut nec rationales earum epe, quae faciunt
imagniaris duci posse scivere.
quod nos c
formulis
ostendemque
ostendum, inde de irratio nalibus generalem dimonstrationem dabimus
sit Aequatio:
speciem
endi
Sed hoc primum de grationalibus
X3 - 13X - 12 10. per regutum Cnus rationalis
radix rationalis vera est 4. Ex regulis autem Cardam est
((3) 6+ Y - . 225 + +(3) 6 = s - 1225 quam quantitatem ostendam
27
Tirie
probo
Quod sic ostendo
sive B vel quididem essi .
 A valet  2 + Y - = sive (et B valet 2 - s - =, utique A 4 B.
sive
B A, 13B valebit 4. Assumtum probo, si cubus a 2 + f  ralet A sive
sive
sive
D sue a
64 f- 1225. n et si cubus a 2 - t Z valit B sive 6 - Y-
utique C 24 +- salebit A, et 2 tu valebit B.
si Ce A. et B D B.
si
-3, 73.. H -2
1CL
+24.
+24 1
+  - 1225
Eadem modo sacite ostendetur
cubum a 2 1 -  dare 6- 1- 1225
27
Ducatur Cmi scipsum
Cubice: C vel 2+ s - = in se ipsum cubice, fier. 6 + s-
+8X
+6
i7
22+
227
Olalo haec ens.
d
per
Y-
- 
27
vel
Sive
AIBLIDTHEBH quae Rursus
RELck
HABIAODENana
semili calculo ostendetum
rationalis
Ilem si radix sit falsa, ut in aequatione
dab
vel
sive
aut
cujus rudix X +6 X p, - 6, id est ex Cardanica
Cardanicam, vatere
led 5582
+  - 1225
36 X - +BX -72 (0
ostendetur formulam
1(3) 36 + 1 - 2900 + 13) 36 - 1 - 2800 valere, - 6
sumendo X esse - 3 + f- 7 - 3 - s - 7
1-2
 +9
5-2
23  3 3