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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 201r, page id 00068195:0401
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3XX + aq =0 et in aequatione x raqu +aar =o substituendo valorem ipsius
X inventum sut S- La4 fiet aqV. aq  aq . aq  + aar =0
seu 341-Ea9 + ar =0 seu aj Hinc si aq est quantitas affirmativa
limes est impossibilis, omnesque adeo radices sunt possibiles. Sed si sit aq quantitas
negativa = =ap siet - 2DY ap + ar =0 seu p 27 p =  rr
qui elites radicu ei possibeleam itaque arY - 2, p3 = 0 est lines
possibilium q radicum binarum, ut aliu dudum constat
Sit aequatio X x apKX + aeqX + ar = 0 multi plicando per 0, 1,2, 3, 4, frit
2a pXX + 3 aa qX + 4 aY ~  vel 3X+ ap  + aaq 3X t 2apX _ + aaq = 0
Harum prio trium aequationum priga multiplicetur per e, secunda W0XX + YX + 1
tertia per 22X + 23 addendoque in hinum duas primae posteriores ce primae aequa
ix secunda--3a+ 4aar,. E
iud
diet
eX+ X +CapXX + CaaGX + Car
 identificanda cum
102a pX + 103acIX10. 4ar +
+IaBX7 + II. 3augX = 4 11. 4aY X
+ 122 ap XX + 12. 3aagX +12. 4 eY
2d3X+ hap  22. 2a p +22 aagr
1. 3X3 +23 2 123mq
23. 2a pX + 23xa9
+23137
ex htia -  - X3 = 2a pX + aaq, : 3
fiet XX = +4 pp X + 2ap9, : 39
1 aV X
= = Z agx - 2aaY
seu X = +2ap : (4 ar.
seu Y U 4 appqi traarq,i 2 arp Bp9ag9
X
F2aa2
ha
l 3ag
quem valorem ipsins X sub itnendo in aequ. 2P∞X +367X + 4aar - 0.
habebitur aequato dans liniitem. videamus
Examinatu operae pretium foret, an haec liminum investigsatio non servial
ad radices irrationales aequationum inveniendas. In secundo certe
et tertio gradu manifeste id contingit videndum et in quarto, qui
et ipse jam dudum in potestate est