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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 7
# Folio 16v, page id 00068220:0032
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X F X + ax nb. aeq. 0. scubatur  H 2 XX +1 X + 2iErqu. a et XX X) aeq. 0.
quae in se invicem duendo fit: X tux 
224 3t aequ b +1a +7
+X + ast b
X1+ axD bX
+IX L 1X + 1b X
+2X +2ax + 2b
In X + ax + b omnuum prima non procedit, nec opus est, quia
non possunt sumi radi aequationes
vent ergo in pentem data aequatione X+ Bx + Cx + dXrexisa
eam mulliplicare per 
e
Bcx tatgiX +2. 32
ergo conferendo crit: 2 aequ a+ 2132 aqu 1b +2
t eXt
+1X + 2X3 et. 0g.. 0. Et productum
19
et comparare ex foccto, quatr harum aequationum.
quinque
XI +2 X+ (25X + 24 aquo N+ uX X +~x + 34 aequ. 0.
atcXZ4de 11
X X+ 22X + h3X + 2400 X + 3IX + 32X + 35X+34 ag. 0
X4 1∞ 3+ 42X + 43X +49090 X5I X2∞5L∞Y3X +54 0y. 0.
is
medios terminos abesse volo, ut pro quaeriendis literis. .21. 41. 41. 51
s. 22. 3244152 et 2 23. 33.43. 53.
et . 3. 44. 54
e tancum opus sit aequationibus ssi, gradus. prosolis autem aesatione
rinvemendis novissimis seu teltimis Terminis. 24. 34. 44. 54. 64
ropus erit aequatione gradus Eti,quam
ita moderari licebit
ut summae horum, et summae rectantulorum, e sumtma.
ernionum, et summae quat ergionum frunt aequales ni
ponantur nihilo. et super sit sola summa quinionum
tilujus quae aequabitur ipsi curdesolide de 64 Hab ita
autem una harum 5, facile habentur reliquae ex
hoc ipso quod posuimus. Sugumam et summam binion
et summam ternionum et summon qualernionum nihilo
aequalem, ergo taum reliquorum summa et summa binionum
vatuo
es summa ternionum let summa qualernio, habatur
dato aequalis ergo singulae habeatur per aequationem
quarti gradus. Sed necesse est ad inventione dicti
quinionis non inveniti nisi praesupposiba aliaru
rei laserarum incognitaum omnium inventione. Etiam
esle quatio producta ex quinus in se invicem multipliralis aequationibus
X Six +SuI XI8 + SII. +XC
quqe Equatuor, o3
unam trum aequationum integrarum quadinto. quad raticarum
inbenire est omnes invenire, quia  earum coefficientes
sunt radices aequationum quadato- quadraticarum nuvarum
sed ultimam seu quiutam reperisse nit prodesti; neque enim.
constat, utrum aliqua radicum moposit aequationis in ipsa
contineatur
quaestro ob mamit gensgo elevation und Tadunque von dorfose
rnabthurinsoder antee cantrrphestus toune. Uffano
mamel eatu obi. as un rogiset et riniod do
Kage mir 6 phucs rosohue lassus gbd schutt weitro in den
porte sustus Lomus. qua d Egopalo ad esse falsum
und tsne derhus veon der hohe mi
dosesd, wt geaealssamro
cenns ein bdu psust, umb sbarit disinge fosro sval salert
toribi aber inst caentro
+
pent