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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
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de incognitis tollendis per aequationum
exaltationem, confer ehediasina ejusdem
diei (de seriebus infinitis pro aequationem possibili
et diversis ejus ra variis radicibus, aequationis
cujuscunque. Hic denique modus habetur
inveniendi radices irlationales, cujus successudemonstra
mulsus: 
cytam
lodus tollendi incognitas hic incidit generalissimus
à me
Eme
quo
res omnis reducitur ad problema jam resolutum totlendu nempe
incognitas ex aequationibus simplicibus.
it aequatio, quaecunque aeqo. a +b X t E +dXE + ....
O aequ a Hy + CX + d y + Cx + fxy erc.
Etrursus 0 aequ. l +my +nX + py +9X + Y Xy
et
Muetiplicetur prior aequatio primum per 10+ 1X + (11) y
deide per 20 + 21 X +61y + 22 X + (22) y + 29Xy etc.
tertio per 30 + 31 X + (317y + 32 X + (y 2) est +22) Xy + 37X
+ B3) yr + 33) Y
primum per: + 2X + 3Y
deinde per B+ 4X +5y + 6X + 7 Y + 8 Xy.
certio
per 9+ 10 X + 1y + 12 X + 13y2 + 14Xy + 15 X + 16 y + 17Xy
+18 Xy2.  quarto per 19+20 X + 21y+ 22X + 137
+2+ xy + 25 X + 2673+ 27Xy + 28 xY + 29, X + 307t +31
Xy + 32 Xy + 34 Xy.
Et prodibunt quatuor
Eodem aequationes novae. Eodem modo multiplicetur
per similes quatuor formutas aequatio posserior
nam quia unam quamque incognitam verbi
gratia X necesse est habere radices quatuor
nam duas habet per priorem aequationem et
duas per posteriorem, quae in se invicem ducendae sunt.
jam 2 in 2. dat quatuor. sicuna aequatio f assurr exisset
incognita aliqua ad unam cadicer tres radices in altera
ad duas videtur in universum aequatio secundum istam
ultimata secundum istam incognitam habitura sex
radices, sed hoc demonstrandum esset accuratius
Vera demonstratio petenda ex ipso (humero terminoru
multiplicando prodeuntium. Nimirum si Nimorum
salis le formata seu ex ipsa methodo nunc expo
nenda qua patebit quousque multiplicando procedi
Sufficiat. Nimirum si multiplices duas aequatione datas
santum per formulus primi gradus hhabebis duas arbitrarias
2 et 3 Docto decim, scilicet co. 2. 3. β. 4. 5, 6. 7. 8.
et tolidem alias quatuodiem aequationem multiplicandam
vel potius seda omissis duabus: a et β. et totidem
aliis similibus. itaque in aequatione ex earum summa
proveniente satis arbitrariarum est ad tollendos
terminos: y. y. Xy. B. Xy. xy. yt Xyt. Xy. X3y
imo forte et ad tollendos aliquos apsius X. sed de
hac dubito, vreler emi igsus it vater. esestano
30 jar. 1679.