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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
# Folio 31r, page id 00068241:0061
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Jra Methodus Universalis literas aut earum
potentias tollendi.
sit aequatio una abxa a +bX + CXX + d X +X  et alia
as qui
Deql + MX + XX aequ. 0. tollenda est X. scilicet multiplicando aequationem
minorem per XKX 2. 3X _XX  habemque duas arbitrarias
cum tamenties sint tollendae, ergo mulliplicabimus potius aequationem
2 per liteo numeros arbitrarios, 2. 3x. TXX. - X et aqu. t. per  et
et aequ. . per 5 et per +X habebimus tollendos 4, et arbitrarias 4.
Rrem ab ouo adiamur oaa +X aeq et 0 aequ l+ X Multiplicetur illa per
illa per + 1. seu maneat qualis est, haec per - 1. addantur fiet: a + l aequo.
Rursus: a +xaequ o. d aequ a +X et oaequ. l+ mX + xX, invenietur
vaeq. (= ma + aa .
Oaequ a + bX + XX et O aequ.  l + X. fier a - bl + ll aeg. 0.
D aequa + bX + XX et 0 aequ l + mx + XX Multiplicetur illa per 2 et per X.
haec per  et per = X. fiet: +2a + 2 b X + 2XX. Y
La
fiet 2 +6 aequ m - b 1E1
2b+6m aequ l- aG prbihrariae 2 et 6.
assumtae
+ aX + bXX + X3
= l X = mXX = X
. 0.
2a 6 laeq. 0 seu 6aeq m - b - 2 aequ l- a - 2b, c seu 6m sb 2.649. l- a- 2b
n
Ergo fiet mm = bm - 2m aequ l - a - 2b. Ergo 2 aequ mm-bm + a - 1
et 6 aeqo m - b - um + m = a +L seu 6 aequ 2mb - bb -mm = ab + 1b
Ergo inmat bma +aa = la egu. (2) mb l- bbl -mm t - ab 1+ 1t
seu mmab= bmab +aab( lab) aequ in Bl - bbl = mnt (= a bD + (2b
en +m ba -
bb m
aeque
Et ita porro semperus res reducetur cd. resolutiones aequationum
simplicium, quae etiam suisjam constant regulis quas cum
istis progressoonibus jungendo non difficile erit omnia desideata
absolvere  quae in hoc argumento desideriu possunt
Consistit autem in hoc unico algebrae totius sublimioris clavis