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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 186v, page id 00068201:0372
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A1sd deatur aequationes duae hab ibB. 10m t non + iatum t en = et
e
et
et H4 + 21 b + 3tC - 0 et no a 100a + (010b+ (00IC = 0
R200C + 02Ob + 002C + 110 ab + 10iac +011bG  = 0, ubi patet si peraego. prvorem
30.
tollamus  c ex ag. posteriore, b non assurgere altiu in nova, ultra bb
sed sint bres aequationes, et ties literae incoenita, b, C, d, et sit
1 100a 901Y 4 = a 00rD + orbe= a ex aeq. 1 fit d= 01eb, : 001 quo
10100
substituto in aeg. 2. fil l1602. 01040bb + 002. 010. 100 + 001. 020 bb P  bi1 b. t +001 10ab
Est jam et tertia aequatio data 003C + onD. +B111cb a = 0, et fiet
sciendum est aut
0 - 01o  610.  -on 0dg orc. 193 1ba
-0030106 -003. 3010. 100b a + et = 0
Ergo ut sciminus ex aeg. 4, et 6, conjunctis oiri aequatio
sed si sint tres literae incognita  d, c, b a. sublet in quarum prima
 et quatiuor aequationestres, ita ut in prima nulla litera assurgat ultra gradum
simplicem, in secunda nulla, ultia quadratam, in tertia nulla ultra ubum, quaeritur
an tolli posit an ultr augblit an sublatis literis aquatio duabus d, et c
aequata a perodeat aequatio, in qua residua incognita b, non assurgat ultra culum
Et quidem ope primae aequationis follendo literam ex secunda, prodibit
aequata in qua et yta, tunc utique fica prodibunt nova aequationes, in quibus
in quarum una, ipsae b, et, c non assurgent ultra quadratum, ut ante
altera, non altra cubum, ititem ut ante jam res eo redit ut
videamus an u an subla quid fiat sublata c. Nempe
in
 Be + bcb +. ba +aa, alterius +eb+ eatbatcaera
ba
ba
63 et ba
quaritur an tollendo B c no  prodeat aequatio in qua , b non assurgat ultra
sint duoe aequationes niusfoima; e
hibum; sed hoc falsum est, perinde enim est ac si scubamus aequationes
mas C  C10CC+ 11C + 12 = 0 et 20(3+ 21CCF22C + 23 =0
quarum oste tollendo, c podibit aequatio in quae 23 assurgit ad bquadra
etrs contineum nova aequatione
tum et 12 ad cubum, jam 12 continet bb ergo
. et proinde nihil actum est,, nisi simul efficiatur ut
b, et b et b non extent; quod qua raioe proestari queat, i
Kips.
Majo 165
apparet. Unde Methodus illa in Actis proposita a duo
d. T. pro bollendis sol terminis per aquarem omnibus
per aqua intermediis per aequationes data inferiores
non procedit altia aequ. cubicam; nisi forte ostendere
possit succedere latia, cum per gradus termini alii jam sunt sublati ex
cum tolluntur pinum unus deinde duo. etc ita it cum duo l sublati sunt ex
aego. ccntica, et sam tertius collendus supirest, oporteret succedere, sed hujus rei
Et vellem saltem in quarto et
quinto et, gradu rem fuisset proscentus autor, nec in solo 2d
demonstratio nulla apparet
Fortasse ante calculum consequi licebit quo usque assusant
summae, ve rudicum, vel sammae restangulorum uc. secundae aequationis
ertio stetise
posito, harum sum sum productat augeri ut evanescit terminus secundus et
ut fiat q, nihilo, et debere eliam summas caleras op nihilo requales ficri