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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 14
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idem est in altioribus formulis, nam si esset cubica h + KX + L XX + X focder 
faciendo X- yte X pro x substituatur e+y, erit ultimus terminus formula nov
exit h+ Re + lec + C ) qu qui aequabitur uni  id est (h) unus ex divisoribus
ultini termini aequationis novae itaque rurgus (h) - h erit divisibilis per e. Generaliter
rataonalis
ergo, ut investigetur an aequatio data sit divisibilis per formustam alicujus
talem
s p.
gradus rationalis integra ordinata secundum X sit divisibilis pers formulam rationalem
inferiorem, secundum eandem literam ordinatem, velut X; notentur omnes
divisores ultimi termini  divisionis datae Aequationis datqe et pro X ponendo 
y+e, notentur divisores ultimi termini aequationis novae; e variundo variando
et ex divisoribus, prioribus seligantur illi quorum differentia a posterioribus sit
divisibilis per assumtam quantitatem e, utcunque e varietur. ita facile excludentur
divisores non succedentes, cum quaevis variatio od excludendum servire possit. Quodsi
nullus  non excludatur divisor ultimi termini aequatiohis datae; non potest ea aequatio
vel formula dividi per formulam talem inferiorem; cujus curque sit gradus;
idque adeo praeclarum huic methodo inest; quod omnes gradus una 
en
u
sit dibisor
e postquorun varrationes ipsiis, e, ali qui
e  uot quecese est qsibi respondentis, seu ynttimum
poterunt etiam inveniri reliqua  caetera eterae coes laeteri coefficientes formulae dividentis
R. 1 m, etc. prout aequatio altius ea scilicet plusmina a minus aut plus assurgit.
Et lit hoc diversa nihil operatione opus est, pro graduum diversitate, est tamen communis
non
processus ut mox pabebit
ed Incipiamusa formula dividente quadratica haket ee e
h+ KX + XX, quae transformata r habebet pe pro x ponendo ety, dabit formulam
dividentem aequationis novae crjus novam cujus ultimus terminus evit h+ kec + CC = H.)
h et fiet fiat (h) hy: c = scribamus (S) h ee : e = 1∞ 10 et
 ob datur (6) k, Ct) H, ob inventas jam h et (5), notamque e unam ex assumtis 
tui respondet (h), fiet habebitur et K =  (h) - h - ee: e quam quantitatem
cum integra sit per compendiam vocabimus Ha, et fiet di Formula dibidens quaesita
inven porro quantitatem (h) - h - ee, e quia recurret per compendium vocabimus 110
Hs; formula dividens sit cubica h + KX + LXX + X, fiet h + K e + lee + e = (H)
et quia (h) = h - e3 divi ai potest per e, proveniens compendio appellabimu, 3 quo et siet
R + l et = 20D. Sed pari jure pro e assumendo L, loco (h) pradibel   sumatur (2h)
et loco (2h) = h - f3, if, assumatur 31 siet K+ 1f = 3t ~I, ergo fiet 
= 310 -311,:, e - f = 370 et fiet K = 310 - 21 = 310 e
Si formula dividens sit biquadratica h + KX + l XX + m X + XY fiet h + KC + lee + MC + C. 1B)
et (H) = h = et : e = 410 adeoque R + l e + M ee = 410 et pari sure faciendo
(2H) - n - (4: f = 411, fiet X + lf + mff = 4+P, unde 41D 4+1, :, e- f vocetur 420
et siet l+ em = 420 et A te l. + ee m = 410 -411, et 410 - 4u, :, e- f vocando 420
fiet l + em = 420. sed pari sure faciendo (3h)- h - g,: g = 412 et 410 - 412, :, c- 9 - 421
prodit, m= d430 et l = 49 420 - (et 5) 430.
R= 410 = 420 C + 430 (e+ f) C = 4 30 ee et firt K = 410 -420 C + 430 ef
Si formula dividens sit surdesolida, h + KX + lXx L mX3 + n X + X5, fiet h + Ke + lee + me tne t C- B)
(H) - h = 13, : e = 510 adeoque R + le + mee + nC3 = SIO et pari jure R+ l.f + nff + nf = 511, sit
sit Sio- SI, :, - f = 520 fiet l+ M (et f) + n (eet ef 1f5) = 520, et pari pure ob g, fiet
L+ m (8+9) + n (Cet eg+ 99) = 52I unde n (f.9) + nC (f.9) + n (H- 99) = 520 - 521, et
posito 520 -521, ig f- 9 = 530 fiet m + nser  ) (s+9) = 530 et pari jure m
m + n (et f+Y) = 53l et n (9 -)) = 530 -531 sit 97 530 - 531, :, 9- 7 = 540
et fiet tandem n = 540 et m = 44 530 - 540 (et 5 +9) - (510
et l= 520 - 530(C +5) + 540 cec+ 2ef + 55 + 89759) -540 (e +es + s5) seu fiat
= 520 - 530 (et 5) + 540 (eft e9+ f9) et R = 510 - 520C + 530 e (815) 540e (eft egt fg)
+540 ep (e+5 19)
seu K = 510 - 520C +530 ef - 540 efg
5408
= 530 et
fiet l+ em = 42, habebimus e (f- 9) m = 420- 42 et 4g0 fiatque 420. + 21, : f. 9 = 430
et
terminum prudmentes) ex hypothisi =
AHini suficit
risores
cdateriqui
un in fra
radicem
quadratium
ivide ad
Hadeo qeabebitu
et formula
quesita
dibidens
quae sita
h+KX + XX