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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 229v, page id 00068201:0458
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formandus est nonnbil, ut scilicet catulus jam factus possit fieri utilis faciendo qui resta. Quare de
red- inchoemus:
) b e + ac 0. et de + a f 170. fier ac  af seu (Acd - L fb, po.
jam poncndo ab rige + gatr. fient aequationes duo: ge  ati e  ac 0. et de + afpo. Unde ex aquatione resubtanti
parentresi inclusa fiet acd - fge - fah po. et pro e  acd- fatr  af. Unde (acd fatd + f ag po
1 In qua equatione resultante, ad usum calenli ordinarii potes am 9 quam d ponere pa. SedNam adhilitae
sunt tantum ad grdum ultra promovendum, et si rursus ad explices nonas ad pletam nt aequationes
duae (HII) ge tahe + a c 10. et le + ame + a f 0. Unde aequati prosime praecedensae
explicata d, dabit cle + el eam + caem - afhle - aftram + fag po sed satius erit, credo
ad hibere aequationem resultantem pene proximum, inqua fiet: ete
ec- fge - fah. po.
tertius ergo gradus reductus est ad secundum: habemus enim aequationes duas: CC2 tam e + a f p. et tcle + cam p0.
aH aC - fg. - fat
et fiet aequatio resultans tertii gradus. C l’ac - 2 clfgac +fg ac (- Clcamn (+ el fatim, + fgcamm = f9 fatim, -
(F Ca mD) aD emfhla + f h la
a
a1
a F
10. siuve c l’ a - 2cf9 in qua equatione
adusum accuomnodanda poni sdeben g et lfja. ubi fit: a C  - 2a lC + f’ac -f aetom, quae
aequatio debet esse divisibilis
supra
+f am.
famh.
+fVt a
Rectra nn succurit alia ratio, datus duabus aequationibus e + d’e + ab Bo. et e + fe + ac po.
d ivenimus resultantem:
Si ita ponamus:
a b - 2abc + aec + d’ab +sac - d fab - dfac p0.
(7) be + a 70. et c e + a 0. fiet (b = c 10.)
sit ab 1  de + af. fer) de + afe + a p0. n et CC + a 10. fiet: de 2t + a ro explicando b - c,o.
fier: expsiunt ressultantem praecedentem: de + af 10. sive ad e + a po. ergo (fC - C  ad)
a
Explicando c siu jomendo ac  ge + ah. fier (211) de +ase r a 0 et ge +ahe + a3 0.
et in locum resultantus parredentis pro Cpoundo ge tah. fei: afge + faba g e 2gahe- aeti ad.
et in locum resultandis primae pro b et c ponendo valores fiei:  de + af pge a n. sive 1d C = ah po.
sive +ad = ag e + a 10. qua juncta cum dE + afe + a fier: f ad - fag ad  2a dus + aeq
=ph +ff
C
sive: dag fa - h+f - a  d- 9, D  ad 2 1 t L
af
+h2 - 2hf + f 2H
quod si jem ponomus dag  -h + f  sive d e + a- h l + fl, func fier.
ex illa aequatione  igas. hls + fl. + aht - a f l, (ade ad fgah + gaf rh l- shl
ponendo - h +f B dug a. sine f⊓ d l = gl + ha fiet.  fa  - a   ad. sinc explicando f,
et multiplicando omnia per V, siet:
itaque si luae suit aequationes:
A (d P - gl + hal - a ⊓ (d 1) sive gl ae = ha l + a p0:
de +d1 C + a. qu. et ge rahe + a,o
u aequatio in quae nulla extat e, erit: (g1- hal + a po.  l si enuim redire oequaso prior tanteur
Ponendo jum ad H  me tan et H pe raq.  habebimus ae quationes
duas:  (IV.)
pre pro e pon
me + an e + aln e + ao et pe x + aqe + ahe + a
ilende fei ex resullante procedente pel taq  hal at  
+ lm..
- lp..
- alg.
+ ah. adeoque:  pla3
e + a.
si in aequatione resultante praecedente o12 - hal +a go pro l ponas hatsa fret tae-raehf +sa +ha  1 sa + a po
lende si  ponas adpi me tan. et agp pe +ag. fiet:
Unde pro e ponendo ejus valtiem:  = a9e- ahe -
dae g
a2m ren.
agl-hal ta
nanc aeh 3h.f
9d2- 2d9 + 92
dag
fo janer a fe - a. fier: q’er ratim e + a
et explicando resultantem praecedentem: a se + a  n a- 2aehf. F  m
sive aren aepe + a n C +aq +h0 f p0.
aetishas im.
a 
aq
 as
tie. hsid np.. =af
amanetan um etan e peran a a m a
qu
aemp.. -2maq.
. ranp. Aranaqu.
 p +2age. + aqu