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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 19v, page id 00068049:0038
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Quantitas verbigratia p)
quantites
Ubi tamen hocc superest objectio quod illa determinata qua
fortasse=.
postremo invenienda est non invenietur nisi peraequadem aliquam
altioris gradus adeoque etiam ambigua est unde quaestrib est, an quaht
an quilibet es ejus valoritus pro e generali salis feciat an vero pro
quovis salore ipsius v alias assamendus sit valor ipsius p, quo
posito nihil egissemus, nic habulssemus valorem explicationem
ipsius y cuivis ipsius  valori communem HoC quae70
maxcini est momenfi pro analysi ambiguorum; et putem unkmquemue
vulorem ipsius P debere soccedere, pro quovis valore ipsius V; quia
quilibet assumtus utu calculum restituit, adeoque sucedit quocunque sumto
valore ipsius V. Est tamen ab altera parte magna ratio
dubtandi Hoc enim odmisso semper formulae possunt transmutari in
pationales, de quo cun dubitebam allas, quae quoad inde-
terminatam sint ratiouales. De quo tamen habebam cur dubitare
quoniam valgari modo rem aggrediendo, et y explicando
rationaliter per f X, et provemiens cubo aut alteri altiori
cuidam potestati aequando, non semper adest numeris sufficiens arbitrariorum
itaque.  quia nondum satis profunde meditatus sum de
Anatysi ambiquorum, rem interim experientiae committam.
alibu
Et quia calculum istum jam peregi, ad hibebo literas piis jam
adhibitas, ut institui cullius possit comparatio calculi.
E sit O loco aequalioms 2 paulo ante positae,
.
scubatur x quaeritur ergo sigi.
1
hiCce
(,dy
sin + hb
AC - yy
cc - tin gy. erg de
cc - yy
2
. Ergo V - cc ithti yy + Ct = O et
tik
est formula aequanda quadrato
4(4)
Sculatum V- E irhit  + E = 0 vel per compendium V + GVV + 9 = 0
sit y   HXX + 11 X + 12, puto enim reliquis albitrariis hic
a
careri posse, eritque y + v= BXX + 1X  + 12 Cujus numerator est
aequandus quadrato seu 
+ vX
L EXX + y X + 12 = DD
quod ut tiat delet+ 2S2. seu t 1 + 2. 1V + vV0  eg
b
4. 1-.
Unde jam ope aequationum 4 et 9 tollatur v. quod variis modis fieri
potest, sed compendio sissime opinor, si aequationem o multiplicemus
per fom.. lam arbitrariam vx + 31 ∞ + 32 et productum erit
V+ + 2. 11. V3 P + 11. 11 VV + 1.1. 31 V + 11. 11. 32 (11)
+ 31 1
41..
- 4.12.31. 4. 12. 32
+ 2. 11.31 .. 4+ 2. 11.32.
+. 32.
0. Unde ti
unde follendo aeq 4 debet eva-
nesagatio e esstai dua
x 11
quod ut fict debet esse 2. 11 + 3120 et 11. 11. 31 - 4. 12. 314 2. 11.32 = 0, est
denius il. 11 4 12  a 2 n 3 + 32, _ (f5 .
 adenique H H. 32 = 2. 1 37= si
+
et 11. 11 = 4. 12 + 2. 11. 31  32 (= A) --
et
(13
l.G CE it hih et 11. 11. 32 = 4. 12. 3c = 9 = esL
Ex 12 est e 31 = - 2. 11 et 13 et 18 fit = 2. 113 +8. 11, 12 + 2. 11. 32 =0 seu fil
32- 11. 11 - 4. 12 1 et ex 16 fit 1er Ht HH 4 1 4 1 1g F 4. n 4. 12
0
117 = 2440. 2. 11. 11. 4. 12 + 4. 4. 12. 12 = C: hh seu 162111 - 4. 12 =  CC: 5 11
seut A 4 1 F cc RA,
quolus vatoribus ex ∞9. 19, r9 et 21 substitutis in aeq. 15
i et ex aeq. 15 per 10 et 19. fi  gu fit BCc: n Si B4. 11. 11 + cc: h s1= ce tih
seu 2des tsi s ht se on
t
etsis s ceca
seu 4. 11. 1 (23) _Ce, 1 + hh + 2h si seu 11 = C 1 + hSi Si = +C 1(4)h - 1
et 312 4
en 125)a
14Ih et 1 AC per 21 et 25. fit 4 12 = CZC, 1+ tih + 2h S. - 4h H = Ec 1s -t s.
hsi itaque ubique feliciter succedit ext A et jam fil
xxtr ict  1. per 0eg. 5. 134, 15  Qud jam an Gucceda Lotudi
Erique y