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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 219r, page id 00068201:0437
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quas duaes aequantiones , et D. explicando fiet: ex  4 nsb 42, 2bh + 3, eb, H + h -15
seu - 240b - 144 hb (160 43) b 413
- 72ac.
=pach 50. vel b +3 hb + 3 ac b (+ 4ti
+ al
-15ach
+ ael
ac esse quantitatem affirmativam, quod nullo negotio efficitur per aliquam praeformationem, ett construi poteno
b. sive inveniri per duarum mediatum inverstionem
porro ex aequatione 3. habebrinus:
23 615b+  4, us bh 46, 25bh, + 4, 5bh + ht, (- 35, 25b 10b 1obh  10b trob
4hb
=125 100b2 +2, 04b4hb + 16t b +8tbac tac
+2, ∞ VaC
 5b 10b3 h1ob3
6hest
. 3acb
ael
-6hbr 7)
hacb
ael
=125
2 5(4
4h b3
3 ac b
rac lb
ae
4lib
quod si ergo collatis his duabus aequationibus; tollamus ipsam b. dubium nullum est, quin aequatio proditura sit altissima;
in qua h. aliaeque literae ascendent ad vigesimum forsam gradum usque et nova b in ipsis ad huc altius;
Sed quoniam semper aliae atque aliae oecurrunt in potestate sunt praeformationes, credidorim talem eligi posse, per
quam ingentem illam aequationem dividere liceat. Sed atterius remedii in mentem venit. Solius prioris aequationis, C, ope,
aequatio data roducta est ad hanc formam: X X agX  as X + a  10.
fari sive.
X X + aq X X as X + at . quae dividatur in duas: X X - s mn X3 X +5mnX, aet po
-5mn..
+5m.
-5m
sive MN -  X MN - aq N 
nempe M_ + co
a2s
et aliam: aqX +as o.  qu
temn. -smin sive m n - X MM - 9qX 2 0
Quae aequatio videndum est an ex duabus producta intelligi queat,
in quarum matia  alterntia nulla extet X. n )
et MN +q2 quibus in se ductis fiet: MN taco M +co X
+ A
=5
nnx
10X . + A, SBo. quam aequationem conferendo cum aequatione 4
Aa
fiet co +A po et  H = N. ex terminis secundis,
sive cop-A
ex tertius vero fict: acot itest AX, 4 et A c, ide it est - N B = as, sive A, tat adu aa
ex tertius vero fiet: a H id est A N    -q sise A  - 4 X. et novissime Aco id est - A2 dt est q
erit p a sxadeoque, redivimus in circulum, nec quicquam actum est, tantum enim invenimus
ipsam q debere eequa aequari ipsi S.
Aliter, habermus: m + n5  a t.
 et XrI mon. ad eoque mac mtam meno Bo
sed his nihil agiter, an ergo aliter exterpemus: et pro a , smibamus a t= aeB + a β.
= 45
et fiet excerpendo: aq X +as X + aB, et ipsa β. erit arbitraria: et ordinando secundum mn, fiet:
ermn...- suin.
ium MN c=p M B diendo in MN =co
+ad..
+c000.
N-sx MX
+cosa
=9 5 Y
=asN
conferendo: Dp = a. et Ap . c0 ex secundis
Ego ex tertiis: co - gat Y. restat
v254
ob numerum detmendonm
a. 25
+ a
pro MA n ponendo g quasi cognitam:
M N - x MN + XY p, 5 Xt ftaq X + 4 a f  5 t MX p X  sit E pot
7 a5t. compendi causa, erit: M, a51
et m et a 5 e asi + nEp, a t, sive. n- at n + a B
ultima aequatio:  =g aH +ga H ~ as   asN
502 50V 2
redit eadem quae ante aequatio, et hac proinde–
Inutilia.
1I. M M - x MN +- aq X
x jam sed haec inutilia fore non dubito
 MN + E X per a M N +coa dat
160
ac dat. M N + _ X MN + WOBCOHX
+omn..
Hov .... + Aa
s
sive nH
T) ab + 44
515,
=1
at +Saet aaesi sivi n at + saet- aa5
est autem me a t - nE, et erit m’ +a t 4 sa t 4a 575
et Xr) (0 ae t + sact 1asi + f at + Saee aabsi
tu
sacb act 3ac b
ubi ponendo et
+hb