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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 301r, page id 00068201:0601
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X   a et
X 1 b 4c
X 1 13bC X ps gX ster
 et erit X bZC - ser v+c.
adeoque sublata jam X habebium aequationem:
b’a + cta = ser p 50 gb + Nq c - 3 abc - 2bc
(Sive NN +59b N X- B) b
separitur haec aequatio in duas, excerpendo: -NrrN 4b.
fiet sT) qb et residua aquatio erit:
bar ca +hab C + 3bC A 4 b 9c
vel b2 + 3c B + 3c b +c
sive C + 3b C pb c + b3
faciamus Cp H- b fier:
Repeterdu est calculus dumlsionis novissimae:
X H b +C. X b3 + 3b0X  agX + a
siet 6+c bC + 3bC, - agb) - aGc = ar 10
Sarmus excerpamus: 2t E be- aqb 10. fiet bg ag- 3c
et bp aq3- 9ae 9  27  ag 17,  3 agu rar
Unde aequntio ponendo fpi 3C. fier: r f 2 + 4f - a 
sive pro f ponenb , fier: 9’ + - a d - ra  videamus
aan haec aequatio sit tractabilis. Nimirum debet esse
P iq reditur ergo ad detenul nationem ordinariaum.
superest alia divulsio: b+ C,  aq b +c. sive devidendo utrobique
per b +c. fier: b + c - bc B ad. quae est aquatio ad circulum
b+ - bc superest alia aequatio: 3bc +3bc p, at
adeoque b7 a 4Dbc - C H a = 3C B
+ -be +) et b 5 aer +3C=0 1a93
oiquiaum et loco Ra ponamus RC
eror novi
rodibit X3H 42bC sed satius erit fere retmere ordinationem et exposteriore aequationefier+ b +C RC dc + bc ec
secundum b. ponendo b, d - a
rumtando c. in a quoniam  C. nullum habet huc usui g
debet esse (a) - 2ag +q’ a
3ar gaera
adeoque 18r  +6X 97)  94
ei 9r + 6r 9 +  f92q - 9r
sive 3rt + 97  s 29 - 9r
1
 quae determinatio adhuc arctior, quam
dr Scipionis ferrei–
quid si aliter divellamus, ponamusque: X 4b-3 abc - 36 0.
fiet b5) N4 3ca. et b27 N g2 - 27 C8 9e 2nq
ut aequatio residuae erit:
Ga 27aCZ 3Ca
erit en ea +ba, et Cn 2 a + 23ab + Va
et fiot novissima aequatio b2+ L,
= 2 ab - ba  2 a + 2ba
RE b + 2 a + 28 a b + b a - - 2abR, - b aR - 2’ aR 0
e ordinud. b (+ 226 b + 2 a- ea R
N qu  174) (9 2 4 - 3X qu C- 3 ra C2 p bi 9 y et
+27a C6) ( qu . 1) quae est aequatio quadrato quadratica
carens termino penultimo. 
pro s ponamya 5 scribatur a. et pro c fiat a
e vaa
C + = 24C = 27 ar e = 18 a 70 aequatro-
quadrato quadratica secundo termino carens, reducibilis ad Tubicam
=6a h= (+ 94) h - 17 2r a e r 7
sue H2 - 6a H - 62 a h - 17. 1 a6r p 0. F sis Hg ta
fier. 8 (+3, 19 +3ag +8 a
im  ea 5 qi   
63 9 012, 2a
b (+ 22a b (+428
E s 
42 an) + C. MF 456 EaX)
-2 a + ZaR + QR aR- ae
R + a - a R
jam ( Q a + ba et Xp, b + c.
Ergo X, EaK b = 2aR +, Za R 4 2GR Sak - a
R3 + aR - a R
do quam dividendo per c jam inventam,
habebimus radicem quaesitam,
Ermutum est. resumatur: 3bc + 3bE H RC.
Ergo  b + bc H RC. componutmr haec aequatio
cum altem b+ c (b
1 2E fiet bp et Ra + Aa a
jam loco b + et p 2C. Pcribendo valores diliendo omniasti
fier ea Ea + Aa - a; + e e + RC fier aequala
2 (ea  Bd( a) r2a 1 D2a +  Ra
s et redit aequatud ab miho data
Eeplicando
b2 a bc at. b aer - beb
N ag-c + bC. Ergo b  a r aqerC
 a gr. et fier aequito bx + eb - a qr
b e et ag - c n X ar - (6b0, et b7 ar agete
et B ⊓ a  - 2 argC + 2ar C, +aC = 2a9ct +
Can usta racinma
aa
iea
quo posito orit autem aequatio autem quadra 
loquadatica superior semperctadirem halebit realem,
3aq p. 29
in eximpito ubi B9. H12
00 Tanim ultiu pcii
trichle cerrumipent