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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 105v, page id 00068201:0210
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 106r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=210
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# Lines: 64 recognised, mean confidence 0.80
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ah. X
X +alX + al per N +am X iaf X + a cX + a d Bo
X  + a hX + a l
X8 X am X +af N + aC X + a d X
ah aham, aha f. ahacX aha) X
ral
a lan aelaf a lac ael
X X ab X ac X at X anx apX aq X ar
esaena Ubi videndum an tibus ullimis terminis p q. r. aequationis quadia
to quadraticae proposite an producta aequatio comparari possit cum alia quadrato quadratica in
qua tres ultimae literae p. 4. r. pro arbitrio sumantur, fiet: Quod fiet si ope quatuor
arbitrariarum m. f. c. d. quatuor primae aequationes, collatitiae possint absolvi aequatro plane.
nempe m ob at b - h.
fM c- l.
Cpi ab  tm  ap =sb +ti
et d B an = hF - lm an = het hl - 11(F hD
Omnis ergo aequatio Tubica attolli potest ad quadrato quadraticam aequationem ectavi
quodus, ju aequationi alteri gradus octavi gradus omnes tres ultimos ter minos arbitrarius
alteri
habenti, comparabilem
Ergo comparabilem resolubili, Ergo aequatione per Geonetiam
planam. Ergo pse quoque rresolubilis est per Geometriam planam. Nam omnis aequatio
octavi gadus tres ultimos habens arbitrarias terminos habens arbitiarios, plana est.
Vugae alibo res intelligatur: aesqatio hi producta E. comparetur aequationi  pagimae praecedentis
bsi ubi. salis apparret remalse assurgere
resumatur aequatio D. conprundo cu s: me Rb + a lb = 3 p ah 34 l
P7 a l.
s tab + C = Cub B ab tab + 3abc + 3er ab + C3.. H
15 ac tab c 1I
Si quaedum radio Cubica cndam aggregito planarum quontatatum aequari potest
.
p3+ a2C
calico pura
X +ael. B0. fat: X F + m X + ae l X + a lm p0. Multiplicando per At m quae
redumetur ad aliam cubicam: _t in y 4 Am Y + 4m t p0. cujus toltendo secundum terminum, fie D.
ponnde g_ X +m fai X +sm X + 3 m X +  9. X  - (m V - , l o
nem X - m
27
+ (m1). 4 pa
cujus rdi secundum terminum facere affirmativum vel negativum in nostro arbitrio est: Unde radice extrahendo:
Yf y 
sive
Se) inila + fs 1M B Bna a a ( ( m) )  fli f 1a
JH 10 1ne t 1a + ln + la
2a
a
+ 16
pone + p+. fer = p. et yB mO + l’a
Im F la + lm = Eae
rique  X (+)7X = LY. Ergo per ea quae habet Huddenius reg. 20. pag. 495.
X + A p  - aet. sie X LA- a s =
fier: X  =EM ut +ga + S. m p L msi nerga + ii Ee yast iga tgn. al
4
 nemrua
H LV + nom -cal . adeoque X1]  qn 4 B s n +ga. + se 4m s nrga (  n ga ( ya +ynaniar
(7m ya
YS n aga Jum X alinde pu a s a l. Unde aequatio  inter duas quantitales cognitat, in qua in pro
arbitrio assumi potest (ed satis intelligo nihil inde posse duci facite. ablatis enim irationalibus quadiaticis rest abit
enon nisi una cubicam vel simplex vel quadrata)  vel 13) 1
X+ X+ anp
sive
unde X, dX + Ap s api
FAH  m +  S+ m +a
Bph - gat 3a