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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 3
# Folio 10v, page id 00068021:0020
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ut cartesi literas relineamus esto AG = B AF= FE = c FC = c+ Z. A(M) =y A
Ponatur jam C. in (C), ent C( = c + 27+ Z + C + 2cy +y. FP= erytM
sam FPCCM = P +
CF
CG2
2X
ce
Ergo FDCMM-AGP CM jam FP + GP = a.
Ct
 CG
Ilem CF = FM + CM et CG = EM + a - 2a TM + FM
Ergo fuic Fp
CF2
=
Gua
E CG
FP2+
.Ergo
FM + CM
a2
FM + CM
PN
a + 2a FM + FM + CM
Ergo a - 2aFP +  = a + 2a FM + , iderque
F p2
v
F et ponendo a L 2FP = Y, fiet - FP = Y =a, et FP = a - Y es Fp~ a - 2 ap+ V
eodem modo a + 2FM = 5. fiet FM  = 5- a et FM = 5- 25a + a
ideoque invertendo superiorem rationem habetimus.
a
= 5 - 25a + a + YCM, inde L 7a + Y = 5 - 2a + 4 + CM
a - 2ar + r2
Ar
AS
sive a + Y - 5 = 8 - C = 0.   lude fie: melius
esse non imponere nomina lineis, et calculum per lineas potius per quam per literas
trusigere, donec ad extremum appareat quae commodius elidantur. Jam
ponamus CM = y. fiet: a5 + r5 - 5Y - a Y - y V = 0. autes capendentem Y
sumla ergo recta Y velut ognita, su niveotigemus Jam si lineam FP velut
cognitam sumamus, et pro arbitrio assumtum, a proinde punctum Y, eadem
erit aequatio cujus duae radices, vel L set y dupliciter assumi possunt.
eadem proveniente aequatione, modo eadem maneat Y, et a. Sed si ex
in nostro casu eas radices cogitandum est esse aequales et (C.M =
ipsi ((C)) (M). Ac quaerenda proinde aequatio ejusdem forma, in
qua tres sint indeterminatae, dua sint incognitae, ciuarum quaelibet
significationum aequalium: cm ad simplicem methdum tangentium.
aequatio duas habens radices, aequales non nisi unius sit incognitae.
forma rostrae est -r Y - r5. + r5 
+a
=aer
y - e, D = Y - 2Cy + e
C
s- 9 5 -  5ps 5 29545 , fict equatio y
vel ducamus in se invicem y - e s- 4 fiet 15 - yf - es + ef. Sed deest
im
 arbitraria quae in hoc productum multipli–
V et 5. deo quaeratur quantitas
cata fin facat.. S 5. iaque tot quoou vitatium
deprua i
literarum diversarum, ut si superiori aequationi data compareturi aequalio obtineatur
Utite focet Bartholmiana de constitutuns et dimitibus aequationum ad eas usu prodacta
quae sint anaruoq et plariut Incognitaerum qut tat ali esitea forno cnhetrentur