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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 67r, page id 00068200:0135
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videtur ac plagula cotiveri verabe dimensione curvae conire Martii 1681
solutio, quod postea scripsi
Scheda2.
quaentur quadratura spatii cujus ordinata 2. ab issa X aquatio
Q aequ. Saa rar faxx + E 12 2ax +ax
2a X + a XX
posito Caequ. 1+ a
secune nam cuvae lnius ordinatae sunt elementis curvae Conicae proportio
nales. Datur autem (7Zdx calionaliter. Ergo ex s
Zago aa  +E yy x
Ergo Zx aqu qu aatE Y dus
149 +4 yy
yy aequ 2aX f a xX. seu XX = 29X + 4ququ qq + 4yy
et X +9 aequ. 149 + 4 yy. et dr + a y ays
X aequ 144+ 2yy + 4
1_ dy aqu E adx + faxdx
Ergo dx aequy us
Efficiamus ut aa +E gy 44 + a yy sit quadratus.
29u - da
AC
n
na
(= 2qp + dor + cda +2CB)
Zaa aeruandus oadnt.
149+ 4 yy
aa + = yy
99+4 77
et compudii causa faciendo +a + C49 aequ da. fict: +c y + dagy t aa que aequ. guadrato 12 y7 + q y
faciamus primo hacus quadcali esse latus esse 3x + aq. fiet:
taaqu t egary
+C. y+ dayy (taaqq. eg 3 or + 2yyqu (+ aa44. et habebimus. + E gy + da aequ 37 rV + 29u
seu fier: yy aequ.
aa
29V. da. Etiam sic quantitas: da  yy-2qu aequanda quadrato:
+
-no
aa
pone v aequ cy. et fiage quadralum ab ey + da fiet :(da e, y-2quy aequ ee gy + rey vafa
et fier. y aequ.  2e sda +24. et vy aequ. Cy + Ida aequ coyy
Fa- et sid pro y substituendo valorem non otur aqualio
a
rationalis, sed alia aeque difcilis ac prima
an sic: += y 4 + da yy (+ aaqqaequ yv +  aq aegu 37 vV + 2aq7v (t aa 49)
et fui: +C y3 + da y aequ. yvv +2aq0. Sed hoc prioribus nihilo meliora
sumta aequatione 29V - da. faciamus ut 290- da. Fc-vr sit quadratus.
+ q- vo
aa
FCy + dagy + aaqque aequ. quadeato fiat:
ergo yy aeqo 
ergo
4
num
m
aa
y aeqo b dvt ac a. aego l a.
a
+a+da llaa +aaque aequ. quadrato. seu
nm
Ergo C. l a + dagunm +qm aequ. quadrato.
Rei  explicanio l. mm. l m. et ordinando:
(7
Pad Vaa dev acdevauede Lee
ad3 qr 2adesqu’+ à des quo +radef adeh
+g
+2ad7h9V +a a  efhg  +2adeti qu
4
+ad3 lqur
S v raphquabas  Vv +4aV + a E
 si ponamus com
~ + fier. acde
equ. sed tunc duae solae literae
o
aeceae grata
de non sutticiunt.
melius facere 3 aequ. 11 (et fuceqo 1.) Ergo et 5 aequ. 9.
et ft et debet esse 5 aequ. (4) 9 et A() 3. 2+
F.
Erqu7.
fv tah
num
clat + daqurum +aaqns
lerum
im
qu
su
Urgo dv + 2da e Da 
l’aqu. dV + d’acv +6d a ev+
daeev + a’e
mon aequ. At, a
d.vn +2da et et
+des vtraestiv de
tradesv adest 2a deti v
l +afV trav +aedtie
m aego fv a Fahi D+65at 4fat ah
sit Orgo povtvs comparad genealis
erit et aequ. p v + 2V+ ipB
compcum:
r4 v+ 2rSv+ 16
3V +5V + 7 v +9V + 1
fiet P aequ 13. et raequ. E. et s’aeqo si
et r’ aequ. . et. G aequ. 8. seu 2ogo 
2su
denique 2B3 sut  aequZ.
quas aequationes succedere necesse est ope trium arbitrariatum
d. e. h. quia una f. manet supernumerariaa
i
11
a
aegoevimu
Haberius ergo retuctionem aeo liaus comlo ad quadhatam rationalem, bt
adeato