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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 214r, page id 00068196:0423
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2 Maji 1696.
Addatur shediasma praecedens 1. Maje
dimensio Curva Conicae reduci posset ad
Quadraturam Rationalem, si posset extra
extrahibiliter deprimibilis reddi. hac fssml ex aula
formula bX +. X +. x +. X. Hoc ut tentemus, sit bXx + ccx+ d3 intte
Itaque re ut reddatur productum deprimibiliter ex trahibile puematur ipsius x
valor talis et rationalis, ut nominator sit quadratus e non assurgens atera ju,
Numerator vero talis,  pariter et nominator, ut rxte non assurgat 
non contineat in valore irrationali nisi  Ly+. y + y; et numeratir
Et 2do valor vero ipsius bxx + CCx + d3 sit exhahibilis Hae–
Haec ut assequamur fiat primum brevitalis eausa. X = lyy +m,:gu
ila , prior conditio obtinebitur nempe a+ =tE+ y ( C) Vyt: y
sed inu et posterior tentanda est fiet
i x = buy + 2blodyytom ∞ fpssy trofyy + an
Cc Ex = ccl. + ccm.
 = d:
ergo bff = bll + ccl + d seu f= Sbll+ ccl +d3. b
rursus 2bf = 2bl + cC sou f = 2bl + ec, : 2b 
Ergo bl F ccl + d3: b = 4bbu + 4blcc +C,: 4 bb. seu fiet
GbbU + 4bl cc + 4bd3 = (4 bbH + 4bl cd + ct. sed ita evanescunt quaesitae
et nihil est actum, nique adeo hac via obtineri ex trahibilitas depressica potes
ot
Faciamus ergo _ X = lyy+ m:,  gyt mytun, et ita  ert
exte erit Setoyu + Ency + enn:, ytn.
a yys tenye
super est ut sit
vel faciamus X = lyy + mmy+ n: gy fiet Sx+C = (t ejgyommy+n: y
b yt Xx = bUly + 2blmmis f ibn yy
+ bm.  + 2b mmay+br
cc X = cel.. + cemm .. + cen.
..
L
bpe  + 2479y3 + 26pV gy
+ b gt yy + 2699y + bp
Quae frmuila aequanda
quadcato a pyyty+n ducto
in B, lyy 
ly t mms jus 
+2l pi tumon  By + 2X py
+ lpp gs t mmpphs 
Ergo sit 49  Y6 = n6 et gu vel siplacet ro - n et qq = mm
et p = 2bl + cc,: 2b = bu + ccL + d3: B. Funde (4bbl1 + abl cett E =(bb l + 4blcd) + 4bd
ubo inciditur. in idem inconveniens quod ante: itaque faciamus,
 X = lgy + nmmus + 13: y+p, et ut interpretemur bxX + cc X + d, fint
ypt XX =  blly + Eblmm y3 + 2bl r yy
+ b n+. + 2bmm Ry + bn
CCyt X =s cel + cemm. + CCM.
+2cc lp +2cemmp.. + 2CCn p.
+ cc. Lpp. + cemmpp. + ccr pp
dg. +4dp +6dpp. +4dp. +d
 per compend.
aequ. quadrato a qu tryt
ducto in a
seu
(∞ agy +2a9ry + ragtys
art yt ra ly
aeus i  taggy + a hy + d a R ∞ agqust ragrus traq
13 = (+) 1 et rr = 15: 2+3 = (+) h: 2k3)
a72. t at y ab
un eex A+ +) 1g+CK +  9b -= 19b - = s’KS
s
Ebmmud + recrep= cemmept 4 D p3 SoulAd
= +ce + (+) 2eH e + (4) Sh: qeK illium temim t rcclp. +ad, Son t Cp
seu + (+) 4 ek g = 8 eeK F fh
2
+2
fit g = +e et 1r = f. 29 = 75: 2C 7 + BK = (X) etr vel 4(+) 5N = + eti
(+) ek AAa
seu 6. Ne autum calgulus Sit X- veo
tit (+) ppIo = F C
vet , adeK3: pp vocemus r
quasi a
tas perinde ac si l et l essent date. Iu f est y vel mon
alit
n
EtG Endem itatabe
inde derivatis aqualitaltina  siumpitur ex hongeniorum ipte p oc im. Hine rilile pulo fima raons ris pt
liter
quar
aqu
Ns ac et i t   eeS   tontrad m da  nbim