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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
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ic modus reducendii curva conicam per duplicem viam,  generalis ratio omnem
commam irvibionalem quadraticam reducendi ad rationatem
 a X + bX + cC. = a X + 2 ab X3 + 2aC N2
conferatur datae
(8)
+ bb XX + 2b ccX + C)
ext + f X3 + gg X X + h X + K4
et a2 se V t ceR cc= YK
et S9g - seK+ =b
2 l9ge - e set = f
bofrete 
Epp Yi 4
 prietirqx
supersunt ergo duae aequationes
et 2 YK 9g - K4 s eK + = h, adeoque ex 6 et7
adeoque sla B3: f = s K: e
sit jam aequatio ad curvam conicam
Iaus Semm. = nyy = co. fiat.
mm= yy
Co p X + 49
D= X + Y
ft e cm nyg mm-nyu. mm yy  m mongus + psmrramextbX+ 
mrgu
= mmnyy
Videans anliat Hujus fractionis Numerator
ponatur designari per formulam 2. et fiet: 
p6
137
irq he = K f.
Ergo
ut
Ex 8.
4mr3- m tnen 2r9+ 2pgr +aupq
chtr marXm  +24X IYX
+H9 F214X Apark
8G2pq rX L pprrXX
n+onpaX+qXtanqX +n BX
D) X 4Y
14
m - pp vi in + np =
= mr-rm ion + nq (( amr-mmprp. a +pY + 4 np g
Et una ad huc aequatio (15) ex aea. 6 explicata.
Quod si calculum retigere in compendium placeat, nova suppositione facta.
+
faciamus b =0 fiet f= 0 et h = 0, et ob b-0 fit g = ek sed ita pro
tribus equationibus non sufficiuant tres literae, quando inter se servant legem homogenecru
quoad incoprita nam gque tgmo pro pualitera quasi essetat; ita enim in effectu
nae sotum sunt imognitae _ K P: Y et 99. ar seu p: r et L: Y
et puto rem
succedere, quia in cognitae non solae servant in ter se legem homogeneorum
ita ob d ob 17 fit r= q  pqt m 4 mn - 2 npp: 2m - m pp- minpo
imil ter ob 18
sisitum reperit.
y habebuntur aequationes.
Sed calculus en protixior.
ita res utiue
Eu ergo aliam
viam simpliciorem, torlamus in forianta 12. duos maximos vel
duos nnimo Qumeruloris terminos, et hrabemrus depressionem
nfingos
ab X ad X. Ut si tollamus duos infimos
potius q. rr
l f21)
fiet mr +ng= manen Yg
ita habetur  vel rr per aequationem planam. et 4M  anpu=m 
et 4m  + anpq = 2r4 + 2peet r m + nin et habetur p; perrationalem.
et ad huc in arbituo nostro, manet aliquid, quantum velimus esse vel er vel qu
modi havem earum proscriplam servenius
imo quod est maiqus sublatis hoc modo duobus terminis et xt depressa ad
XX, licel potro XX  deprimere ad X, et ita rdeere omnem indetermi
galam ex radice eximere.
Et generaliter hac methodo pergere licet
lam in radicilu universalibu reducendo eas ad singulare. et deinde
ex singularibus red eximendo indeterminatam certe hoc loco
Ex oq. 2 fiet a L n n q 4 m itn = m in = m rt = mr it intnn - An = mY ,n
+nn
aun
ann
ann
4(29)
fit q- mt x Fa = +m p n seu g3) mr c vel q =  nir vel 99  de
Su qu meti
ex aeg. 22 fit  in 69. 22. substituendo hmr in locum Bubi h = H1 vel. sn)
et 4m + anptom = e  2hhm + 2thnm + phG 2phm F Eptnm
 P = 2m = hh m - hhnm,: h + Dhn = 2n H, ubi posito esse A Cx h= +1 fiet
si facimus et sit
X P = +M i-n: 1 = n seu p = + n sin sit n- sn
y = +m X4 + MY,: X+ Y quod est absurdum sit enim y= t Ergo 6 dentemus ad hibendo n
fiet qu
rgo h= in fiet Am + n sn P = Lnm + L num + Xp In XB + Zph i
_ 2- n. nn: C. n+  rna et y BY m 1 n na X + mr In: X+Y
M. nor2an
seu y - p inmumn X x mrantiam quod jucedit
PPxX + EP
x tirxim
 + qt Xx + EpuX
sid
XY+2YX + X
9. +293f21117