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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 25
# Folio 1r, page id 00068070:0001
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eopeem litora
Resolutio rationalium fractionum unius indeserminatae
 respectuetus rationalium in partes, se maxime simplices respect indeter secundum ipsam
le 1 ay.
b xtdC Xia Xrb
eta, xib Xtb xta  a. b
(+) . ..,  =  - L, 1 -.- 
Rta, xe
xta, x+b, xtc
Xta, XtC Mb, XtC
seu fiet xta, xtb, xtC
XtC Xta a-c Xtc Xtb b- c ) a - b
XtC a- c. a- b. bc Xtb a-b, b-c xta a- b, ac
ba-at R + 1, 
Vel ut omnia enuntiemus homoeoptotos
xtar
a-
xta, xtb, Xtc
Xta, XIb, XIC, XFd
e
Xta, bia, aC
Xta,  ac
Xta, a -b, auc, a- d
Mra, aebactsga bud
Xta, Xeb xra, A. b Xeb, b a
Et similiter
X+b, b. d, b-c
Xtb, b-a, bac bad XrC, Ca, C b, C. d XFd, D. ad .b, d. C
a + aa
G22a J. 2a + aa =X  xra
73 - 3aZ + 3a - a = XX + 2aXF aa = a = XX - ax +fau - a
XROR sit X+a = Z fit X = Z- a. et fit XX =
Ac et similiter X = Ei via  a
et similiter X = x - a xx taax -a xra
=3ax3aa Z
Et ita porro.
dy=, smX +a posito V esse rationalam ex X
itaque resolutio est absoluta
Sit jam summanda quantitas de axtap
nat Huc enim
Sit jam summanda quantitas dus= Ax. V smxta. sit  t Cet
bxtap
sit mxtan L
bxtac da
omnes quadratyrae Conicae revocari possunt.
) a(ZZ- ar et dx=
aamX + an = bx 2Z + a(7Z. Ergo X=
Ergo dy = V3
aam - b73
C2ab CZ3 d2) + 2CC MZ  + 2abc Z3d3- 2a bn Za
(2) - b32+ aam
seu dus vZZ 2v7Z aZ, em -b2
lEt b22+ aam
Reslvatur t 
praee
b Faam racsque - ac dn 26
(2- bZZ+ dam
1S. v= aa. X fint dy- 
(7) eb 1X raam L. 2aim
1: 2a tm
AXC BZ aim, Zibraim IZobtom, Esb =aim
(2)Zib- aim b7- aum
1:2am
rarm
posterius ilerum resoloi potest s nam v. aam 2b -aim Zibtarm
1. radm
yb-aam
gobtatm, Zib asm F. gsbratm
Ergo - 1: aaam (- 1: +aamm
1. gaam
b tata
siri Ro bZZ scribatur coco, et pro maa scribatur hh, fiet. I: () coco- fihi
(elbZ2- aan (217 1b -aim b72- aam).
Pscocontin = aht esconti cocatito  corhi
Ergo sit estu. naa =  Etebaam BEE. na   2b r ami
e)  1: + mar
sesoren sebreta
cZZ aan, aam. b2
(A) 1aim - 1. a im. Exquibus prioris summatio datur
14 b7Z aam
(25Zsba num, btaem.
Resolvatur (B2 ma
Jam 
 denique quia
iml + +naa rmua + 1: dma sa
at
o eir
v tti  et coct coth fiet
 1. 8 ma sm
2
1. 4a
bz Z- dans
Ad usum quadraturarum