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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 43r, page id 00068000:0085
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et q
ubi C et noccurunt
mm + rr = Il
pp+nn =mm
pptrr = qq
tantum semel nm = l -rr sit m = l+Y, f:a fiet Ur =  r, s r, ffiaa = (- r
seu n 47af:, aa + m = Y, aa +f5 + aa ff, Sr: faa 15, a), seu
y e. q ae aa aq 
et m = l, a a Aa - 
m -I, ds 1t aat A
Aursus
pp = mm-nn sit. p = m+ R, g: a, et fiet
m+n, gg: aa = m -n seu miq + ngg = aam- aan, seu m H, aa + g9,:, aa gg
et p = R, aa -99 +aa +g9, (9: a): aa gg seu p= 2ag, aalgg, denique
seu p= 2agr r, 4aagf
 pp = 49- rY sit p= qtr, h: a fit, qur th.: aa = q- Y
i seu ghh + phh = aaq - aar Et fit r = q, ua hh, :, aa +hito e
aa ff, an tg9
et p = 9, aa thh +aa -hh, hi: a):, aa +hh, seu p = 2ah g:, aa +hR
= n, aa +99
Et ob duos valores ipsius M fit l, 2af
aats
Et ob duos valores ipsius Y, fit l, aa- ff=
aa +f
iinique ob duos valores ipsius p, fit n a ad
2
aa 9d
aa = 99
seu L=
M
9, aa th, seu-
ad +hsi
=9, rah, seu n = a h, 
aathto
l= nO = qd fit n = 9d: O = 98, fit tandem D = 90
Ergo
aa =hh, aa +f
a Z= un = ay = nm = ax Ergo ax = mm - nn + ay = U- ay se Ergo ray = H +nn - nn
ax + ay = U
ax + az = mm
a aytaZ = HM
Ergo 2ay = U+nn = mm 2aX = U + mm -nn 2 aZ = mm +nn - l
ita ax tay  2ax + ay = ill EaX + 2ag = 2mM et 2ay+ 2aZ = 2 nn
ax - ay = pp ax - aZ = 49 ay = aZ = YY. Hinc aZ = ay -YY = aX = 99. fit ax = (ay)tqg. rr = pKt ay)
Hatem 1 G9 = x Y + pP
ax =  tay  aZ= ay - rr
Dx= ay = pp ax - aq = p (A3 7 p X ( ay) t 1Y = 99
ay  YY
Ergo I1 +mm - nn =, ay t pp = Zax Mm + nn - Il = 2ay -2rr = 2aZ
2a9 = l+ (ma) - nn - 2pp = (mm, + nn -U + 2rr, et fiet U = nn +pp + rr, seu l = an +99
et ate nn = mm. + p p
Scupirest Lay = U + nn- um = llamm-un tpP et fint 2nn = amm + ipp seu nn = mmt pP
Ergo res reducta est ad fres aequaliones gq = Yr+PP et q et II = nn +94
seu 99 - rr = pp et UF nn = 49 fiat fg+ fr = ap et nn - pp = mm
aap
fiat ffqs ap GAr = sp: a fiet f9- fr = ap et aq + ar = fp afquaf r afgt asr = si p et fiet
et fiet 2atq= aap + ssp, et rafr = fp-aap
seu qu Htaor et aa
fial ln = gq: a fiet 2agl = 9g9 + aaque et 2agn = 199- aaque l.
Ergo ragt = 2a92 afl= 24 f999+ 2afaaq seu 4aa fgl = e (99taa) (Ff r ao)p seu l= 39 taa sptan 
Et 2a92a5, = 2a5994- rafaaque seu 4 anfgnr = (99 - aa) (55 +aa) p et n 99- aar fstaap +aasg
Aaa fg
ray = 2aX -  A seu  ray = mM rqg P EpB H vniue 2a2 X mm - 9c
(2aX = TC + mim -. nn seu 2aX = mm +9
) et denique raz = m 94. seu 2ax = Aaa fmm PF _Sp t  + 2aa BP et 2az taagnu spp. a dp. 2ep
4aa f)
raass u t P a dpt F ep + rausseD  astet
El 2ay2
daaff
(
Haas
aem et p= hh- aa m
rati
ex 4 et b fil A = 98P- aa, Hi aa hd laa = (ex 5) hh+ am. Eno tandem D9- aaffica, hh-aa = Aaafg. sntua
2a6
Faciamus h=S fieret gg aa. smna 4 aat
8∞3fgh
sed uliter aneca n = m+ pAb fiet nm Fpp + Emp D2bmDibp  mm +pp. unde 
Faeciumus f 2. lob. idest _ h~ 4.
fiet m = bb = 2b p, : 2b - 2p et, no (p. b) 2(ba p) +  2bb + abp; c Cb p) -  abb  ps bp tubp p P. 
P
ptb.D
Et n =: 1b -Ebp) +. 2bp -2pp -(lb(t 2bp: 2b - 2p seu n = 2bpa 2pp -bb9 1, 2b ip
site m abp -. bb, :9 2p - 2b et n = 2pp + bb - 2bp3 :, 2p - 2b, sed supra n = gg -aa, f taa, p: 4aafg
et firo  tandem 2pp + bb - 2bp =. (99- aa, 55aaa, : 40as9), 2 pp - 2bp
J seu r = l, aa- :, aa +
2af, aa- 94
dat H, aa +99
= O
aa-vld+ - )
aa- aa +hk
 C
G, aa +hh