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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 93r, page id 00068197:0185
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Proponitur (XXtab, Xx tac) x = aydx summanda fomila quadratuera rationali. sit
Xi de 1O+ SD, 1B fiet xx: aa = ∞ + D+ 2D:  eff  O500
et dx = 18d0. 16 -. 014.  L g_ + 1YdD: sD - (Dd q. : 28. vocetur O+ D- t
I fict d = fg- 2aG:C
b+c-pC
Eh+A4D +4 On = ff0 +  9) CD
a+
e ad +..
aest et  a
et fiit faath. Fqaa OD + afgih spatih + bc Haq + abC aatit- abe atgete =0
ees
ee
dov et
 4bc - ee = - qu (b-c) fit -d et fiit: dd aaht + dd asyt + A aa CD  asse- agq D + effe
fietis
a
et
et Cl
seu 00
quatu0- quad
e
(=0 jam D-t
t ddee af  Aaa (D B + 4ane e0O = bc ft =0
doaa
u
dd + ee =, 2bG + 2CC, sit (2bb+ 2CC) aff  Z
piet Gt+
aiqu
ddaa
oeaa
aa dd
H, ubi l’est constans
au
t + uf- 8 leeffo tise00
Bletf +16500-16edd50-4bc ddfc4 ad) lebet posterius aequationis
4d4
O
107C- dd)
lf4
 +
lf4 - 4bcddf
16 (ee- dd) aa
fiet 
latus aequari quadrato
dormo tum
aall abcdd sed ita eganescit f et res reducitur ad datas
contrihus pothesin
16(ec- dd) aa 
videamus an rem melius possimus consequi,  si non facamus H = g9, et
resumamus -dd aati + d0 afgt + 4aa BD- ase -aggd +  Ag (bC: ee) et pro D ponendo 
4 qu (e .dd)
ft dd patit d acut qua F () in Aaa dD in (B apat tg  fgg(bCo) =0
 +fd
seu -d aa d = dd aa D= 2dd aa 0D + dd afg = dd a5g
et
  = GaOC) + 
ee
ee agq
+ qua 1D+
∞ Aaec- 2add)(D 2gdd-Bet) 
1. 
il
d eeg
d
agalu
1D. S
aue d dd
ed et  (add- H∞- atu et ddt G aDD abili tc bb
et
compandio sit aca e t2add= mam =2a B D2acc  - qubc - a abb Ladce 8lbC B +b
et fgid seec aatm Agdd + sec = aux et +fdd Deet= p Aaq. na, bb toqu)
00aG tatsooru et fint Aa CC. + aa m D + aapf
afO = aggD
seu
ea
tumDD + 2am pfD ra pptS
i 4d+
ammDD+ 2umps+ appff, + add ag - aad 1D = 4ddg aaque D + 4ddbc ffg9
dd
a.
pa
quod latus posterius aequationis redienduum est extrahibie. sit samm aad = a
et 2a (mpf 4 2dd94)= zat eta ff (a pp + 4ddbegu= ffaes,
et fit CaYDD + 2a tD + ff aj  aequ. quadrato seu 9D + 2at D + H = quadrato
delet esse aaH: rr = sH: Y seu matb = r Sf
e
Yth app+radobigque = rsff
aat= aa mmppt + 4ampt ddgueq. + 4a gg 49.
siet (anmpx)L 4 a mddpatus + 4 ad 29 4g = rpost + ab. dd Hgg
app= d f dgq.+ e - 2dd eefg Et explicando petque Ca mmps. aci
 duf + gg - 2ddeC5)
hit 4amedtu (dd ec( +sg) - fy (d + C 3) + d (d stregus redee tu)
ac, + ddeeft + ddeegus - e +9
nqLst ui dividendo per 55g,
 aequ. AcrbcddHg- (d +e-2dde ef9)
+ad ffg9 + 4ddvg -9dvefg3= Anammbetsgu
ubiue habetur in nisi P.d ) et q. f, _ sit apF Y + ) - 4 AbCffgu L D
fg9. dde28 eef9 aaerc
t tiit 4a  X+4a SV+ ad = gaerbedd seu 4anV + yV+ dd~NK = ammbc-44a 0bC
it  aidit
 tere
.a
94
qu ultu are
a p9= S