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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 94v, page id 00068197:0188
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_ quaritur quadratura rationalis pro Y(Xx + ab, XxtaC)  = ayax. sit
= X: a = 1O + D, . se, fit Xx = 0+ D + 2YOD,: Y jet fiet
+2 YCD
XX + ab, Xx tac = at F2a OD +bQ, at+ 2a +OD + CL  = aagy
et Beyu = aatrh + 4aa d D +a et
fs sit & = 10 +ua, : 00, et fiet
+b.4 + 4aat 1OD, =ua 
00.00 uahue +4 vatatur  4 a t
10. 10 bc Gh + 2. 10. 11  + 1I I1 bC aa
00. 10. ae hh +00. 11 ae at
+ 2ae4...
Z. 00. 10. Ciutaque 4 2. 00. 11 tat aa
G=O+Y
C= b4C
sit OD = at
constanti
HoD = - at
00aa 4 = conpndi Mth + +paa
= m, th+ nat + Paa
debet esse p: m = uniamm
seu amp=nn
videamus an liceat contraher calutum ut sit 10bC+ 00ae = D itafiet n = 00. doa l +10. 10l + 00. 10ae =  a
et  et 11bcR.2. Doevat. =0 ita siet p = 00. 00 4a F F 11. 11bC + 2. 00. 1e dat = 00.44+
ogel ooetut
sed supra erat nn = 160G. 00 at, qui duo valores consentiant inter se, et positis
Vatoribus HD et H, quales assumsunus bit 160090 at = qu (00. soavat)
quae aequado est identica et proinde assumtis 10 et 11, ut fecimus sponte fit Amp-nm
osi ad = fati 2tat et y = =C: bc)4  + etat. bc) sed video hoc
non licere nam ita fit gu = aade: 88 aaee: bbcc, seu y = a9: 8 = aae: bc
44
ut in vatore ipsius d0 destmamus h. et t. ut restet ttu, f
3b. Tr fist 11. 1 = 2.00. 11 esat: bc) + 00. 00.  sat : bbcc) = 00. v0. Meente 00. 00 atbc, : bbcc
taque elsieim 
 et fit 11 = 00 etatu oosat, ee - 4bc) : bc sed ee - 4bc = qu (b ), et fiet
1 = 00(b +C)F + 00(b=9), sat : bc seu 1 = 200 Vat : C vel 2.00 lat: b
et Ob h. fiet = 00 a + 2. 10. 200 l_ + 2 00 ab: C) (+200a) -2. 00. 10C, = 0 abalinc
sed seu 1Oip= a = ab.c)  2b - e sen 10 =  a (c- b) : C (b - C)
en fit  oiadC, rt fit d = - (a: C) t + 2a :b) a
n C et
sed ita etvans citC
nam omnia in vinculo siunt aequalia nihilo. Itaque nec
odaatin ∞ Op a sat atu = vd na 2Q- ooat
hoc compendio uti licet
1.. 1
si siad
H. 11bCaa
+200. uetataa
fiat.  26. atu = BCaa) (2100.M C Vack lIbC = 4. 00. 00at)
A
=oat nbea L00. 11. nae- 2. 00. 10C a lat
et 10. 00aa D tolobe + 0esoetu  H + 
20a
et sit 100. 00aa Z: - v a) t
20a
Ergo om cob d mp = un fint 4 dota  (66. 1 bca 200. 11 etat a 
raa
1
de
10. 0o bc 4a t1. 1 bc a C 10. co. 1HC We sata
(10.10. 00a0 4u t  00. 10 1 aebcat 1 10. or. 1. e. eataa  4 80. 10 ea a
+Bonidria detat n tr
1t fiet . 00. ile a (RbC- ec) + 00. 10 a t (40c- e0)ebeurat
at ) det Bbea e
A ebb+ ce+6be 2abe taee hebe= rabe pabbive pabe ebbe bc
sendalleereti i na qu (b1) habeta luc)
1600. 10. 11. at Cabc 
fie 11. 114  1bact c 114+ 04 at. bla 64 a hbe  4qu (b. c) a, sia b. dc quasbs0 nti 
Earoseuat
b-C seu 1 F 10
4bc - ee = - qu(b -c)
sed dispical. quod 1o a I non tpacdantur eodem modo ee vertanasnes terror calculi
bbna sus bac)
12 a . fu 2b+C)
10.10u (enc) 10 subiqu (b -c) arbiqu ()
00aG tatsooru et fint Aa CC. + aa m D + aapf
tet a
oto. natCeehe htana
ratiC,S
et fiet amp =1. 16. 0st a t = nn: jam n = quo q val t 2,0. 1be + 00. Ha eA ooxetat dd tac. bbru
 et pro 10 et 11 substituendo vabres, silea  atat + a ve ∞0. P Vat aet 2id acerat
 per destructionem fit n = . a aat.
tem
400. 16 a tau -1600. 10. 1 abe rabt oa lai a pre
tq o. 12BN Ia eta  onto pe a
opaeuo io iclees
Crutnabb
prater