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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 9r, page id 00068197:0017
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st Xea=   +D, Q sit XX = 0 + D + 210D, _, et natab  sit  = O+D et e = b +C
 abeolatit + aaa C + 4aatue 10D -9 gy Ubi explicare oportet item assumtas, ut aldi ipsius
taeqt
+2ae  16D.
00.00
QZyy fiat extrahibilis: Assumatut OD= at
 et 8= 10Z +ua, : 00 
gus aat  raa sat q +aat
1y firt 4Qgy = 00. 00aa tt 4. 00. 00 aatat t +4. 00.00  compen
quaeritur quadratura Rationalis prosummanda formula XX+ ab, XX + ac) x = aydr
 Orellaaeat.  ml- t  sist XX + ab Xx + ac = at +2a 0) +b8, at + 2al OD + CZ.: 48 = yet multiplicatione facta
Et ex p
10. 20 bc hh. +210. 1 aBcK t + 1. 11. 11. aabc
00. 10a et + 1. 00. 11 aae Y
compendio = mtir + nh + paa
+2. 00. 10 aerat R +2. 00. 11aae Vat
itaque erit 4, 00. ∞ aa +4. 00. 00 aet = qus t4. 00. 00aa tat
10. 10 bc. F1. I1. 11 aabc
+2. 10. I abC
00. 10 a 42, 00. 11. aae Vat
+1. 00. 11 aae
12. 00. 10. aetat
00. 117 H
et multiplicando actu ipso
quod ut aequetur quadhatet, fiet
a, Gt+na t +  aap
adeoque Amhtur natitaap)= m, Et
1400.00 a 400. 00 D+ 00. od a 11. 1 ab c B0. 00a aelat u 4600 iac
10. 10 bC. 4. 00. 00 aa t( 10. 1 bC 11. 11 abc + 10. 10bc. 2.90. 1ae Vat) 4. 10. 1 bbccae 
(00. 10,90. 400. 00 aat+ 00. 10 ae 11. 11 abc (4 00. 10a8. 2.00. 11aelat
+1. 0d 11 aaee + 160d a b0. 10
+400. 10geuia
Unde destructis destruendis fit (11. 11. at + 4 18 aC) (abc + ee) 
Be abc = b1(C + 2bc Abe = bb + CC 2bC = qu b. C) =  ttr fie et set ua ato quiuui
Ittaq+ 1 ( a 16na es alet 0 
11.N + 2. 8bc Vat 11 + 64bbbccat- 64 bbccat = 4at atat
10. 10
ahh. 10
aaha
atgat
et liet 11  qtat,  abc  V(16bbcc - h+). jam y =
purro y-, tr + un a, 1ot + na. Compendii causa ut m fiat valde simplex
R  409. 00 a araL = 10. 11 abe-2(0bge sa
d tac
e bes 2iaavat, lin (ubc. eo) - eeal; hdibe posto q re tat. al. L B2 = aaq
Zmatba Intum cosreiaRii be
et y = 4(00. a GnGi, 10t + na et n= 400 a v et 1 = 2
pollumus, facere (o. 10
n22.B uat, itoac
6bb ce +.) at
oss.
videamus an tat ab sic assumere liceat, ut pa lor ipsius n contaatur
et n = -4. d à dat 2:-
qbe.
iitaque si laceremus 24 ate
Del (+Nl6bbcc tor 44bc). + et
Dn  betch 1 ee (+ Hisblic) thh + +bC)
ecifinet
caiat ) 
orpliando u sitar dobali oucertei cet nadt uu meatremu,  i derea atvet
( +
Pqoiat abt . od. ae ra
et ( (tn =  abc taslla a  elibicet  1. ab.
e 
n = 2Vat 0 = 2 Re(G ebbbCc ht + abc +hh)
(16 - 
va n = 2aa fat, - 2 - ee (4.  Fet
seu n = 2aa fat, -2 -ee Y (4L F F
p = 2aa tat, - 2 hh b
Atibe
i
d +4 + 
boce 
(1 = Y) +.
ee (_ F, (16bbc C -h) + abc +hh)
bbbe bE 2bbcC) = (DbbbC - (a ccC (8 bbec = b - ct ( 2bbcC
 -(bb +CC) bC, lb bib qu (b+C) +bc
 qu (bb +CC) = 5DC (bbF cC) =
Nouc bd (cc b C AbC + 4bC (6 bb c)
gu (ob- qu (bb cc) +bc u (b+ c) = qu (b +C)
16bbcc h 4bc + tih, 4bc = hh = qu (b +C), 4bc = qu eb-c). Ergo M1bbba h)-(b+C) + bC6. 
edes
A(ebC = sgit Cb CD) sit ium limilatu vt erid dy = 4 b dc 44C db = ZCb+G) (2b - 4),. - (abc- qu baG
en in hac curate o eailionem ab: dem vis b limituu. Si altentra costansse voines cit db
et fiet nnaa aap seum
at, 10. 1b cL. 9. pl bre s 1 a
at 00. 1 40. v. 1abe voloP
lat
snlatae
bcotat
00. 00. a Vat. 10. 1 (ee- 9b0)
unef haieit
2.1 qu e dat
4 aaeeat al
unbe  eeat aallte
hbbec
itbCe)  00h1a ces. bC
cest carja 
sun
 i id e per differ
tiatem 
siet q
ie, dec
sn
rotet ti
(B N sed cum mul  dicuc
methodus
vinimus
entes cessat
manimi
differentialis, et
recurrendum est ad liq otr
ensa gua bb ec
he R 5,  et.
i diverri cadi
Aatene, in paginabias iat
: nobc
itaque si dapes relatio inter b et C, uli es
 in hac cuto ahe   ab de  eca blimitatu s allerta cpusse   et