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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 68v, page id 00068197:0136
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Ex aeq. 9 datur LM = NP. Ergo hoec aequatio sepanatur
ponamns K = 0 tentandi brevioris calculi causa. Ergo ex aeq. 8. fiet S= -  L fingum 1 - 8 L. E+ m
imgo ex aq. 10 fiet
2a bcC 2 + 2 a 22
ae hon eu tanchno + rachi p + raach RR
-2a cts  =qualt b n 42 - 2aabfi mn L
ta
ut follaltur L et Q, fint acc : b = bfll: aa se acc = bbfll, seu lI = a c bbf
0
et m =0
Ergo sit R = ep _f- . sed  haec video postea nonlicere, quia ita LM et Np haberentur
per mera in Z
si tollatur geosen fiat aecc =bbfll, et ponatur reliqua aequalio extrahibulius, fiet
tiatque
243L ab lfm g - 2a abtum G +RR7 et volia delemus esse extrahibile aequadem
raact
2aach
aubfr bfrum = 2R Vaac blsm
hy aeq. 10 fiet (+2ab  24
ahq
=ra ac aXE)
si
- 2 acbs ll 42
pi T= E ff L) R
-4 abf.L n Q - rasibtum = 2aa cF h R)
et fie et extractio per se procedet, fietque Abf. L.9+ m = cR Y. 
seu R fB+C F: h), L2+m
Hic pro (contandis imaginaris, si b sit negatura prioieva, erit 3 posituva
et si b sit privativa, eut fetiam prvaliva. Vicissim si, b sit positua, erit h privatua,
at si b sit positiva eut f etium positiva. Itaque h et f habent signa autraria
superest aeg. 11. in qua Ntiam K = 0 fiet
R. 5) l 8 + 2 a h a b (.3
afH 2
RG l (a 3)
-2af a m
agbe
an
ah F bb (
+Ed min 2
=af mn qG
Ex 2. sisi p.  aaut. Aegebit, P, due
b alicm - facch +Llbgl, L3: hac
mosi, poaesrum a i erta
+ 6 agbb f I mns Z + a a g btst n Q + a
ah ax
Habenque ut luc extrahibilitatem efficiamus, habemus b L, et m
da
ace
celia
Si dastionemus 23, fieat H- (4 c5,: reg9bb: cehu C (1Z uetras ce haaf: 2 gffob. seu l-
Hic toli sensu h et u hatebunt signa eadem
aa
b
ec 49
Pestesta
les
29bb
destmanus jam et 9 fiet cca -  7 f hcc + 9 fibb hh f -o ita evanescit ec, et deberet
2966
in datis esse a = th + q fk seu 4a9 = 3th seu g = 3th: 4a
b0
itaque haec via non est permissid, sed sine destructione, tentetur an formula possit fieri
reu trahibilis compendio sit, 10. 10 Z + 00. 1 aR + 00. 00. 12 aa 9q. + 903 13439 + 00. 14. 14 a
un puoce aeq. fit hic gg   10. v. ni Z 14. 14 : 13: 13 Cs  = 10. 10: 11. 11, fiet
abgfm.
att
obilit  aech
dyb isfllm: Cttiaa
seu acch
bb fBumm
ag bbstm =gu. gbb m al stl m es biclll
acth- aThbbcell-aafh bb cell + gb Cna Bcchat
ccta
ahflam CC i affurm, a th + b g9 1 L 2a ab b ccghill 3: aBth et
Ve- L = a th - 2a bb cct u + b Zgl
atrae, aCh - 2a bbcc fII + (912
9. 14
s esse A =P
16f a cthh - 2albbCC gn+ (2 g9 H
+EC B. RR A2L = qu, be L. e
gRR
Moacoporeet u e
norem LM, et valorem
are icurant  sico
seu Y aacC, aa 2+ + abig R3 + atia 2ERR = bbcu qu CL M Xp)
Hic statiu sucederet ex tractio, si esset 2a ahg: ) = abcr atiq. 5) seu  att +a an (Hrg) iffiet taaahus: G = aahit trggui
ser + agf = hf +hgg + 25gh, seu A = 4agf: fs +99 + 2fa, quo casu succederet extracdio, et fieret
R((+) ag:, 9) vidiamus an hoc effici possit
indatis, sit  ad fa:Woid + aB, fiat W = A V, et siet apX VB + a5,:
pa et fiet
a
LM - Np, _ 6+bb: q = a QZ A R AR ((9:f 
et divident nominatore vel mulspliando finctionem per _: aa) fint as_  + ad,  ∞0 + ad
 ates pubi sim n ai ats e
+
qu, ropt
R- q+ p