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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 71r, page id 00068197:0141
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vellem
ttat d=
ande X - b =
Hoc omnia melius minore scheia longa, adjecta
Y, X- b, X- C) aeg, de primere ad extractio
nbr + 2h0 test aaff
a, vv + 2rV + rr
a. Unde
hhove alif+ aaf= ab (voruBen) hotas +vrriab, hutas (vtr) tab
a, vo + 2rvtrr
a vv + 2v +i
sihov dahisvtacts-ac Curturven) a) ab r af ver) tac
a, Wv+ErVI
a, vot iretir
fiat hv +af  -( +V) Yab, m = Hchv+ af- (∞ + n Vac, n
Ob v suc, hm - insab = hn-ntac, seu h = mn Lab - n tac, :; m - n
Rursus V, afm = rm Vab = afn = rn Vac, et Y = af (m- n)  (ntub.
sit
Un de hr = af. Et fiet 
V + af -7 ab ~ V+ at = rsac
ac
ha vab
et
Fh) rhi abasrac rabo ~ Castrttacera. 1
sed ita in determinatu, atiab
Th(tab -itac) exine seit = a f(sab = itaC)
siet rh= af inde X= hhvD+ rhhrveriti
a, notarotu
seu x= hh: a, quod non prodest
+mmab
IVV +2a (m-n) f (m Vab- n Nac) V + mm jaaf
ima a Vbc
x+
ave
mn
 L
un jaass. Am Dabu
Fmmab quV +2af (m- n) (n vab -n VactoH m
t un ac
-2mnasbc
Ascendamus altius, et ponamas X  quadratum a si at_ aaque
V+ rV+ at
o -2n
2mnib.
+aassus nes
roptraltxtaate
X-C, F) (nvtrrtat) = huvt afv raaque + (notrorat) sac, lrrtaseraaq (vtrnrat) Vac
e
intnab
hh_V + 2afs. V+ 2aaglaB
Vitus, cat V
X- b, L)CR_ F rrat) = lY tafvraag t (NVtrvtat) sabe, lwvtas vrang (vvaretat sab
quaeramus unam ex radicibus ipsius C), eamque ducamus in 6, Ed et productum in M.) Haec duo producta coin–
- --  .. . . .... et productum in n cidentientur
sed si haec producta coincidentianda sunt, necesse est et fria producentia aliquo modo
Quod si sucederet habetetu desideratum.
1
coincidentiari. Itaque cujusque ex C, D, S, G, binae radices scribantur, tum quaeratur ny
aliqua fiat electio talis, at tribus  ex O et 6, et totidem ex D et e electis, possu possit
quae vit ollis ex illis in constantem ducta, cum aliqua ex his, etiam in constrntem
(h + Vab) vo + (af + rVab) V + aagt atisab, compundao lur + amv raan fini dividatur per l fiet
ducta coincidentiari
inde vn +am B, aan vyVtp Hg= an:l q= amil -p pq= aan. 
qu aam. l si t: amp. Ipp = aan
vo + amp + aamm= aamm:  taant
seu V --am + gamm-anes
vico
au
seu V + (aS+rsab) - Y(aa H F rrab + raErVab - A(aaqD +at tab) h + Sab))
2h + 2 Vab
( la sabsam- astrsabe san= 9 +F sab
A =h - valit an = f- r sab
aV = ag - Yab
fiet v3 + a WV + aavv
+am - Hcaa tm - guanl) xv
+
ul
oo
+ a- Y (aaq Ana s P) VB
+ aqV V
ila
v siuper
vv + an v + aaV, mult. per V  am-aum  an
Mutliptintur
∞ = h- tac
assa
+aamarssiamm 4 aant v
+ na v
=4 
Etpu b 2
8= ag- H Cn au - 4aa 5p
Habemus tres coincidentias efficiendas
m, n, 
 
as
1
+ a-at (aage- 4aa CF) V + a a st at aaa Caagu dansp)
icexo agacor + aa vaco ~ V HaK. D) on t autatv. Db
v apeetaarv 2]
2T
Ex v’fit V8I = rCPK Acd =_∞ + BA: pA
2t +nco =2nKC Ele C
+a on + aak _Y + aatda Ep 2+  Efk n  N : K
u
br
nem ex prodine
=2mn
im