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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 87v, page id 00068198:0174
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Qvaeritur ax S(tabM + aC) sit X = lal + Jan Ergo x- al + rata  et
xyy = cappt pflu
de
+2aab
In =yy = qu (apt filn)
+rafp sln
quos duos ipsius qu valores coincidentiando fiet ex irrationalibus aequatis sp = 2al. + ab, seu p = c (n) + ab
Cellatis rationalibus fit aapp +ffln = aa l + bacln t aabh, et explicando p fiet aa Utbactnt aabt = +aa l.8 au tu+ Y aa b l. + aa bb a
seu tuta ((I
44+s un
+saaf In + aat(b, l = a bb
= Ca
8a
alberu taesc
un-fslu
S-a DC
5 + 4a af + 2aaff - ga dividi potest per fs- 4aa, et ideo fret
C’ac
aa II + raa In + aa bl + a bb + = 0 sit H- qua = ag firt aal - at tanst. - al - 0
nn - ff
ff. 4aa
Sit +aa - f5 = ag fiet  aH +4 un +  abst H aabb = 0
in = 
AS  d N1 = a 1. 2 - (129) (   -= p 2 - d1 Ego d 1 - : 1 43
lvco
Si aquana hsfe- ageraaac sobb
Y2, dt 120+ Y2
F pro aequatione C scribamus 120ll + 111 In + 1100t + 100 = 0, et Ponamus
Fl = C v+ ae m = 9V tah et fiet +12OCC DV + (20 ecev. + 120 aa eCC
v +8
vi
Ut tollatur ve abetuntur C at gsi
erit relatio inter c, 9, a
ut tallatur v prodit similise
relatio inter e, h, 8
denique ut tollatur v, est prodit
relatio in qua se habent c, g, a, ut e, h
120 ggvV + 2 120 a)hv + 120 aa hh
11I Cg vB+I achv + 1I aa et
111 agen
110 ac vV + 10 ac DV + 110 aa C
ag vV 110 a g V 110 aa t
110 aaev
pa aahv
100 aa vv Zrv0 aaGV + 100 aa 
consideremus
aequationem 120CC +gg. CC +g9 + 11I c9 + 10 ac + 100 aao divellamus in
120 C
120 ag
vael (ec  gg ibi si esset 11: 120 =  - 2 firret 9 2a, : a = - 2 seu q-0 quod
non licet si faliamus 11: 120 = 2 fiil AX q 2a, : a = 2 seu q= 4a, sed ita foret
f=0 quod eliam non licet
4. 12010
2. 120
2. 120
jam siC 1II. 111 = 4. 120. 120 = 99-4a9+ 4 aa- 40a ergo faciamus 124 10 a V = cc nifiet
g = = 111 c sed si eodem modo tractaremus e et h, fierent l ipsis in proportionales
quod non licet ergo quia e in V (99cC = 4agce + 4aa al) sic explicabimus, ut
sit qucc 1a (9- 2a) t+ Aa H et fint Y (4qce taqce t aacet 8. 2 (q.2a) acet
+a =, 4aacc + 2(9 - 2a) 4aa p = aaa aatt 40 debet esse l 4C =  16 a  D seu O = 4  ) D
in 5q. D restat
2a
H0a  + 100 aa + alp. ( 20 = 110 4C+ 1o a + CC- 2(q. ca)C L + H
su g = Bc 1  H   1 eC (9 2a)et + - (+ 1114. ic 4 et
ab 
seu _g = , 1b lac + b (an) + cc - 2. 20 et 11 2 (4, - 1) 22ac 4 et
=A_ bb laa) - ++ = + 2t, ita habebitur 1t qu  rele aequalio divudi potent
per c. sed per istam excerplam  non habetur ratunaliter
habetur quidem q, sed eadem 9 postea ad euc semel invenienda foret per D
quando h et e tractabium ut C et 4
in eri pota alsumemus +- Y C, ut evanescat cc. id quici ita Y salte irratimaliter habebitur,
ideo praetabit aequadem si relinquere qualis est, et ope et quaerere 4
ergo = sit D = a ent O = AHta, et pudibil 44e1p = quacc + 2(9. 2a) c. 4at + 4a4 Ht - +aa, ce - 2( -1) c t , 4 2ua, ap
et hit 1 (99 Cc - 4 aqcc + 4aa cc + 2(9- 2a) cgut + 16a aH) = a (9- 29C + 4 at = 96 7 2ac
seu g = +
obi faliendo
Fa)
ce + aY seu g+ 112 C = 1(. M 4 1o nocC + 3 1 10a p) - (9geC. dage C HaB) e11. 0 C 1M M1 seu seu 11- 242
 scribamus ergor eet gg + ut cg = al
et fiat 99 + 11I eg + W. 1I CC = MII. 1ICC
120 4. 120. 12
120
aab
Zaa
et fiet n =
seu n-
2aa
(2+3)l + beg 4 + b ba4a+
 n 
+ 1+ 3V
=Eaal + aab