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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 125v, page id 00068199:0250
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y = + (_, X+L, XIm, Xtn). quaeritur extractio.  productum est a X 1XX +m X + lma a quandum quadrato
sit x = ( 100 ( + 112 (O. erit XX = H1OB.vo GG + 2. 100. 12 BD a N -100 + 12  OD, ac
+II2. 112 BD
compendio rmen vocetur p, imtinama vocetur aque
310o. l  +3L 18R..
Quabratum, lum quo aequatio institui debet, sit excitatum a at 2O ta ZD, nempe aa BO + 28 1OD q
+(WE
px 11 1agu   + lmn = = aa  aequ (Grs
troa W0op
l+ 3 100.in9BB ∞
os
400
P0VZPOY
A qui
Eoosntg
+ 05. 100a9
00
1.122OD) _F 1b ag
-
C
a
+ cc8dua
 aa
Q
 20 a8 1()
P. tatos
Ex irrationalibus
aa2
Fiat 9 = 102 +ua
007 = 308131a
O5 = 10. 30 2 9. 10. 3 (e 8 1979
11.30
004-204+4a
300. B0100. 100. 112 ZC + 20 u s ev. 12 p C2 +00. 80. 0002 OVaq ~ _2. 0020  + 2. 00. 1aa
1. 10.30. 12. 112. 112 Q 1. 10HI J. 1. 112 a Q + 11. 31. H12. 12. 12 aa
fit 3. 00. 170 + 10. 30. 115 =0 vel 100 = 112 1(- 10. 30: 3): a  f20 = 2. 00. 100. 112P 208.4 = 00 aq
200
11. 30
in Rationalibus ot evanes cat e3 fit ve 00. 100 43. 12. 10 30. et 100 = 1 (3 0 ) . Wu. 31G ,112 a
Ia 1131. 113 aa
quos duos valoras aequano fit absundam, ha3 Ex Btionalibus Talisergo Hypothesis non succedit,
184058 + 0op 4 + 0. 100 age + eo lmn fat x= A  +4 +On
3. 1V0. MIGOD -15. 100ul 10 to Y + J. 1 3L vort a GQ + 3. u3 s 1B 12 aaq in p halebimus 8 et 3 0 tor
1. 02 M2 8
sicesit in tat Aa latus t + l2 Y(D tytu +2t4 SOD
X = 85 + AVOD asentit ad 56 . 1 ti D sCD
2401
si Latus SVZZ + 7h+OD, ascendil ad 513 775B, (t Y 1GG0D et Si B131OD.
ut ita demum institui potest comparatio
sitonditur ad sextum gradum explirando omnes por eandem; Euso opus in parte rationari 7
7. Cgq. in irrationali ryque 6. summa 13, ad literae autem sunt 1 20, ob 10 variantes simplire
caetem prom et ino liteae ob 66 sunt tres, ob 7Ihes, ob 0D, tres sunt 9, sb 5.73, 4.
ob 73, sunt 3, in tumma 16 ex quibus etiam binae videntur superfluae
deberent. +46 +GVOD, et 46 + +D habere divisorem communem
s
N7 = +95 + qYOD  sZ = 4 + t (OD
+m
5 =. 103 + +07Q. 192 7 - . 107+ . sDE 3 -. 109 +. +94
517 in S 3 in 23 =  sst 7733, 517 = X I 5Z = X + m 7B = X + n
debent aequai. S  - l NZ -m 23 - n Hoc maxiinc succedere, debere videatur
et tamen non successit: ine si N  = NZ -mtl hit _ 7 = Z + 
 
et p et pari jure S Z = =B +H- m fiit s = Y +H m
S - 7 =   (it  addendo s0 -3 - l-  +
m. L
et pari jure 6 +3 = s B = n -m et 2 -5 = n m Ergo FC s - X = lam _n - m - 3F
= lm
Z
  108+ ADQ in a1 +OO + 12. 15Q debet esse, 11 = 31 - 21 et 12 = 2. 32
XL+ IaKA CaX + CNNEX+N =21 +C. 2 194 ita productum fit rationale. Sid hoc fieri deber adhuc semel
DO constans et si O = 10X +M a ut D = 20X +2 a feret 11. 1 - 12. 20 = 0
X taLLI ax FM2a X + AnEXXL (Q ax HL B. . 32a 3(31. 35. 10 = 31. 20 Ergo 10 : 20 = 12: 11 = 31: 31
10X + a f - 1
sed pari pne ficot etium
fiet H 12: 11 = + 31: 32
30Xtta, 20X + 2 a, 30 X131 10X - a f- 1
c
aXX 12210.
I1. 2
10XFIA 20X +21a IOX tUa, 30X +31a
10.2DXX + Z 1WX L L 10 sXa t 1N, 1dXa =na 10 exa +na -10 tx a + 11a
10, 10XX F2, 10. 1a X + 11. 1a4 20 20 Xx +2. 20. 2 ax + 21. 2 a 2 0. 31. y. ( X = + 2. 1511 253IX 411. 4. 3
to Lax La 10X 10. 10- 2040. 30. 30 X 2.10. L1
110. 2021 3. HX + ~191I. et H p 2. X +2.
deona, XX + 2. 2 ax + _ d. aa, _ Ax + 231 ax + g1 21 ai test et 3
u
2010
Or  2. HiloaX+
1.3
3
10.10. 20. 20. 3030 X + 2 1  +2-10 1 21
ex
a
XX+ uax + 12aa
XX+ 2laxtmaa
I1. 2 auX