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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 177r, page id 00068198:0353
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068198&page=353
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 123 lines, status machine
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10a +, 11 d. sit 10a + 11B, dv. ponamusque V = vat. eit do = adque: tatu
20a +21V
fint 10a + 11 taque, adtue
20a aex at + 2c _t
20a + 21V
deu 10. 21 al + 11. 21at a atu
11. 20 aat  10. 20 aa tatu getur
21. 21 aa tt. 20. 20a1F
sit atque = x tab XX + ac euit adt = (4X + 2 abX, dx
et 11. 21 X + 11. 21 ab XX + H1. 22C, 4 X + 2abX e tatu
= 10. 47
+ 21. 21 cabb  + 2. 21. 21 abcXX + 21. 21 a cc
21. 2 X +2. 2. 21 ab X + 2. 21. 21 acX
imo sic.. 10 a + 11V  do
20a +21V
= 20.20 X = 20. 20 ab XX - 20.20 aC
sit v = O atqu et du = d0 satu + Cd adt = d9, atu d0 + a0 dt
vel do -  2atido + ac dq, tatu
+020aa (10021 aV
10a + 11V = 1. 21 vV + 1. 20 aV
20a +21Y
20aa -2130V seu
+ 11. 20 aOF
10. 21
104 + 11V
20a tV
2 tat
2 sat
=11. 21. 00at
20 a - 2100 atq
Q manentibus
2 aht0. 20a + 1. 20 Ciph 2atid0 +a dh lati
Ix = =11. 2100 ah
 19
20 a= 2160 at
Vati, 2atu d + aC dque = 10 a + uD do
s
rat ((2d(3 + adt) = fi 1eg00t
O
2at
ratu
20aL2D
elem.
A( tat): O tatu= Tog dat
sit simmmanda C:. pitut finge. VB + v, vdo -.  v +. vD +. D
sati
esse . V +.. VB +. . V, Xe
est autem de = vdo
posit vv=ab
fet a.. a +.. at +.. aat pecc; dt = . 1. +. : 00 +. . v +et, du
ipi +.. vp +sM
a +. at+. aatsi tati idem est quod .a + dh). A) +. AB M
tale ergo semper reduci et ad quadrituras ratinales
e + nt +atitrero rati
si esse - V + - vv +.. v 7 erc, do : .. v +. , V + v eca
ut x = (Z l fiat .. a +..  +. hE ten,  2 dG - t 12,
24
29
.. a +.  +.. hh + er, VZ
ui
sed idem est uc sifecisum n = 1hDt et iae = 2 dG 3) -  d 2 12 = 2, 169 - 2 42 154
E3
22
1((+b), +C). .x+ b + p + C
A+C) Yk+ ) AXtb, XtC,
(Ax + ab)
XX + ac
1GG
un bta clat.
y bumm acillua tedmmun a vedlena abolmua tat imna
Kollatur termonus summus summus nuu in sentratore 
quam montutae erit gradus certi. havant jam commanem siutore
Y(XX + ab) AXXFaC) - ab + ac
sRx. ( + ab NC + aa b+) Mentor t adminator, et res ertu rerncti ad : XF.
IXX +AC S(x + ab)
inr.
seu ad quadinura, itdnatis
 (1ODZ+ (4) = 1(0not 4. + 2910D). sit BD4+ E+
 au, qODE + +0D +  + D + d Z a  DE H O +D) + + 2F rab (DZ + 2461 0 + 2ad 4 D = 7y
2bc
2bd
+ 26d0
tollatur irrationales in producto d= - ab. C = act b sit bb = CC d - - bc: a fit aa =CC
eut rgo c = +a b = (t) c = (+) f a d =) - a, () Fa, +a = (7) a
seu c - +a b = (+) +a d -(+) a
SV 1
qu fbYOD+ FOC +d +DE +4) = bb8) t 2 a b D + cac toq L ad (8
2600
2cd7 +2b d3
destnc possunt irrationales in quadrato; es judu st O () c 1. XX + aa et similiter D 
10 Bq
potest pu potest 4 bbC3 D + ccC Z + dd D deprimi destuncto temino summo vel ultems
primu. auter licet sarientur signa ipsom b, exd, quae plis diffeuunt signis tamen prodire
videtur etiam nimium hinc sequi ptam utcunque varientur signa idem est bb ce, dd dphusbo
F = et ∞ et () ~ + et erit c = =a et b = - a et d = L a
si sit 4 C. + et (+) ∞ + fint c = a ut b = a et d = - a
sit ego
Si sit + ~ = et (+) ~ - fiat c = = a et b = a et d = a
s
pros 2g sit O3. _ OD = mn DE = na fiet  D = l: D = nn: 8 fit UD Q = Cmn: U = nmm: C fit O mt: A
A sit = ~ F A(=) ~ = fint C = Fa C= a, et b = = a et d =
ODe = im in tup = lmn
( = fit  Hun F Il Aln +u =y = matima + Cm en la iat hatma
C
fis O = m lm: n
Exs A. taposit a = -  et
n
bu. K In: m E = mn : l
fiet qu lma + laec fiat latla possnt
esu
la ut absit 1ODE redlunn ;lna
nicu in po s t d a es a nominutore pert
e
ttaqu ar pmrous
an d lthmu llma + 2bd Imat
prua
roxtua
(B m non i
careti
itus qualuor
modes quaesi
obtonem potest
u eflisu