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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 38v, page id 00068049:0076
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 39r); this page is its left half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 67 lines, status machine
# Lines: 67 recognised, mean confidence 0.81
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pay. V
hy + aby y + aaeis ∞ quadrato. fiat y = quadrato seu y = mmax + ramux + aanu =∞
∞
sa
et fict ahyus taabus + ac ∞ quadhato s + b sest 13 + C. + 4
seu hmet aahmnX + baahmmnuxx + 4a hmnX + ahn
CPR + +aC p qX + 6 aac pp 99 Xx + 4 a  p q X + ac9
bmuppi t rab mapus X + aa b mngus XX + 2a0 magus X + abunque
rab ppma X aab pp nn (X + 2ab puna X
Haab mmpus XX
Lito
10X + 1 X + 12 X X + 13 X + 14 = Ato
sit radix AXX + aB X + aa C  ju
crilejus _t AA X + 2A ABX + 2. AAACXX
11 l14 = 13 Sio dabil
+ 1aa BBXx + 2aBCX + at CC
As
egtbunoque. ho tcrbnm
faciamus M = n et p = - 4
he+ cq+b ungu
A = Ho C = s14
 B - 1: 2A B = 1: 2C
fit 11C = 13A seu 11Y4 = 1310
jam 12 = 2AC + BB.
Ergo 12 = 2 H0.4 + 1. 13 seu 1. 12 Mo14
+hmn + acp q + 2b m Bq+ Ebp sum
Ahmu + 4Cpq + 2b mu19 + 2bpgmm
et ex hac aequi fit t
fiet 10 = 14 et 11 = 13 et aeq. 11S14 = 13 s0 erit praestita
Superest aequatio 8. 10. 14 = 4 i ton4 + 1. 13 = 4. 12 s1o. 14 vol 8. 10.10 + 11. 1 = 4. 10. 12
ob n= m et et 9 = - p fit, 10 = h m + cpt + bmmpp et 11 = et hm orep E b imm pp + 2b rAm eP)
et 12 = Ch m= +6Cp (+ 2b mmgq - (b mn gu
8. 1810 + H1. 11 = + +. 10 12 Oriri +hc = bb  hypollus
sed hoc posito video in aeq.
An ergo Sufficiet ponere 10 = 0 : et I1 = 0 haberentur mm app, et n: 9
si esset 9=0 fieiet ∞ 10 ut aute, sed 11 = 4hoa +2abpp nn 12 = 6hmmn +bxpun
4. hn
13 = 4k mB
Aliter egitus, hoc modo videtur dari, fiat 10 = 0 et 11 = 0 inventa
per illud relationem inter in et p, per alterum relationem inter n et g.
restat 12XX + 13X +14 aequ. ~t, quod fieri pt non per identificationem
cum quadralo, sed per faciendo 12XX + BX + 14 = ((IXX) Ax S v + vV
et habetur X ralinaliter
et fiet _ 4hmueistim st abumpe) = ahm n + rabpoma, . B 4 H, Aurei abii = abneruti  - c
et 4. (shmmna +beruu  unsh sum reptebmmpp = B. h a t ( ho rep tabmm.) + 16th e
sed ita rursus evanescit n
+Babh mn u sp
810 = 8,
4 1o1 810. 14 + 11. 13 11 = 16
L
sit um +  b p M + Z pp =0
fiet um + pm + bb pp =
4
 m = -bP + pNbb-anc seu
p X + aq
eps
op.
topxx F rapgX + aa q 33
Cpp XX F 2aC p9X F, aa c 19
Obm P XX + abnqus X + aaenque
at)
p - Sbb - 4hc - b, : 2h s
sit jam rursus 2ak mn + racpqs + aomq + ab np = 0 et fiet:
Zah 2 + ab
mop = 2ac4 = abA: raha 1 abq = - 2ac - ab n
n:g= seu rat P 2  2ahlmh +2ac + ab m + abn. Et = 0.
et fiet n = - hac = ab m,: 2 ab  + ab.  ubi  ubi nihil videoeisudi