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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 4
# Folio 60r, page id 00068049:0119
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 59v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 73, 2026-08-27T15:28:38Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.77
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# After the first blank line: the recognised lines in reading order, one per line.

constat sy.y nm-ngy. mm -g reduci possead quadraturam ratioualem quaeritur an hinc
sequatur et sag. isum. niu. mungsue reduci posse ad eandem; seu si una somut iiationats summa
ierationalem quantitaltud continens reducta sit ad quaduturam ravalem, quaeritur an alia quavis
tandem tantum irationatem continens ad rationatem quadraturam reduci possit
Et video si res obtineri queat  prior; sola issumto rationali valore ipsius y; tunc et sosterirm
quad raplex aequalitas
 + a gt Y + b =   at 2 + c = v H v + d = vtn
dalo sem t
psse adticeri
∞0 v+ acd ohit v+ bco = gHK E102 4 +  = 1 L + d = nn Ex 3 et 4
s
fit acd - bc = gtih - gkk exsel6 et C - d  U-nn ex 7 et 8
v cdm: 1-nn ex
DaE ae q et n est   - c. nn
Cd  Ghh- KK: a - b ex
et s=d d Lh. XX
b
et x= alit -
bel v= (Cghhi  by th. ( agtitat agtr
ne-d
vol = duF t Cnm vel cd = enn - dU
ad
Ergo ex 14 et 12. fit 9atK - bhh  - nn = m a- b. cad
et ex 17et 1. fit GhIi - KK Cnn- dI = m anb. cnd
Unde sublatis m et 9 res omnis redit ad hanc aequationem, resoliendam
 a enameris frationaliter resolvendam: akk -bhh= dl-enm
U- nn
KR = titi
Hanc aequationem resolvamus in duas KK - hh =  -nn et akK - bhh = dell-cenn
sit K= h+ p fint KK -tih =(hB + hp + pp ChB = eHl- enn seu h= ell= enn - pp, : 2p
et hh= ee 1 -2eCUlnn+ CC n = 2C lpp + 2 e nnpp + pY;: app
seupak btia = a - b Cet  rcellnn+ ee n-rellop t renapp +p + 4 app ell. 4ap ∞ en, (. 4a p + ap)
29
et KK = Ergo akK - bhh = tatih + 2 . p tap p
helam adeque 20 Sc esset n =  527 9 et h = Z+Y et l = s2 + F et n = 2+ W fiet
= app 4d ellpp= gc ena pp 17 (2
afZ+ 2a59Z +a99 = bZ 2b rZ2 brr, in, 52+ 25tZ+ t - 2 - 21oZ - W
equ. d5 Z + 2d st Z+ d Et =, cZ- 2cWZ - Wu, in, f2q + 2592+99 - Z - 2rZ- Yr
 quae aequatio debet esse; identica, unil, fiet
(25)
affss - at - b55 + b = d 55ff + d5s + cff = c = 0
 2aFst- 2affW +4 a595s. 4asqu a: 2bst + 2bu - 4brst + 4bru
-20