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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 57r, page id 00068194:0113
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=113
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 34 lines, status machine
# Lines: 34 recognised, mean confidence 0.97
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Duo puncta fixa A et B X unicum suae ad ipsa
relationis adeoque _ su   X. A. B  Z AB. sit X  Z
erit X recta
si in plano duo circuli centris
A et B descripti se lungant in
puncto C, erit punctum
C in recta transeante per centra
A et B
si centris L et M descripti circuli
aequales se secent in punctas, ut N
erunt omnia hujusmodi puncta ut
N, (N), P, (P), Q, (2) in eadem recta
Ergo si punctis N et (N) per punctum p
describentur circuli duo, ii se eangent in p
Nam si secent sese in A et (H) utique H et (H) eodem modo se
habebunt ad N determinative produitur
Ex punctis L et M determit linea omnium punctorum
X eodem modo se habentium ad L et M ergo et  linea punctori
um duo in ea puncta ut N et  p Ergo et linea
punctorum  ad N et P unicorum. quae si non esse
quae punta x si caderent in puncta Y, orirentur semper lineae novae, adeoque
pu linea L et M producerent non lineam, sed superficiem
Aliter planum secatur a recta AB in duo
segmenta utriaque eodem modo se habentia. idem
fiat per rectam, necesse est rectas sibi occurrere
cum  alicubi in F, quia  puncta lineae LM
sunt in utraque parte plani, ergo quia ipsa contiaaa est, etiam
in communi seguento. He duo plan has duas rectas non
sibi occurrere nisi in uno puncto. Nam si occurrant adhue semel in G
vel coincident FG et FMG, seu duae rectae habebunt partem communem vel
unstum ilicet Y inclinent sane si recta
cuilibet puncto ut M supra AB, respondet N infra. ergo portio ipsius lineae LFM
spatium comprehendem
supia, sud infra indese respondebit 1C