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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 14
# Folio 19r, page id 00067976:0037
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 20v); this page is its right half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067976&page=37
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 39, 2026-08-27T09:55:26Z — 46 lines, status machine
# Lines: 46 recognised, mean confidence 0.96
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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corpus finitum est cujus quodlibet punctum quodlibet ab alio
aliquo distantiam habet R minorem distantia aliqua certa.
omnia puncta cnus quorum quodlibet ab uno
puncta numero finita intra corpus finitum includi
omnia puncta quorum quodlibet ab aliquo puncto
possunt.
distantiam habet minorem distantia aliqua certa intra
corpus finitum includi potest possunt
Si corpus punctum sumatur intra corpus, et aliud extra
corpus, neutrumque sit in ejus superficie, poterit punctum
reperiri, in superficie, quod minus distet tam ab uno quam ab
altero minus distet, quam ista distant inter se
Si ambo puncta sumantur intra corpus, neutrumque sit in
superficie, poterit punctum reperiri in superficie quod tam
ab unoquam altero magis ab altero eorum magis distet
quam ipsa distant inter se.
data recta in
eia recta potest sumi major includatur cenim in corpore
finito sphaera cujus alterum ejus centrum sit alterum rectae
a
extremum, utique punctum extra sphaeram magis a recta
Recta produci potest. sit  recta AB, dico eam posse produci
sumatur alia recta major, erit ergo ejus pars LMN cujus pars LM aequalis
distabit
sit ipsi AB. applicetur ad AB, sic ut LM et AB congruam coincidant
ABN est
ter idem demonstravi ex matum similitutines rectarum
id est LMN) recta AB producta Alde contra demonstrati potest exsomad punctum datum
Duae rectae non habent segmentum commune. seu recta 
ex uno extremo non nisi uno modo produci potest sint si ABC
duae rectae diversae si fieri potest, sic ut non omnia cadatque tota
st
AC extra AB ita ut ires duae AB et BC, item nullam habeant punctum
commune praeter B, et similiter AB et BD. Dico omne punctum alterutria
et ABd
ut BD cadere et cum altera sit altera majon altera BC vel BD sit altera
maior, vel sint aequales; ponatur ea quae minor non est, esse Bc, dico quodlibet
punctum ipsius BD cadere in BC. Esso id punctum ipsum D. Et quia BC seu BEC
militer jam ABC est recta. Ergo (pars rectae ABC) ergo AB. E. un.
liam BD( BE ex hypothesi  AE ( AD (quia AE _ = AB+ BE = AB + BD = AD)
major B et
Ergo A. B. D ∞ A. B. E. Ergo (quia A. B. E un) erit D ∞ E.
apnom posse
rectam majorem
data recta
EsC