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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 14
# Folio 28r, page id 00067976:0055
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si recta A, B, C sunt in eadem recta, et
AB + BC non ∞ AC nec erit AB + BC = AC
sed erit AB + BC p AC
punctum quod in recta non est a duobus
Odusdem si nin puncta sint in eadem
recta, punctum quod si ex tibus punctis
ejusdem rectae, unum a reliquis duobus aequi
distet, cadet n semper in eam portionem
in qua rectae in quam ambo puncta cadunt
a quibus aequidistat
generalius: si punctum tantum distat
ab uno puncto ejusdem recta quantum
ab altero, distantia ejus ab alterutio
cerit dimidia distantiae ipsorum inter se
suores
si de magnitudines non habeant partem commu
nem, component, totum aequale omnibus simul.
cotinua
si duo magnitudines habeant unum extremum
commune, nihila aliud component unum continuum
aequale ambobus AB+ BC AYB+ BZC.
et AY + YB~ AB, et BZ+Z C∞ BC et non
aliqu et nullum _Y est Z. Eut AB+BC7
producta est recta AB si sumitur BC et non nisi
(3 Coe labens aum AM
torvea
si ABC sunt in eodem recta, et AB _Let est
minus AB, et pars ejus cadit in AC totum cadet
Si AB, AC, BC sunt in eadem linea
in AC
nec habent partem communem, erit AB+ BC ∞ toti
lineae in qua sunt. Ergo si AB et BC, non habent
partem communem, tota comprehendentur in AC
a qcqu est in AC cum eotm constituant, quic
quid est in AC comprehenditur in ipsis. Et in recta ipsa
uuba etim comprohenduumm in AC. Siduae rectae sint
in eadem recta; et habeant extremum commune, et aliud praetere
punctum, alem eorum teria in altera comprehenditur