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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 68v, page id 00068194:0136
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=136
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dist.
dist
ANO recta si AY ~B + YB = AB erit AYBR ∞ ret AB.
()si dist. AY + dist YB = dist AB arit rect AB + rect YB ∞ rect AB
Alias enim si non C. Est AB (3) pone nn congruere. () symatur
B) est ABp AY (uam ex h 1. dist AB id est immgnibid e st  B, fi dist. AY)
Sergo potest intelligi AZ   AY rect. Ae AL + rest ZB∞ A ect AB.
ita ut sit AZ = AY. (ex definitione maj. et mini) Ergo B Y
16) Ergot ret ZB = rect YB. (per 1 et 5). Ergo Zejusdem estsitus
si A. B. C sint in eadem recta erit aut AB+ BC = AC, aut
AC + CB = AB aut BA+ AC = BC. Sit AC _ ceteris majus
seu ACp AB. seu AC~ AE + EC posita AE = AB seu A. AB
sut AC p BC erit AC = BC + DA AB = BC = DA- EC seu EC.BC
DA- AB Iineae
Si duae rectae terminentur ad idem punctum, nec habeant
Aliud punctum com commune component totum
caquale ambobus
AB BC
si luae nec partes ejusdem recte
si itia sint puncta A, B, C in eadem recta.
Si duae sint partes ejusdem rectae AB, BC ad
consistentes ad commune punctam B nec habeant partem communem
aequabes component unu totum contenuum cui ambae simul
Nam AB est in ABC et BC sunt in ABC recta AB una cum rect
aequabuntur
AB +. BC. C per  SC) et non habet partem communem ex hyp.
Erg. Ergo _ AB+ BC _ AB. nam (per AX 7 toturvatur
coincidit omnibus partibus simul sumlis partem communem
non habentibus jam AB et BC sunt in aliqua rectae seu partes
rectae sex lyp) Ergo sunt ipsae rectae (pe 4) Ergo per prop. 9.
AB+BC v rectae AtC.
2
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