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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 1
# Folio [13]r, page id 00067960:0025
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AXioma 13 Eucliclis (uti numerat
clavius) demonstratum.
A
Asserit Euclides rectam quae alteri rectae cd
propior fit, tandem productam productae
occurrere in E
C (F). M
a dato pncto Apducatur recta
intermitato in sit est dpucta
atiun
u terminenta At
agate
udus
Acpss rectar.D inAL
sit susnem ad puncto
qunntum detre remntum
in recta A sumatur AGaqualis AB, et recta
ACH
AG moveatur cirea 1B) donec intermsin s
G incidat in punctum B et F sin 1
Est auter A
ata ve AH in definite
magnus aneoque H ad easdem partes a quas
est , alioqui
a a puncto A remotiore in recta AB, ducatur
AG AF ad punctum tans rectam interminatam CD situm
F recta AF quantacu quantum satis est n longa
quia et punctum F a puncto A quantum satis est
remotum esse potest. in recta AF sumatur AF aequalis
AG. _e centro A  radius AGF moveatur, donec C incidat
in B et F in H. pono autem H esse ad huc trans
rectam (D. quod esfici posse sic ostendo Ponamus tum
sec H non esse frans rectum CD sed citra (in (H) eag
recta A(F) extremum (F) jam a antequam perveniret
ad (H) secabit rectam CD in M fnam cum (F) prius
esset insra Cd jamque sit supia necesse est ut
nlicubi transiert per d, nempe in M). sed ne
hoc non fecisset si recta AF sumta fuisset
euno ilem
longior quam A(F vel AM
et n lonum assumi potestet ut in millo puncto
cumque idem effici remedium ad haberipossit in quocunque
puncto secare infelligatur anlequam G
pervenit in B. sumendo scilicet Af obintio
majorem, qualm est recta ab A de ilud punctum
G.