Biancani, Giuseppe, Aristotelis loca mathematica, 1615

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1D F E, F B A, ita vt quælibet figura tot angulos externos ſortiatur, quot
habet latera; cum exproductis lateribus oriantur.
Vt autem propoſitio ve­
rificetur, ſingula latera ordinatim ſunt producenda, hoc eſt, verſus eandem
partem, vt in figuris appoſitis vides.
Quæuis igitur figura rectilinea, ſiue
trilatera ſit, ſiue quadrilatera, vel etiam millelatera, & proinde mille quo­
que angulos externos habeat, hanc tamen mirabilem proprietatem (quod
vix credi poteſt) poſſidet, vt omnes illi anguli externi ſimul ſint æquales
quatuor rectis angulis.
vnde tres externi anguli trianguli, & quatuor exter­
ni quadranguli, & quinque externi pentagoni, &c.
ſunt æquales quatuor tan­
tum rectis, nec aliter res ſe habet in figura millelatera.
Ex quo fit, vt an­
guli
externi cuiuſuis figuræ ſint æquales angulis omnibus externis alterius
cuiuſlibet figuræ.
Ariſt. igitur inquit, quando cognoſcimus, quod quatuor
angulis rectis ſunt æquales exteriores omnes anguli alicuius figuræ, quo­
niam figura illa eſt triangulum ſcalenum, adhuc talis cognitio eſt defecti­
ua, quia non illi competit illa paſſio, quia ſit triangulum ſcalenum, neque
competit ſcaleno, quia ſit triangulum; ſed his omnibus competit, quia ſunt
figuræ rectilineæ, cui hæc proprietas ineſt primo, & vniuerſaliter: qui igi­
tur ſcit, ſcalenum habere prædictam affectionem, ex eo, quod ſit figura re­
ctilinea, perfectius ſcit, quia nihil amplius quæri poteſt, quia illa figura re­
ctilinea illud vniuerſale eſt, cui primo competit; reliquis autem per illam.
qui igitur vniuerſale ſcit, perfectius ſcit; quod volebat Ariſt. demonſtrare.
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