Valerio, Luca - De centro gravitatis solidorum

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PROPOSITIO IV.

Datis duobus triangulis ſcalenis ſimilibus, &
dato puncto in altero eorum, vnum duntaxat pun
ctum in reliquo triangulo prædicto puncto ſimi
liter poſitum poteſt inueniri.

Sint data duo triangula ſcalena ſimilia ABC, DEF,
& in triangulio ABC datum punctum G: ſint autem
hæc triangula ſimiliter poſita. Dico in triangulo DEF,
vnum duntaxat punctum puncto G ſimiliter poſitum in
ueniri poſse. Iunctis enim AG, BG, GC, ponatur
angulus EDH, æqualis angulo BAG, & angulus DEH,

10[Figure 10]
æqualis angulo ABG, & HF iungatur. Manifeſtum
eſt igitur ex præcedentis Theorematis demonſtratione,
triangula EDH, HDF, FEH, ſimilia eſse triangulis
BAG, GAC, CBG, prout inter ſe reſpondent poſi
tione, quorum ſex triangulorum binis quibuſque binæ ba
ſes homologæ reſpondent: AB ED, AC DF, BC

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