PROPOSITIO III.
In ſimilibus triangulis rectæ lineæ, quæ inter
centra, & alia in ijs ſimiliter poſita puncta in
terijciuntur, proportionales ſunt in proportione
laterum homologorum.
centra, & alia in ijs ſimiliter poſita puncta in
terijciuntur, proportionales ſunt in proportione
laterum homologorum.
Sint triangula ſimilia, & ſimiliter poſita ABC, DEF,
quorum ſint centra O, P, in ijs autem triangulis ſint pun
cta ſimiliter poſita K, L, quæ cadant primum in rectis
BG, EH, quæ ab angulis æqualibus B, E, baſes bifa
riam diuidunt. Dico eſſe OK ad PL, vt eſt latus AB,
ad latus DE. iunctis enim AK, KC, DL, LF, quo
9[Figure 9]
niam angulus KAC, æqualis eſt angulo LDF, & angu
lus KCA, angulo LFD, ob ſimiliter poſita puncta K,
L, triangulum AKC, triangulo LDF ſimile erit, & vt
KA ad AC, ita LD ad DF: ſed vt CA ad AG, ita
eſt FD ad DH, expræcedenti; vt igitur KA, ad AG
ita erit LD, ad DH, circa æquales angulos: ſimilia igi
tur ſunt triangula AGK, DHL, & angulus AGK,
quorum ſint centra O, P, in ijs autem triangulis ſint pun
cta ſimiliter poſita K, L, quæ cadant primum in rectis
BG, EH, quæ ab angulis æqualibus B, E, baſes bifa
riam diuidunt. Dico eſſe OK ad PL, vt eſt latus AB,
ad latus DE. iunctis enim AK, KC, DL, LF, quo
9[Figure 9]niam angulus KAC, æqualis eſt angulo LDF, & angu
lus KCA, angulo LFD, ob ſimiliter poſita puncta K,
L, triangulum AKC, triangulo LDF ſimile erit, & vt
KA ad AC, ita LD ad DF: ſed vt CA ad AG, ita
eſt FD ad DH, expræcedenti; vt igitur KA, ad AG
ita erit LD, ad DH, circa æquales angulos: ſimilia igi
tur ſunt triangula AGK, DHL, & angulus AGK,
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