Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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184FED. COMMANDINI itemq; ſimilia triangula a b c, e f g; & a c d, e g h. idcir-
coq;
latera ſibi ipſis reſpondentia eandem inter ſe ſe pro-
portionem ſeruant.
Vt igitur duplum lateris a b unà
cum latere e f ad duplum lateris e f unà cum a b, ita eſt
duplum a d late-
ris unà cum late-
e h unà cum a d:
& ita in aliis.
Rurſus fruſtum
bafis, &
æqualis
altitudo eandem
proportionẽ ha
bet, quam fruſtũ
ſi, &
æquali alti-
tudine:
& ſimili-
ter quam l h fru-
dem, quæ ex ea-
dẽ baſi, &
æquali
altitudine con-
ſtat.
nam ſi inter
ipſas baſes me-
diæ proportio-
nales conſtituan
tur, tres baſes ſimul ſumptæ ad maiorem baſim in om-
nibus eodem modo ſe habebunt.
Vnde fit, ut axes K l,
q r, t u à punctis p s x in eandem proportionem ſecen-
tur.
ergo linea x s per p tranſibit: & lineæ r u, s x, q t in-
112. ſexti. ter ſe æquidiſtantes erunt.
Itaque cum fruſti a g latera