Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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7757LIBER I. GM, ideſt, vt, AD, ad, GH, ergo permutando, BA, ad, AD,
116. Sextr
Elem
.
erit vt, IG, ad, GH, &
anguli, BAD, IGH, ſunt æquales, er-
go
, BAD, IGH, erunt triangula ſimilia, ergo anguli, ADB, G
HI
, æquales erunt, ſunt autem ęquales etiam, ADF, GHO, er-
go
reliqui, BDF, IHO, erunt æquales, eſt verò, BD, ad, DA,
vt
, IH, ad, HG, &
, AD, ad, DF, vt, GH, ad, HO, ergo ex
æquali
, BD, ad, DF, eſt vt, IH, ad, HO, ergo triangula, BD
F
, IHO, pariter ſimilia erunt, &
anguli, DFB, HOI, inter ſe,
necnon
, DBF, HIO, inter ſe ęquales, ergo anguli, ABF, GIO,
ADF
, GHO, erunt etiam ęquales, &
figurę, ABFD, GIOH,
æquiangulę
, &
cum, BA, ad, DF, FB, binæ ſint in eadem ratio-
ne
cum, IG, GH, HO, OI, patet, quod etiam circa ęquales an-
gulos
ſunt latera proportionalia, ergo ipſæ figuræ, BADF, IG
HO
, ſimiles erunt.
Eodem autem modo oſtendemus ſimiles eſſe, B
CEF
, IMNO, patet autem ipſas, BF, IO, eſſe earum latera ho-
mologa
, quod erat demonſtrandum.

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