Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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10581
LEMMA VI. PROP. XXXXVI.
Si in quocunque triangulo ABC ducta ſit quæpiam linea DE
baſi BC parallela, rectangulum ABC ſuperabit ADE rectangu-
lo ſub DB, differentia altitudinum, & ſub aggregato baſium
BC, DE.
PRoducta enim BC, ac ſumpta CF æ-
73[Figure 73] quali ipſi DE, & completis in angulo
A B C parallelogrammis AE, AC, DF.
Conſtat parallelogrammum AC ſuperare
parallelogrammum AE gnomone DCG,
ſed gnomon DCG æquatur parallelogrã-
mis B E, GC, & GC æquatur DC, ſiue
EF, quare AC ſuperat AE parallelogram-
mo DF, hoc eſt rectangulum ABC ſupe-
rat rectangulum ADE, rectangulo DBF; ſed DB eſt differentia altitudinum,
& BF aggregatum baſium BC, DE. Quare patet propoſitum.

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