10581
COROLL.
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.
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.
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.
THEOR. XXV. PROP. XXXXVII.
Similes Hyperbolæ concentricæ per diuerſos vertices ſimul
adſcriptæ, ſunt inter ſe nunquam coeuntes, ac ſemper propiùs
accedentes, & ad interuallum perueniunt minus quocunque dato
interuallo.
adſcriptæ, ſunt inter ſe nunquam coeuntes, ac ſemper propiùs
accedentes, & ad interuallum perueniunt minus quocunque dato
interuallo.