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PROPOSITIO IX.
Si recta A B, ſit ſecta bifariam in C, &
in D, E, æque
remotè à C, & pariter in F, G, æque remotè à C; ſit-
que rectangulum A F B, æquale quadrato D C. Erit
etiam rectangulum A D B, æquale quadrato F C.
remotè à C, & pariter in F, G, æque remotè à C; ſit-
que rectangulum A F B, æquale quadrato D C. Erit
etiam rectangulum A D B, æquale quadrato F C.
CVm enim rectangulum A F B, diuidatur in re-
ctangulum ſub A F, in D B, & in rectangulum
A F D, nempe in rectangulum ſub F D, in G B. Er-
go rectangula A F, D B; F D, G B, erunt æqualia
quadrato D C. Quare addito communi rectangu-
lo F D G. Ergo rectangula A F, D B; F D, G B;
15[Figure 15] F D G, erunt æqualia quadrato D C, & rectangulo
F D G; nempe quadrato F C. At rectangula F D G,
& F D, G B, faciunt rectangulum F D B. Quod cum
rectangulo A F, D B, facit rectangulum A D B.
Quare etiam rectangulum A D B, erit æquale qua-
drato F C. Quod & c.
ctangulum ſub A F, in D B, & in rectangulum
A F D, nempe in rectangulum ſub F D, in G B. Er-
go rectangula A F, D B; F D, G B, erunt æqualia
quadrato D C. Quare addito communi rectangu-
lo F D G. Ergo rectangula A F, D B; F D, G B;
15[Figure 15] F D G, erunt æqualia quadrato D C, & rectangulo
F D G; nempe quadrato F C. At rectangula F D G,
& F D, G B, faciunt rectangulum F D B. Quod cum
rectangulo A F, D B, facit rectangulum A D B.
Quare etiam rectangulum A D B, erit æquale qua-
drato F C. Quod & c.
PROPOSITIO X.
Si conoides byperbolicum includatur intra fruſtum conicum
habens oppoſitas baſes parallelas, & latera trapezij geni-
toris frusti ſint partes aſymptoton hyperbolæ
habens oppoſitas baſes parallelas, & latera trapezij geni-
toris frusti ſint partes aſymptoton hyperbolæ