Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

9. PROPOSITIO II.

Si quatuor magnitudinum ſit prima, ad ſecundam, vt tertia,
ad quartam; ſitque ablata pars primæ ad ablatam par-
tem ſecundæ, vt ablata pars tertiæ ad ablatam partem
quartæ et ſint partes primæ proportionales partibus ſecun-
dæ. Erit reliqua pars primæ ad reliquam partem ſecun-
dæ, vt reliqua pars tertiæ ad reliquam partem quartæ.

SIT vt prima
A B, ad ſe-
cundam C D, ſic
tertia E F, ad
quartam G H; ſitque k B, ad
L D, vt MF, ad
N H: pariter ſit vt Ak, ad k B, ſic E M, ad M F. Dico etiam A K, eſſe ad C L, vt E M, ad G N. Quoniam ex hypotheſi componendo, eſt A B, ad
B k, vt E F, ad F M; & vt k B, ad L D, ſic M F,
ad N H; ergo ex æquali, vt A B, ad L D, ſic E F,
ad N H. At pariter eſt vt A B, ad totam C D, ſic
E F, ad totam G H. Ergo & A B, erit ad reliquam
C L, vt E F, ad reliquam G N. Rurſum, quoniam
conuertendo, eſt B K, ad k A, vt F M, ad M E. Ergo componendo, & conuertendo, erit Ak, ad A B,
vt EM, ad EF. Erat autem vt AB, ad CL, ſic EF, ad

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