PROPOSITIO VII.
Sit recta linea AB, cuì perpendicularis exi
ſtat AD, quæ ex parte D producatur vtcunq; vſq;
ad C; connectaturq; CB, quæ producatur e
tiam vſq; ad E; & inter AB BE lineæ ſimiliter
vtcunq; ducantur BF BG ipſi AB æquales; à
punctisq; FG lineæ FH GK ipſi AB æquales,
ipſis verò BF BG per
pendiculares ducantur;
ac ſi BA AD motæ
ſint in BF FH BG
GK: Connectanturq;
CH CK, quæ lineas
BF BG productas ſe
cent in punctis MN.
Dico BN maiorem eſ
ſe BM, & BM ipſa BA.
101[Figure 101]
ſtat AD, quæ ex parte D producatur vtcunq; vſq;
ad C; connectaturq; CB, quæ producatur e
tiam vſq; ad E; & inter AB BE lineæ ſimiliter
vtcunq; ducantur BF BG ipſi AB æquales; à
punctisq; FG lineæ FH GK ipſi AB æquales,
ipſis verò BF BG per
pendiculares ducantur;
ac ſi BA AD motæ
ſint in BF FH BG
GK: Connectanturq;
CH CK, quæ lineas
BF BG productas ſe
cent in punctis MN.
Dico BN maiorem eſ
ſe BM, & BM ipſa BA.
101[Figure 101]Connectantur BD BH Bk,
& centro B, interuallo quidem
BD, circulus deſcribatur. ſimi
liter vt in præcedenti demon
ſtrabimus puncta kHDOP in
circuli circumferentia eſſe, trian
gulaq; ABD FBH GBk in
ter ſe ſe æqualia eſſe, atq; lineam
Pk maiorem OH, angulumq;
PKB minorem eſſe angulo O
HB. Quoniam igitur angulus BHF æqualis eſt angulo BkG,
& centro B, interuallo quidem
BD, circulus deſcribatur. ſimi
liter vt in præcedenti demon
ſtrabimus puncta kHDOP in
circuli circumferentia eſſe, trian
gulaq; ABD FBH GBk in
ter ſe ſe æqualia eſſe, atq; lineam
Pk maiorem OH, angulumq;
PKB minorem eſſe angulo O
HB. Quoniam igitur angulus BHF æqualis eſt angulo BkG,