PROPOSITIO VI.
Sit AB recta linea, cui ad angulos ſit rectos
AD, quæ ex parte A producatur vtcunq; vſq;
ad C; connectaturq; CB, quæ ex parte B quoq;
producatur vſq; ad E. ducantur deinde à pun
cto B vtcunq; inter AB BE lineæ BF BG ipſi
AB æquales; à punctiſq; FG ipſis perpendicula
res ducantur FH GK, quæ & inter ſe ſe, & ipſi
AD conſtituantur æ
quales, ac ſi BA AD
motæ ſint in BF FH,
& in BG GK; con
nectanturq; CH CK,
quæ lineas BF BG
in punctis MN ſe
cent. Dico BN mi
norem eſſe BM, &
BM ipſa BA.
99[Figure 99]
AD, quæ ex parte A producatur vtcunq; vſq;
ad C; connectaturq; CB, quæ ex parte B quoq;
producatur vſq; ad E. ducantur deinde à pun
cto B vtcunq; inter AB BE lineæ BF BG ipſi
AB æquales; à punctiſq; FG ipſis perpendicula
res ducantur FH GK, quæ & inter ſe ſe, & ipſi
AD conſtituantur æ
quales, ac ſi BA AD
motæ ſint in BF FH,
& in BG GK; con
nectanturq; CH CK,
quæ lineas BF BG
in punctis MN ſe
cent. Dico BN mi
norem eſſe BM, &
BM ipſa BA.
99[Figure 99]Connectantur BD BH
BK. & quoniam duæ lineæ
DA AB duabus HF FB
ſunt æquales, & angulus
DAB rectus recto HFB eſt
etiam æqualis; erunt reliqui
anguli reliquis angulis æqua
les, & HB ipſi DB æqualis.
ſimiliter oſtendetur triangu
lum BkG triangulo BHF æqualem eſſe. quare centro B, inter
BK. & quoniam duæ lineæ
DA AB duabus HF FB
ſunt æquales, & angulus
DAB rectus recto HFB eſt
etiam æqualis; erunt reliqui
anguli reliquis angulis æqua
les, & HB ipſi DB æqualis.
ſimiliter oſtendetur triangu
lum BkG triangulo BHF æqualem eſſe. quare centro B, inter
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