## Full text: Bithynius, Theodosius: Theodosii Tripolitae Sphaericorum libri tres

minus erit, & proinde & recta: BD, minor, quam recta DC. Abſciſſa erge
recta DE, ipſi BD, æquali, erit EC, differentia inter ſegmenta BD,
gulo ſub BC, EC, comprehenſo. Quia enim recta BE, ſecta eſt bifariam in
D, eiq́; addita in continuum recta EC, erit rectangulum ſub BC, EC,
contentum vna cum quadrato rectæ DE, qua-
communi rectæ AD, erit rectangulum ſub BC,
hoc eſt, quadrato rectæ AC. Maius ergo eſt qua-
dratum lateris AC, quam quadratum lateris
AB, rectangulo ſub BC, EC, comprehenſo. quod eſt propoſitum.

### 463.1.

47. primi.
@. ſecundi.

tra triangulum in baſim CB, productam, vt in
figura poſteriori. Abſciſſa recta DE, ipſi DB,
æquali, erit recta EC, compoſita ex baſe BC, & EB, quæ dupla eſt lineæ DB, inter perpendicu-
larem, & angulum B. Dico rurſus, quadratum
lateris AC, ſuperare quadratum lateris AB, rectangulo ſub BC, EC, com-
prehenſo. Eritenim rurſus rectangulum ſub BC, EC, vnà cum quadrato re-
lateris AB, rectangulo contento ſub BC, EC.

### 463.1.

@. fecundi.

dratis ex AD, DB, quadratum ex AB, æquale eſt: idem erit exceſſus qua-
quadratiex DC, ſupra quadratum ex DB, per pronunciatum 17. lib 1. Eucl. Sed quadratum ex DC, ſuperat quadratum ex DB, rectangulo ſub BC, CE,
D B, vel ex DE, in prima ſigura, vnà cum rectangulo ſub BC, CE, contento. Igitur & quadratum ex AC, ſuperat quadratum ex AB, rectangulo com-
prehenſo ſũb BC, CE. Quocirca, Si ab angulo trianguli cuiuſuis duobus
lateribus inæqualibus com prehenſo linea perpendicularis ad baſim ducatur,
& c. Quod oſtendendum erat.

47 primi.
@. ſecundi.

## 464.COROLLARIVM.

Perpẽdicu
laris in lſo
ſcele ſecat
baſim bifa
riam.

EX demonſtratis conſtat, In Iſoſcele perpendicularem ſecare baſim bifariam. Nam ſi in
lia, & proinde rectæ BD, CD, æquales.

47. primi.

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