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,
DC. Dico quadratum lateris AC, ſuperare quadratum lateris AB, rectan-
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-
drato rectæ DC, æquale. Addito ergo quadrato
communi rectæ AD, erit rectangulum ſub BC,
EC, vnà cum quadratis rectarum DE, AD, hoc
eſt, rectarum BD, AD, hoc eſt, cum quadrato
rectæ AB, æquale quadratis rectarum DC, AD,
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.

331-01
47. primi.
332-01
@. ſecundi.

CADAT deinde perpendicularis AD, ex-
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-
ctæ DB, quadrato rectæ DC, æquale. Addito ergo quadrato communi rectę
AD, erit rectangulum ſub BC, EC, vnà cum quadratis rectarum DB, AD,
hoc eſt, cum quadrato rectę AB, æquale quadratis rectarum DC, AD, hoc
eſt, quadrato rectæ AC. Excedit igitur quadratum lateris AC, quadratum
lateris AB, rectangulo contento ſub BC, EC.

463.1.

@. fecundi.

ALITER. Quoniã quadratis ex AD, DC, quadratum ex AC; & qua-
dratis ex AD, DB, quadratum ex AB, æquale eſt: idem erit exceſſus qua-
drati ex AC, ſupra quadratum ex AB, qui quadratorum ex AD, DC, ſu-
pra quadrata ex AD, DB: Et, ablato communi quadrato ex AD, idem, qui
quadratiex DC, ſupra quadratum ex DB, per pronunciatum 17. lib 1. Eucl. Sed quadratum ex DC, ſuperat quadratum ex DB, rectangulo ſub BC, CE,
comprehenſo; propterea quòd quadratum ex DC, æquale eſt quadrato ex
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.

463.1.

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
priore triangulo latera AB, AC, ponantur æqualia, erunt eorum@uadrata quoque æqualia. Quare cum quadratum ex AB, æquale ſit quadratis ex AD, BD; & quadratum ex AC,
quadratis ex AD, CD: erunt quoque quadrata ex AD, BD, quadratis ex AD, CD, æqua-
lia: Ablatoque communi quadrato rectæ AD, reliqua erunt quadrata ex BD, CD; æqua-
lia, & proinde rectæ BD, CD, æquales.

464.1.

47. primi.

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