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

SI in ſphæra duo circuli ſe mutuo ſecent, maximus circulus ſe-
cans bifariam duo illorum ſegmenta quæcumque, habens tamen
arcum inter illa ſegmenta poſitum ſemicirculo inæqualem; tranfit
per polos ipſorum, duoq́; reliqua ſegmenta bifariam ſecat.

85.1.

14.

_IN_ ſphæra duo circuli _ Ab CD, Eb FD,_ ſe mutuo ſecent in punctis _ B , D:_ Et
maximus circulus _A F C E,_ ſecet
duo quæcumque illorum ſegmẽta,
nempe, _ B AD, B ED,_ bifariam
in punctis _A, E,_ & arcus _A F C E,_
interceptus inter dicta ſegmenta
non ſit ſemicirculus. Dico circu-
lum _A F C E,_ tranſire per polos
circulorum _ Ab CD, Eb FD,_
ſecareé; reliqua ſegmenta _ B CD,_
_ B FD,_ bifariam. Si enim circulus
_A F C E,_ non tranſeat per ipſorũ
polos, deſcribatur, ſi fieri poteſt,
alius circulus maximus _A G E,_ per
eorum polos, qui ſegmenta ipſo-
rum bifariam ſecabit; atque adeo per puncta _A, E,_ tranſibit. Secabunt ſe igitur cir
culi maximi _A F C E, A G E,_ in _A, E,_ bifariam: ac propterea ſemicirculus erit
_AFCE._ Quod eſt contra hypotheſim. Tranſit ergo circulus _A F C E,_ per polos cir-
culorum _A B C D, Eb FD._ Quare omnia ſegmenta ipſorum ſecabit bifariam. Quod
eſt propoſitum.

85.1.

050-01
9. huius.
11. 1. huius.
9. huius.

86. THEOR, 10. PROP. 10.

15.

SI ſint in ſphæra paralleli circuli, per quo-
rum polos deſcribantur maximi circuli; paralle-
lorum quidem circunferentiæ inter maximos cir-
culos interceptæ, ſimiles ſunt; maximorum autem
circulorum circunferentiæ inter parallelos circu-
los interceptæ, ſuntæ quales.

SINT in ſphæra circuli paralleli A B C D, E F G H, quorũ polus I: (ſunt
enim paralleli circuli in ſphæra circa eoſdem polos.) Per I, autẽ circuli maxi
mi deſcribantur vtcumque A E I G C, B F I H D. Dico circunferentias paral-
lelorum A B, E F, ſimiles, nec non B C, F G; Item C D, G H; & D A, H E:

Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer